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var(--ifm-color-emphasis-100);color:var(--ifm-color-black);display:flex;height:var(--docusaurus-announcement-bar-height)}#__docusaurus-base-url-issue-banner-container,.docSidebarContainer_YfHR,.hideAction_vcyE>svg,.navbarSearchContainer_Bca1:empty,.sidebarLogo_isFc,.themedComponent_mlkZ,[data-theme=dark] .lightToggleIcon_pyhR,[data-theme=light] .darkToggleIcon_wfgR,html[data-announcement-bar-initially-dismissed=true] .announcementBar_mb4j{display:none}.announcementBarPlaceholder_vyr4{flex:0 0 10px}.announcementBarClose_gvF7{align-self:stretch;flex:0 0 30px}.toggle_vylO{height:2rem;width:2rem}.toggleButton_gllP{align-items:center;border-radius:50%;display:flex;height:100%;justify-content:center;transition:background var(--ifm-transition-fast);width:100%}.toggleButton_gllP:hover{background:var(--ifm-color-emphasis-200)}.toggleButtonDisabled_aARS{cursor:not-allowed}.darkNavbarColorModeToggle_X3D1:hover{background:var(--ifm-color-gray-800)}[data-theme=dark] 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.dropdownMenu_qbY6{background:var(--search-local-modal-background,var(--ifm-background-color));box-shadow:var(--search-local-modal-shadow,inset 1px 1px 0 0 #2c2e40,0 3px 8px 0 #000309)}.searchBar_RVTs .dropdownMenu_qbY6 .suggestion_fB_2{align-items:center;background:var(--search-local-hit-background,#fff);border-radius:4px;box-shadow:var(--search-local-hit-shadow,0 1px 3px 0 #d4d9e1);color:var(--search-local-hit-color,#444950);cursor:pointer;display:flex;flex-direction:row;height:var(--search-local-hit-height,56px);padding:0 var(--search-local-spacing,12px);width:100%}.hitTree_kk6K,.noResults_l6Q3{align-items:center;display:flex}html[data-theme=dark] .dropdownMenu_qbY6 .suggestion_fB_2{background:var(--search-local-hit-background,var(--ifm-color-emphasis-100));box-shadow:var(--search-local-hit-shadow,none);color:var(--search-local-hit-color,var(--ifm-font-color-base))}.searchBar_RVTs .dropdownMenu_qbY6 .suggestion_fB_2:not(:last-child){margin-bottom:4px}.searchBar_RVTs .dropdownMenu_qbY6 .suggestion_fB_2.cursor_eG29{background-color:var(--search-local-highlight-color,var(--ifm-color-primary))}.hitFooter_E9YW a,.hitIcon_a7Zy,.hitPath_ieM4,.hitTree_kk6K,.noResultsIcon_EBY5{color:var(--search-local-muted-color,#969faf)}html[data-theme=dark] .hitIcon_a7Zy,html[data-theme=dark] .hitPath_ieM4,html[data-theme=dark] .hitTree_kk6K,html[data-theme=dark] .noResultsIcon_EBY5{color:var(--search-local-muted-color,var(--ifm-color-secondary-darkest))}.hitTree_kk6K>svg{height:var(--search-local-hit-height,56px);opacity:.5;width:24px}.hitIcon_a7Zy,.hitTree_kk6K>svg{stroke-width:var(--search-local-icon-stroke-width,1.4)}.hitAction_NqkB,.hitIcon_a7Zy{height:20px;width:20px}.hitWrapper_sAK8{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;margin:0 8px;overflow-x:hidden;width:80%}.hitWrapper_sAK8 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svg{display:inline-block;height:1.6em;width:1.6em;fill:var(--ifm-alert-foreground-color)}.breadcrumbHomeIcon_YNFT{height:1.1rem;position:relative;top:1px;vertical-align:top;width:1.1rem}.breadcrumbsContainer_Z_bl{--ifm-breadcrumb-size-multiplier:0.8;margin-bottom:.8rem}.title_kItE{--ifm-h1-font-size:3rem;margin-bottom:calc(var(--ifm-leading)*1.25)}.searchContextInput_mXoe,.searchQueryInput_CFBF{background:var(--ifm-background-color);border:var(--ifm-global-border-width) solid var(--ifm-color-content-secondary);border-radius:var(--ifm-global-radius);color:var(--ifm-font-color-base);font-size:var(--ifm-font-size-base);margin-bottom:1rem;padding:.5rem;width:100%}.searchResultItem_U687{border-bottom:1px solid #dfe3e8;padding:1rem 0}.searchResultItemPath_uIbk{color:var(--ifm-color-content-secondary);font-size:.8rem;margin:.5rem 0 0}.searchResultItemSummary_oZHr{font-style:italic;margin:.5rem 0 0}@media screen and (min-width:600px){.container{--ifm-spacing-horizontal:1.5rem}}@media (min-width:997px){.collapseSidebarButton_PEFL,.expandButton_TmdG{background-color:var(--docusaurus-collapse-button-bg)}.lastUpdated_JAkA{text-align:right}.tocMobile_ITEo{display:none}:root{--docusaurus-announcement-bar-height:30px}.announcementBarClose_gvF7,.announcementBarPlaceholder_vyr4{flex-basis:50px}.collapseSidebarButton_PEFL{border:1px solid var(--ifm-toc-border-color);border-radius:0;bottom:0;display:block!important;height:40px;position:-webkit-sticky;position:sticky}.collapseSidebarButtonIcon_kv0_{margin-top:4px;transform:rotate(180deg)}.expandButtonIcon_i1dp,[dir=rtl] .collapseSidebarButtonIcon_kv0_{transform:rotate(0)}.collapseSidebarButton_PEFL:focus,.collapseSidebarButton_PEFL:hover,.expandButton_TmdG:focus,.expandButton_TmdG:hover{background-color:var(--docusaurus-collapse-button-bg-hover)}.menuHtmlItem_M9Kj{padding:var(--ifm-menu-link-padding-vertical) var(--ifm-menu-link-padding-horizontal)}.menu_SIkG{flex-grow:1;padding:.5rem}@supports 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a/assets/js/00d86d8d.fcfdf225.js b/assets/js/00d86d8d.3221d223.js similarity index 99% rename from assets/js/00d86d8d.fcfdf225.js rename to assets/js/00d86d8d.3221d223.js index b340784e..d484a189 100644 --- a/assets/js/00d86d8d.fcfdf225.js +++ b/assets/js/00d86d8d.3221d223.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[3285],{2750:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>m,contentTitle:()=>d,default:()=>u,frontMatter:()=>o,metadata:()=>h,toc:()=>p});var a=s(4848),i=s(8453),t=s(1432);const c="&control\n calculation='scf'\n pseudo_dir = '../pseudos/',\n outdir='./tmp/'\n prefix='fe'\n/\n\n&system\n ibrav = 3,\n celldm(1) = 5.39,\n nat= 1,\n ntyp= 1,\n noncolin=.true.,\n lspinorb=.true.,\n starting_magnetization(1)=0.3,\n ecutwfc = 70,\n ecutrho = 850.0,\n occupations='smearing',\n smearing='marzari-vanderbilt',\n degauss=0.02\n/\n\n&electrons\n diagonalization='david'\n conv_thr = 1.0e-8\n mixing_beta = 0.7\n/\n\nATOMIC_SPECIES\nFe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS alat\nFe 0.0 0.0 0.0\n\nK_POINTS AUTOMATIC\n14 14 14 1 1 1\n",r="&control\n calculation='bands'\n pseudo_dir = '../pseudos/',\n outdir='./tmp/'\n prefix='fe'\n/\n\n&system\n ibrav = 3,\n celldm(1) = 5.39,\n nat= 1,\n ntyp= 1,\n noncolin=.true.,\n lspinorb=.true.,\n starting_magnetization(1)=0.3,\n ecutwfc = 70,\n ecutrho = 850.0,\n occupations='smearing',\n smearing='marzari-vanderbilt',\n degauss=0.02\n/\n&electrons\n diagonalization='david'\n conv_thr = 1.0e-8\n mixing_beta = 0.7\n/\n\nATOMIC_SPECIES\nFe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS alat\nFe 0.0 0.0 0.0\n\nK_POINTS tpiba_b\n6\n0.000 0.000 0.000 40 !gamma\n0.000 1.000 0.000 40 !H\n0.500 0.500 0.000 30 !N\n0.000 0.000 0.000 30 !gamma\n0.500 0.500 0.500 30 !P\n0.000 1.000 0.000 1 !H\n",l="&BANDS\n outdir='./tmp/',\n prefix='fe',\n filband='fe_bands_soc.dat',\n/\n",o={title:"Spin-Orbit Coupling",keywords:["Spin orbit coupling","SOC","SOC calculation","SOC calculation in DFT","SOC calculation using Quantum Espresso","Non collinear spin calculation","Bandstructure calculation for GaAs"]},d=void 0,h={id:"hands-on/soc",title:"Spin-Orbit Coupling",description:"In order to consider spin orbit coupling effect in our electronic structure",source:"@site/docs/hands-on/soc.mdx",sourceDirName:"hands-on",slug:"/hands-on/soc",permalink:"/espresso/hands-on/soc",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/soc.mdx",tags:[],version:"current",frontMatter:{title:"Spin-Orbit Coupling",keywords:["Spin orbit coupling","SOC","SOC calculation","SOC calculation in DFT","SOC calculation using Quantum Espresso","Non collinear spin calculation","Bandstructure calculation for GaAs"]},sidebar:"docs",previous:{title:"DFT+U calculation",permalink:"/espresso/hands-on/dft-u"},next:{title:"Bi2Se3 (TI)",permalink:"/espresso/hands-on/Bi2Se3"}},m={},p=[{value:"Non collinear spin",id:"non-collinear-spin",level:2},{value:"Strategy for convergence",id:"strategy-for-convergence",level:2},{value:"Bandstructure of Fe with SOC",id:"bandstructure-of-fe-with-soc",level:2},{value:"SOC calculation for GaAs",id:"soc-calculation-for-gaas",level:2}];function x(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,i.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsxs)(e.p,{children:["In order to consider spin orbit coupling effect in our electronic structure\ncalculation in quantum espresso, we need to use a full relativistic pseudo\npotential. Following settings are needed in the ",(0,a.jsx)(e.code,{children:"&SYSTEM"})," card:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n noncolin = .true.\n lspinorb = .true.\n ...\n/\n"})}),"\n",(0,a.jsx)(e.h2,{id:"non-collinear-spin",children:"Non collinear spin"}),"\n",(0,a.jsxs)(e.p,{children:["In simple spin polarized calculation (",(0,a.jsx)(e.code,{children:"nspin=2"}),"), the spin quantum number (up or\ndown) is considered in the calculation. In non-collinear case, the spin has more\ndegrees of freedom, and can be oriented in any direction. Non-collinear\nmagnetism is quite common in nature, where the spins are not parallel\n(ferromagnetic) or anti-parallel (antiferromagnetic), rather they orient in\nspirals, helicoids, canted or disordered. Non-collinear magnetism can occur\nbecause of geometric frustration of magnetic interaction. It can also occur due\nto the magnetocrystalline anisotropy which is the result of interaction between\nthe spin and lattice interaction. This relativistic effect comes via spin-orbit\ncoupling."]}),"\n",(0,a.jsx)(e.p,{children:"We can constrain the magnetic moment:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n constrained_magnetization = 'atomic direction'\n ...\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Starting magnetization can be specified by ",(0,a.jsx)(e.code,{children:"angle1"})," (angle with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"z"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"z"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.04398em"},children:"z"})]})})]})," axis) and\n",(0,a.jsx)(e.code,{children:"angle2"})," (angle of projection in ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mi,{children:"x"}),(0,a.jsx)(e.mi,{children:"y"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"xy"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"y"})]})})]}),"-plane and with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"x"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"x"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"})]})})]}),"-axis). Also check the\npenalty function (",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"\u03bb"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\lambda"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"\u03bb"})]})})]}),")."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n angle1(i) = 0.0d0\n angle2(i) = 0.0d0\n lambda = 0.5\n ...\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:[(0,a.jsx)(e.code,{children:"i"})," is the index of the atom in ",(0,a.jsx)(e.code,{children:"ATOMIC_SPECIES"})," card."]}),"\n",(0,a.jsx)(e.h2,{id:"strategy-for-convergence",children:"Strategy for convergence"}),"\n",(0,a.jsxs)(e.p,{children:["Spin-orbit coupling calculations are often hard to converge. Use a smaller\n",(0,a.jsx)(e.code,{children:"mixing_beta"})," for such calculations. First perform a collinear calculation with\nnon-relativistic pseudopotential, and then start from the obtained charge\ndensity to perform non-colinear spin orbit calculation."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&ELECTRONS\n ...\n mixing_beta = 1.0000000000d-01\n startingpot = 'file'\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:["When starting with non-collinear calculation from an existing charge density\nfile from a collinear lsda calculation, we need to set ",(0,a.jsx)(e.code,{children:"lforcet=.true."}),". It\nassumes previous density points in z direction, and rotates in the direction\nspecified by ",(0,a.jsx)(e.code,{children:"angle1"})," (initial magnetization angle with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"z"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"z"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.04398em"},children:"z"})]})})]}),"-axis in degrees),\nand ",(0,a.jsx)(e.code,{children:"angle2"})," (angle in degrees for projections in ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mi,{children:"x"}),(0,a.jsx)(e.mi,{children:"y"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"xy"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"y"})]})})]}),"-plane and with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"x"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"x"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"})]})})]}),"-axis)."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n...\n angle1(i) = 0.0\n angle2(i) = 0.0\n lforcet = .true.\n/\n"})}),"\n",(0,a.jsx)(e.p,{children:"Also, make sure that energy and charge density cutoffs are sufficient. Certain\npseudo potentials might have issues, try with pseudo potentials from a different\nlibrary. In case of metallic systems, remember to apply smearing."}),"\n",(0,a.jsx)(e.admonition,{title:"Common Errors",type:"danger",children:(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:[(0,a.jsx)(e.strong,{children:"S matrix not positive definite:"})," This error might appear due to numerical\ninstability from overlapping atoms. Check atomic positions carefully. In one my\ncalculations, this error was resolved after setting higher ",(0,a.jsx)(e.code,{children:"ecutrho"}),"."]}),"\n"]}),"\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:["Simplified LDA+U not implemented with ",(0,a.jsx)(e.code,{children:"noncol"})," magnetism, use\n",(0,a.jsx)(e.code,{children:"lda_plus_u_kind=1"}),"."]}),"\n"]}),"\n"]})}),"\n",(0,a.jsx)(e.h2,{id:"bandstructure-of-fe-with-soc",children:"Bandstructure of Fe with SOC"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pw.scf.fe_soc.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsx)(e.p,{children:"Run the scf calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.scf.fe_soc.in > pw.scf.fe_soc.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Prepare the input file for ",(0,a.jsx)(e.code,{children:"nscf"})," ",(0,a.jsx)(e.code,{children:"bands"})," calculation:"]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pw.bands.fe_soc.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsxs)(e.p,{children:["Run the ",(0,a.jsx)(e.code,{children:"bands"})," calculation:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.bands.fe_soc.in > pw.bands.fe_soc.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"Finally post process the bandstructure data:"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pp.bands.fe_soc.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsxs)(e.p,{children:["In this case ",(0,a.jsx)(e.code,{children:"spin_component"})," has been removed and we add ",(0,a.jsx)(e.code,{children:"lsigma(3)=.true."}),"\nthat instructs the program to compute the expectation value for the ",(0,a.jsx)(e.code,{children:"z"}),"\ncomponent of the spin operator for each eigenfunction and save all values in\nthe file ",(0,a.jsx)(e.code,{children:"fe.noncolin.data.3"}),". All values in this case are either +1/2 or -1/2."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 bands.x -i pp.bands.fe_soc.in > pp.bands.fe_soc.out\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(2623).A}),(0,a.jsx)("img",{src:s(4774).A,alt:"fe-soc-bands"})]}),"\n",(0,a.jsx)(e.h2,{id:"soc-calculation-for-gaas",children:"SOC calculation for GaAs"}),"\n",(0,a.jsxs)(e.p,{children:["Please check the respective ",(0,a.jsx)(e.a,{href:"https://github.com/pranabdas/espresso/tree/master/src/GaAs",children:"input files"}),"."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.scf.GaAs_soc.in > pw.scf.GaAs_soc.out\nmpirun -np 8 pw.x -i pw.bands.GaAs_soc.in > pw.bands.GaAs_soc.out\nmpirun -np 8 bands.x -i pp.bands.GaAs_soc.in > pp.bands.GaAs_soc.out\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(5466).A}),(0,a.jsx)("img",{src:s(1841).A,alt:"GaAs-soc-bands"})]})]})}function u(n={}){const{wrapper:e}={...(0,i.R)(),...n.components};return e?(0,a.jsx)(e,{...n,children:(0,a.jsx)(x,{...n})}):x(n)}},1841:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-soc-bands-518e9ab7f6ba3c38e10d21c1fe40ce9b.png"},5466:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-soc-bands-e9b5feae2abd0018c3cc7a90c6e32a87.webp"},4774:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/fe-soc-bands-de6c4f09552c8c90ba653e2309a8751a.png"},2623:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/fe-soc-bands-78fdcffe376232aeb31d423fb4864d81.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[3285],{6679:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>m,contentTitle:()=>d,default:()=>u,frontMatter:()=>o,metadata:()=>h,toc:()=>p});var a=s(4848),i=s(8453),t=s(1432);const c="&control\n calculation='scf'\n pseudo_dir = '../pseudos/',\n outdir='./tmp/'\n prefix='fe'\n/\n\n&system\n ibrav = 3,\n celldm(1) = 5.39,\n nat= 1,\n ntyp= 1,\n noncolin=.true.,\n lspinorb=.true.,\n starting_magnetization(1)=0.3,\n ecutwfc = 70,\n ecutrho = 850.0,\n occupations='smearing',\n smearing='marzari-vanderbilt',\n degauss=0.02\n/\n\n&electrons\n diagonalization='david'\n conv_thr = 1.0e-8\n mixing_beta = 0.7\n/\n\nATOMIC_SPECIES\nFe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS alat\nFe 0.0 0.0 0.0\n\nK_POINTS AUTOMATIC\n14 14 14 1 1 1\n",r="&control\n calculation='bands'\n pseudo_dir = '../pseudos/',\n outdir='./tmp/'\n prefix='fe'\n/\n\n&system\n ibrav = 3,\n celldm(1) = 5.39,\n nat= 1,\n ntyp= 1,\n noncolin=.true.,\n lspinorb=.true.,\n starting_magnetization(1)=0.3,\n ecutwfc = 70,\n ecutrho = 850.0,\n occupations='smearing',\n smearing='marzari-vanderbilt',\n degauss=0.02\n/\n&electrons\n diagonalization='david'\n conv_thr = 1.0e-8\n mixing_beta = 0.7\n/\n\nATOMIC_SPECIES\nFe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS alat\nFe 0.0 0.0 0.0\n\nK_POINTS tpiba_b\n6\n0.000 0.000 0.000 40 !gamma\n0.000 1.000 0.000 40 !H\n0.500 0.500 0.000 30 !N\n0.000 0.000 0.000 30 !gamma\n0.500 0.500 0.500 30 !P\n0.000 1.000 0.000 1 !H\n",l="&BANDS\n outdir='./tmp/',\n prefix='fe',\n filband='fe_bands_soc.dat',\n/\n",o={title:"Spin-Orbit Coupling",keywords:["Spin orbit coupling","SOC","SOC calculation","SOC calculation in DFT","SOC calculation using Quantum Espresso","Non collinear spin calculation","Bandstructure calculation for GaAs"]},d=void 0,h={id:"hands-on/soc",title:"Spin-Orbit Coupling",description:"In order to consider spin orbit coupling effect in our electronic structure",source:"@site/docs/hands-on/soc.mdx",sourceDirName:"hands-on",slug:"/hands-on/soc",permalink:"/espresso/hands-on/soc",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/soc.mdx",tags:[],version:"current",frontMatter:{title:"Spin-Orbit Coupling",keywords:["Spin orbit coupling","SOC","SOC calculation","SOC calculation in DFT","SOC calculation using Quantum Espresso","Non collinear spin calculation","Bandstructure calculation for GaAs"]},sidebar:"docs",previous:{title:"DFT+U calculation",permalink:"/espresso/hands-on/dft-u"},next:{title:"Bi2Se3 (TI)",permalink:"/espresso/hands-on/Bi2Se3"}},m={},p=[{value:"Non collinear spin",id:"non-collinear-spin",level:2},{value:"Strategy for convergence",id:"strategy-for-convergence",level:2},{value:"Bandstructure of Fe with SOC",id:"bandstructure-of-fe-with-soc",level:2},{value:"SOC calculation for GaAs",id:"soc-calculation-for-gaas",level:2}];function x(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,i.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsxs)(e.p,{children:["In order to consider spin orbit coupling effect in our electronic structure\ncalculation in quantum espresso, we need to use a full relativistic pseudo\npotential. Following settings are needed in the ",(0,a.jsx)(e.code,{children:"&SYSTEM"})," card:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n noncolin = .true.\n lspinorb = .true.\n ...\n/\n"})}),"\n",(0,a.jsx)(e.h2,{id:"non-collinear-spin",children:"Non collinear spin"}),"\n",(0,a.jsxs)(e.p,{children:["In simple spin polarized calculation (",(0,a.jsx)(e.code,{children:"nspin=2"}),"), the spin quantum number (up or\ndown) is considered in the calculation. In non-collinear case, the spin has more\ndegrees of freedom, and can be oriented in any direction. Non-collinear\nmagnetism is quite common in nature, where the spins are not parallel\n(ferromagnetic) or anti-parallel (antiferromagnetic), rather they orient in\nspirals, helicoids, canted or disordered. Non-collinear magnetism can occur\nbecause of geometric frustration of magnetic interaction. It can also occur due\nto the magnetocrystalline anisotropy which is the result of interaction between\nthe spin and lattice interaction. This relativistic effect comes via spin-orbit\ncoupling."]}),"\n",(0,a.jsx)(e.p,{children:"We can constrain the magnetic moment:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n constrained_magnetization = 'atomic direction'\n ...\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Starting magnetization can be specified by ",(0,a.jsx)(e.code,{children:"angle1"})," (angle with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"z"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"z"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.04398em"},children:"z"})]})})]})," axis) and\n",(0,a.jsx)(e.code,{children:"angle2"})," (angle of projection in ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mi,{children:"x"}),(0,a.jsx)(e.mi,{children:"y"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"xy"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"y"})]})})]}),"-plane and with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"x"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"x"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"})]})})]}),"-axis). Also check the\npenalty function (",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"\u03bb"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\lambda"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"\u03bb"})]})})]}),")."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n angle1(i) = 0.0d0\n angle2(i) = 0.0d0\n lambda = 0.5\n ...\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:[(0,a.jsx)(e.code,{children:"i"})," is the index of the atom in ",(0,a.jsx)(e.code,{children:"ATOMIC_SPECIES"})," card."]}),"\n",(0,a.jsx)(e.h2,{id:"strategy-for-convergence",children:"Strategy for convergence"}),"\n",(0,a.jsxs)(e.p,{children:["Spin-orbit coupling calculations are often hard to converge. Use a smaller\n",(0,a.jsx)(e.code,{children:"mixing_beta"})," for such calculations. First perform a collinear calculation with\nnon-relativistic pseudopotential, and then start from the obtained charge\ndensity to perform non-colinear spin orbit calculation."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&ELECTRONS\n ...\n mixing_beta = 1.0000000000d-01\n startingpot = 'file'\n/\n"})}),"\n",(0,a.jsxs)(e.p,{children:["When starting with non-collinear calculation from an existing charge density\nfile from a collinear lsda calculation, we need to set ",(0,a.jsx)(e.code,{children:"lforcet=.true."}),". It\nassumes previous density points in z direction, and rotates in the direction\nspecified by ",(0,a.jsx)(e.code,{children:"angle1"})," (initial magnetization angle with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"z"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"z"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.04398em"},children:"z"})]})})]}),"-axis in degrees),\nand ",(0,a.jsx)(e.code,{children:"angle2"})," (angle in degrees for projections in ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsxs)(e.mrow,{children:[(0,a.jsx)(e.mi,{children:"x"}),(0,a.jsx)(e.mi,{children:"y"})]}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"xy"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,a.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"y"})]})})]}),"-plane and with ",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{children:"x"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"x"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,a.jsx)(e.span,{className:"mord mathnormal",children:"x"})]})})]}),"-axis)."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n...\n angle1(i) = 0.0\n angle2(i) = 0.0\n lforcet = .true.\n/\n"})}),"\n",(0,a.jsx)(e.p,{children:"Also, make sure that energy and charge density cutoffs are sufficient. Certain\npseudo potentials might have issues, try with pseudo potentials from a different\nlibrary. In case of metallic systems, remember to apply smearing."}),"\n",(0,a.jsx)(e.admonition,{title:"Common Errors",type:"danger",children:(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:[(0,a.jsx)(e.strong,{children:"S matrix not positive definite:"})," This error might appear due to numerical\ninstability from overlapping atoms. Check atomic positions carefully. In one my\ncalculations, this error was resolved after setting higher ",(0,a.jsx)(e.code,{children:"ecutrho"}),"."]}),"\n"]}),"\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:["Simplified LDA+U not implemented with ",(0,a.jsx)(e.code,{children:"noncol"})," magnetism, use\n",(0,a.jsx)(e.code,{children:"lda_plus_u_kind=1"}),"."]}),"\n"]}),"\n"]})}),"\n",(0,a.jsx)(e.h2,{id:"bandstructure-of-fe-with-soc",children:"Bandstructure of Fe with SOC"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pw.scf.fe_soc.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsx)(e.p,{children:"Run the scf calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.scf.fe_soc.in > pw.scf.fe_soc.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Prepare the input file for ",(0,a.jsx)(e.code,{children:"nscf"})," ",(0,a.jsx)(e.code,{children:"bands"})," calculation:"]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pw.bands.fe_soc.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsxs)(e.p,{children:["Run the ",(0,a.jsx)(e.code,{children:"bands"})," calculation:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.bands.fe_soc.in > pw.bands.fe_soc.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"Finally post process the bandstructure data:"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/fe/pp.bands.fe_soc.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsxs)(e.p,{children:["In this case ",(0,a.jsx)(e.code,{children:"spin_component"})," has been removed and we add ",(0,a.jsx)(e.code,{children:"lsigma(3)=.true."}),"\nthat instructs the program to compute the expectation value for the ",(0,a.jsx)(e.code,{children:"z"}),"\ncomponent of the spin operator for each eigenfunction and save all values in\nthe file ",(0,a.jsx)(e.code,{children:"fe.noncolin.data.3"}),". All values in this case are either +1/2 or -1/2."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 bands.x -i pp.bands.fe_soc.in > pp.bands.fe_soc.out\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(2623).A}),(0,a.jsx)("img",{src:s(4774).A,alt:"fe-soc-bands"})]}),"\n",(0,a.jsx)(e.h2,{id:"soc-calculation-for-gaas",children:"SOC calculation for GaAs"}),"\n",(0,a.jsxs)(e.p,{children:["Please check the respective ",(0,a.jsx)(e.a,{href:"https://github.com/pranabdas/espresso/tree/master/src/GaAs",children:"input files"}),"."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw.scf.GaAs_soc.in > pw.scf.GaAs_soc.out\nmpirun -np 8 pw.x -i pw.bands.GaAs_soc.in > pw.bands.GaAs_soc.out\nmpirun -np 8 bands.x -i pp.bands.GaAs_soc.in > pp.bands.GaAs_soc.out\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(5466).A}),(0,a.jsx)("img",{src:s(1841).A,alt:"GaAs-soc-bands"})]})]})}function u(n={}){const{wrapper:e}={...(0,i.R)(),...n.components};return e?(0,a.jsx)(e,{...n,children:(0,a.jsx)(x,{...n})}):x(n)}},1841:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-soc-bands-518e9ab7f6ba3c38e10d21c1fe40ce9b.png"},5466:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-soc-bands-e9b5feae2abd0018c3cc7a90c6e32a87.webp"},4774:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/fe-soc-bands-de6c4f09552c8c90ba653e2309a8751a.png"},2623:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/fe-soc-bands-78fdcffe376232aeb31d423fb4864d81.webp"}}]); \ No newline at end of file diff --git a/assets/js/0394bdba.f7646e3a.js b/assets/js/0394bdba.6557bbe8.js similarity index 99% rename from assets/js/0394bdba.f7646e3a.js rename to assets/js/0394bdba.6557bbe8.js index 89d25002..a9c7f9d2 100644 --- a/assets/js/0394bdba.f7646e3a.js +++ b/assets/js/0394bdba.6557bbe8.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9046],{8699:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>r,contentTitle:()=>i,default:()=>p,frontMatter:()=>o,metadata:()=>l,toc:()=>c});var t=s(4848),a=s(8453);const o={title:"Quantum Espresso installation",sidebar_label:"Installation",keywords:["Quantum Espresso installation","Installing Quantum Espresso","PWTK"]},i=void 0,l={id:"setup/install",title:"Quantum Espresso installation",description:"We can install Quantum Espresso on our personal laptops or desktops to run",source:"@site/docs/setup/install.md",sourceDirName:"setup",slug:"/setup/install",permalink:"/espresso/setup/install",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/setup/install.md",tags:[],version:"current",frontMatter:{title:"Quantum Espresso installation",sidebar_label:"Installation",keywords:["Quantum Espresso installation","Installing Quantum Espresso","PWTK"]},sidebar:"docs",previous:{title:"Setup",permalink:"/espresso/category/setup"},next:{title:"High Performance Computing",permalink:"/espresso/setup/hpc"}},r={},c=[{value:"Installing PWTK",id:"installing-pwtk",level:2}];function d(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsx)(n.p,{children:"We can install Quantum Espresso on our personal laptops or desktops to run\nrelatively less computationally intensive calculations. If we intend to perform\ncomputationally heavy tasks, we would need access to better computing resources\nwith large number of CPU (or GPU) cores, memory, bandwidth, and disc IO."}),"\n",(0,t.jsx)(n.p,{children:"Throughout this tutorial, I will be using a Ubuntu system for smaller\ncalculations while other computationally intensive calculations will be done in\nHPC clusters."}),"\n",(0,t.jsx)(n.p,{children:"Perhaps the easiest way to install Quantum Espresso is from the package manager\nof respective Linux distribution. This should work fine for us and this is\nrecommended option. Following commands are for Ubuntu/Debian. First make sure\nyour system is up-to-date."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt update && sudo apt upgrade\n"})}),"\n",(0,t.jsx)(n.p,{children:"Install Quantum Espresso from apt repository:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n libfftw3-dev \\\n quantum-espresso\n"})}),"\n",(0,t.jsx)(n.admonition,{type:"tip",children:(0,t.jsxs)(n.p,{children:["Pre-built binaries of Quantum ESPRESSO for Ubuntu is included in my GitHub\nrepository ",(0,t.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/releases",children:"releases"})," for easy\ninstallation. Please refer to the release notes for more details on how to\ninstall."]})}),"\n",(0,t.jsx)(n.p,{children:"If you want to compile from the source yourself, here are the installation steps\nfor the Quantum Espresso version 7.2 in a Ubuntu (LTS 22.04) system. I will be\ncompiling for single processor. First install the recommended libraries and\ndependencies:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n autoconf \\\n build-essential \\\n ca-certificates \\\n gfortran \\\n libblas3 \\\n libc6 \\\n libfftw3-dev \\\n libgcc-s1 \\\n liblapack-dev \\\n wget\n"})}),"\n",(0,t.jsx)(n.p,{children:"If you want to compile for parallel processing, you also need to install:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n libopenmpi-dev \\\n libscalapack-openmpi-dev \\\n libelpa17 # use libelpa4 on Ubuntu 20.04\n"})}),"\n",(0,t.jsxs)(n.p,{children:[(0,t.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"Download"})," Quantum Espresso (latest\nversion 7.2 at the time of writing):"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\n"})}),"\n",(0,t.jsx)(n.p,{children:"Un-tar the source files:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"tar -zxvf q-e-qe-7.2.tar.gz\n"})}),"\n",(0,t.jsx)(n.p,{children:"Go to the qe directory and issue configure:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\n./configure\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Here we can provide various configuration options. Read the manual in oder to\nproperly understand. But in most cases we will be just fine with the defaults,\nit should detect the system configuration automatically, in case you don't get\nwhat you want, try the various configuration ",(0,t.jsx)(n.code,{children:"flags"})," with configure."]}),"\n",(0,t.jsx)(n.admonition,{type:"caution",children:(0,t.jsxs)(n.p,{children:["Note that certain programs/utilities bundled with Quantum Espresso might not\nwork correctly in parallel compilation, so we may need serial compilation for\nthose by ",(0,t.jsx)(n.code,{children:"./configure --disable-parallel"})," option in case parallel option is\nautomatically detected."]})}),"\n",(0,t.jsx)(n.p,{children:"Finally, compile the source files and create the binary executables:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"# compile individual packages\nmake pw\n# or compile everything\nmake all\n# we can parallelize e.g., below command uses 4 CPUs\nmake -j4 all\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Now, the binary files or their symbolic links (shortcuts) would be placed in the\n",(0,t.jsx)(n.code,{children:"bin"})," directory. It would be good idea to include the executable path to your\n",(0,t.jsx)(n.code,{children:".bashrc"})," (or ",(0,t.jsx)(n.code,{children:".zshrc"})," or whatever shell you use) file:"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"# use the correct path if it differs from mine\necho 'export PATH=\"/root/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Finally, you may need to restart your terminal or ",(0,t.jsx)(n.code,{children:"source .bashrc"}),"."]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"source ~/.bashrc\n"})}),"\n",(0,t.jsx)(n.p,{children:"You can compile the documentation by going to particular directory (e.g., PW or\nPP) and execute (you need to have LaTeX installed in your system):"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"make doc\n"})}),"\n",(0,t.jsxs)(n.p,{children:["If you want docs in PDF format, you can use ",(0,t.jsx)(n.code,{children:"latex"})," commands to create them as\nwell:"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pdflatex filename.tex\n"})}),"\n",(0,t.jsxs)(n.p,{children:["We are now ready to run Quantum Espresso ",(0,t.jsx)(n.code,{children:"pw.x"})," (or any other program) using\n",(0,t.jsx)(n.code,{children:"mpirun"})," by following command:"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x -inp inputfile > outputfile\n# For parallel version\nmpirun -np 12 pw.x -inp inputfile > outputfile\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Where ",(0,t.jsx)(n.code,{children:"-np 12"})," specifies the number of processors. ",(0,t.jsx)(n.code,{children:"-inp"})," stands for input file.\nAlternatively, we can use ",(0,t.jsx)(n.code,{children:"-i"}),", or ",(0,t.jsx)(n.code,{children:"-in"}),", or ",(0,t.jsx)(n.code,{children:"-input"}),", or even standard input\nredirect ",(0,t.jsx)(n.code,{children:"<"}),". But beware some systems may not interpret all the different\noptions, I think safe option is to use ",(0,t.jsx)(n.code,{children:"-i"}),"."]}),"\n",(0,t.jsxs)(n.p,{children:["Once installation is completed, optionally we can run tests if everything went\nOK. Go to the ",(0,t.jsx)(n.code,{children:"test-suite"})," directory and run"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"make run-tests\n"})}),"\n",(0,t.jsxs)(n.p,{children:["If all is well, we will see ",(0,t.jsx)(n.strong,{children:"Passed"})," messages and we are good to go."]}),"\n",(0,t.jsx)(n.admonition,{type:"caution",children:(0,t.jsx)(n.p,{children:"Note that the above installation steps may not be the most optimal way to run\nQuantum Espresso in your computer. There are multiple implementations of same\nlibrary. For example, you can replace openmpi libraries with Intel MKL or MPICH\nimplementations. Please do research yourself or ask help from someone who has\nknowledge about high performance computing."})}),"\n",(0,t.jsx)(n.h2,{id:"installing-pwtk",children:"Installing PWTK"}),"\n",(0,t.jsx)(n.p,{children:"We will install a very hand scripting package PWscf Toolkit (PWTK). First we\nneed to install following dependencies:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install tcl tcllib\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Download the file from - ",(0,t.jsx)(n.a,{href:"http://pwtk.ijs.si/download/pwtk-2.0.tar.gz",children:"http://pwtk.ijs.si/download/pwtk-2.0.tar.gz"})]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:'wget "http://pwtk.ijs.si/download/pwtk-2.0.tar.gz"\n'})}),"\n",(0,t.jsx)(n.p,{children:"Above command will download and save the file to your current directory. Next we\nneed to just un-tar (no need to compile):"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"tar -zxvf pwtk-2.0.tar.gz\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Add the path (modify below as appropriate) to ",(0,t.jsx)(n.code,{children:".bashrc"}),":"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"echo 'export PATH=\"/root/pwtk-2.0:$PATH\"' >> ~/.bashrc\nsource ~/.bashrc\n"})})]})}function p(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,t.jsx)(n,{...e,children:(0,t.jsx)(d,{...e})}):d(e)}},8453:(e,n,s)=>{s.d(n,{R:()=>i,x:()=>l});var t=s(6540);const a={},o=t.createContext(a);function i(e){const n=t.useContext(o);return t.useMemo((function(){return"function"==typeof e?e(n):{...n,...e}}),[n,e])}function l(e){let n;return n=e.disableParentContext?"function"==typeof e.components?e.components(a):e.components||a:i(e.components),t.createElement(o.Provider,{value:n},e.children)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9046],{4980:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>r,contentTitle:()=>i,default:()=>p,frontMatter:()=>o,metadata:()=>l,toc:()=>c});var t=s(4848),a=s(8453);const o={title:"Quantum Espresso installation",sidebar_label:"Installation",keywords:["Quantum Espresso installation","Installing Quantum Espresso","PWTK"]},i=void 0,l={id:"setup/install",title:"Quantum Espresso installation",description:"We can install Quantum Espresso on our personal laptops or desktops to run",source:"@site/docs/setup/install.md",sourceDirName:"setup",slug:"/setup/install",permalink:"/espresso/setup/install",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/setup/install.md",tags:[],version:"current",frontMatter:{title:"Quantum Espresso installation",sidebar_label:"Installation",keywords:["Quantum Espresso installation","Installing Quantum Espresso","PWTK"]},sidebar:"docs",previous:{title:"Setup",permalink:"/espresso/category/setup"},next:{title:"High Performance Computing",permalink:"/espresso/setup/hpc"}},r={},c=[{value:"Installing PWTK",id:"installing-pwtk",level:2}];function d(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsx)(n.p,{children:"We can install Quantum Espresso on our personal laptops or desktops to run\nrelatively less computationally intensive calculations. If we intend to perform\ncomputationally heavy tasks, we would need access to better computing resources\nwith large number of CPU (or GPU) cores, memory, bandwidth, and disc IO."}),"\n",(0,t.jsx)(n.p,{children:"Throughout this tutorial, I will be using a Ubuntu system for smaller\ncalculations while other computationally intensive calculations will be done in\nHPC clusters."}),"\n",(0,t.jsx)(n.p,{children:"Perhaps the easiest way to install Quantum Espresso is from the package manager\nof respective Linux distribution. This should work fine for us and this is\nrecommended option. Following commands are for Ubuntu/Debian. First make sure\nyour system is up-to-date."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt update && sudo apt upgrade\n"})}),"\n",(0,t.jsx)(n.p,{children:"Install Quantum Espresso from apt repository:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n libfftw3-dev \\\n quantum-espresso\n"})}),"\n",(0,t.jsx)(n.admonition,{type:"tip",children:(0,t.jsxs)(n.p,{children:["Pre-built binaries of Quantum ESPRESSO for Ubuntu is included in my GitHub\nrepository ",(0,t.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/releases",children:"releases"})," for easy\ninstallation. Please refer to the release notes for more details on how to\ninstall."]})}),"\n",(0,t.jsx)(n.p,{children:"If you want to compile from the source yourself, here are the installation steps\nfor the Quantum Espresso version 7.2 in a Ubuntu (LTS 22.04) system. I will be\ncompiling for single processor. First install the recommended libraries and\ndependencies:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n autoconf \\\n build-essential \\\n ca-certificates \\\n gfortran \\\n libblas3 \\\n libc6 \\\n libfftw3-dev \\\n libgcc-s1 \\\n liblapack-dev \\\n wget\n"})}),"\n",(0,t.jsx)(n.p,{children:"If you want to compile for parallel processing, you also need to install:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"sudo apt install --no-install-recommends \\\n libopenmpi-dev \\\n libscalapack-openmpi-dev \\\n libelpa17 # use libelpa4 on Ubuntu 20.04\n"})}),"\n",(0,t.jsxs)(n.p,{children:[(0,t.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"Download"})," Quantum Espresso (latest\nversion 7.2 at the time of writing):"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\n"})}),"\n",(0,t.jsx)(n.p,{children:"Un-tar the source files:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"tar -zxvf q-e-qe-7.2.tar.gz\n"})}),"\n",(0,t.jsx)(n.p,{children:"Go to the qe directory and issue configure:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\n./configure\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Here we can provide various configuration options. Read the manual in oder to\nproperly understand. But in most cases we will be just fine with the defaults,\nit should detect the system configuration automatically, in case you don't get\nwhat you want, try the various configuration ",(0,t.jsx)(n.code,{children:"flags"})," with configure."]}),"\n",(0,t.jsx)(n.admonition,{type:"caution",children:(0,t.jsxs)(n.p,{children:["Note that certain programs/utilities bundled with Quantum Espresso might not\nwork correctly in parallel compilation, so we may need serial compilation for\nthose by ",(0,t.jsx)(n.code,{children:"./configure --disable-parallel"})," option in case parallel option is\nautomatically detected."]})}),"\n",(0,t.jsx)(n.p,{children:"Finally, compile the source files and create the binary executables:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"# compile individual packages\nmake pw\n# or compile everything\nmake all\n# we can parallelize e.g., below command uses 4 CPUs\nmake -j4 all\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Now, the binary files or their symbolic links (shortcuts) would be placed in the\n",(0,t.jsx)(n.code,{children:"bin"})," directory. 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0.83333333 0.66666667 4.629630e-03\n 0.83333333 0.83333333 0.83333333 4.629630e-03\n",r='&inputpp\n outdir = "/tmp/"\n prefix = "silicon"\n calculation = "eps"\n/\n\n&energy_grid\n smeartype = "gauss"\n intersmear = 0.2\n wmin = 0.0\n wmax = 30.0\n nw = 500\n/\n',c={title:"Dielectric constant"},o=void 0,d={id:"hands-on/epsilon",title:"Dielectric constant",description:"First we perform self consistent field calculation:",source:"@site/docs/hands-on/epsilon.mdx",sourceDirName:"hands-on",slug:"/hands-on/epsilon",permalink:"/espresso/hands-on/epsilon",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/epsilon.mdx",tags:[],version:"current",frontMatter:{title:"Dielectric constant"},sidebar:"docs",previous:{title:"Bi2Se3 (TI)",permalink:"/espresso/hands-on/Bi2Se3"},next:{title:"Fermi Surface",permalink:"/espresso/hands-on/fermi-surface"}},h={},m=[{value:"Resources",id:"resources",level:3}];function p(e){const n={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h3:"h3",li:"li",math:"math",mi:"mi",mn:"mn",mrow:"mrow",msub:"msub",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,a.R)(),...e.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)(n.p,{children:"First we perform self consistent field calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"mpirun -np 4 pw.x -i pw.scf.silicon_epsilon.in > pw.scf.silicon_epsilon.out\n"})}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/pw.scf.silicon_epsilon.in",showLineNumbers:!0,children:l}),"\n",(0,i.jsx)(n.p,{children:"Especially, notice following changes:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-fortran",children:" nbnd = 20\n nosym = .true.\n noinv = .true.\n"})}),"\n",(0,i.jsxs)(n.p,{children:["We turn off the automatic reduction of k-points that ",(0,i.jsx)(n.code,{children:"pw.x"})," does by using\ncrystal symmetries (",(0,i.jsx)(n.code,{children:"nosym = .true."})," and ",(0,i.jsx)(n.code,{children:"noinv = .true."}),"). This is because\n",(0,i.jsx)(n.code,{children:"epsilon.x"})," does not recognize crystal symmetries, therefore the entire list of\nk-points in the grid is needed. Secondly, we calculate a larger number of bands\n(20), since we are interested in interband transitions. Also, note that\n",(0,i.jsx)(n.code,{children:"epsilon.x"})," doesn't support the reduction of the k-points grid into the\nirreducible Brillouin zone, so the PW runs must be performed with a uniform\nk-points grid and all k-points weights must be equal to each other, i.e. in the\nk-points card the k-points coordinates must be given manually in ",(0,i.jsx)(n.code,{children:"crystal"})," or\n",(0,i.jsx)(n.code,{children:"alat"})," or ",(0,i.jsx)(n.code,{children:"bohr"}),", but not with the ",(0,i.jsx)(n.code,{children:"automatic"})," option. However, the automatic\nk-points option seems to work. If necessary, we can perform ",(0,i.jsx)(n.code,{children:"nscf"})," calculation\nwith finer k-grid."]}),"\n",(0,i.jsxs)(n.p,{children:["Next step is to prepare the input file for ",(0,i.jsx)(n.code,{children:"epsilon.x"}),":"]}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/epsilon.si.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsxs)(n.p,{children:["The variables ",(0,i.jsx)(n.code,{children:"smeartype"})," and ",(0,i.jsx)(n.code,{children:"intersmear"})," define the numerical approximation\nused to represent the Dirac delta functions in the expression for ",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"2"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_2"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"2"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),"\ngiven above. The variables ",(0,i.jsx)(n.code,{children:"wmin"}),", ",(0,i.jsx)(n.code,{children:"wmax"})," and ",(0,i.jsx)(n.code,{children:"nw"})," define the energy grid for\nthe dielectric function. All the energy variables are in eV."]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"mpirun -np 4 epsilon.x -i epsilon.si.in > epsilon.si.out\n"})}),"\n",(0,i.jsxs)(n.p,{children:["We will see the results are saved in separate ",(0,i.jsx)(n.code,{children:".dat"})," files. We can plot the real\n(",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"1"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_1"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"1"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),") and imaginary (",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"2"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_2"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"2"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),") parts of dielectric constants:"]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-py",children:'import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\nplt.rcParams["figure.dpi"]=150\nplt.rcParams["figure.facecolor"]="white"\n\ndata_r = np.loadtxt(\'../src/silicon/epsr_silicon.dat\')\ndata_i = np.loadtxt(\'../src/silicon/epsi_silicon.dat\')\nenergy_r, epsilon_r = data_r[:, 0], data_r[:, 2]\nenergy_i, epsilon_i = data_i[:, 0], data_i[:, 2]\n\nplt.plot(energy_r, epsilon_r, lw=1, label="$\\\\epsilon_1$")\nplt.plot(energy_i, epsilon_i, lw=1, label="$\\\\epsilon_2$")\nplt.xlim(0, 15)\nplt.xlabel("Energy (eV)")\nplt.ylabel("$\\\\epsilon_1~/~\\\\epsilon_2$")\nplt.legend(frameon=False)\nplt.show()\n'})}),"\n",(0,i.jsxs)("picture",{children:[(0,i.jsx)("source",{type:"image/webp",srcSet:s(1621).A}),(0,i.jsx)("img",{src:s(712).A,alt:"silicon-epsilon"})]}),"\n",(0,i.jsx)(n.admonition,{type:"warning",children:(0,i.jsxs)(n.p,{children:["Ultra-soft pseudopotentials do not work with ",(0,i.jsx)(n.code,{children:"epsilon.x"}),". Also note that the\nabove example is not tested against the k-mesh. We usually need finer k-mesh for\n",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsx)(n.mi,{children:"\u03f5"})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.4306em"}}),(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"})]})})]})," to converge. By default the maximum number of k-points is set to\n40000 in Quantum Espresso, if we need more k-points, we can change\n",(0,i.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/blob/develop/Modules/parameters.f90",children:"Modules/parameters.f90"}),"\nand recompile Quantum Espresso."]})}),"\n",(0,i.jsx)(n.h3,{id:"resources",children:"Resources"}),"\n",(0,i.jsxs)(n.ul,{children:["\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)("a",{target:"_blank",href:s(3402).A,children:"Epsilon.x manual"}),"\n"]}),"\n"]})]})}function x(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,i.jsx)(n,{...e,children:(0,i.jsx)(p,{...e})}):p(e)}},3402:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/files/eps_man-ab3fac19eb366509dd129c37fbf94ac0.pdf"},712:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/images/silicon-epsilon-6e55dab7b29cb772e78678d57ff267f9.png"},1621:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/images/silicon-epsilon-83924adfcef99d6186800decced9800e.webp"}}]); \ No newline at end of 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0.83333333 0.83333333 0.66666667 4.629630e-03\n 0.83333333 0.83333333 0.83333333 4.629630e-03\n",r='&inputpp\n outdir = "/tmp/"\n prefix = "silicon"\n calculation = "eps"\n/\n\n&energy_grid\n smeartype = "gauss"\n intersmear = 0.2\n wmin = 0.0\n wmax = 30.0\n nw = 500\n/\n',c={title:"Dielectric constant"},o=void 0,d={id:"hands-on/epsilon",title:"Dielectric constant",description:"First we perform self consistent field calculation:",source:"@site/docs/hands-on/epsilon.mdx",sourceDirName:"hands-on",slug:"/hands-on/epsilon",permalink:"/espresso/hands-on/epsilon",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/epsilon.mdx",tags:[],version:"current",frontMatter:{title:"Dielectric constant"},sidebar:"docs",previous:{title:"Bi2Se3 (TI)",permalink:"/espresso/hands-on/Bi2Se3"},next:{title:"Fermi Surface",permalink:"/espresso/hands-on/fermi-surface"}},h={},m=[{value:"Resources",id:"resources",level:3}];function p(e){const n={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h3:"h3",li:"li",math:"math",mi:"mi",mn:"mn",mrow:"mrow",msub:"msub",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,a.R)(),...e.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)(n.p,{children:"First we perform self consistent field calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"mpirun -np 4 pw.x -i pw.scf.silicon_epsilon.in > pw.scf.silicon_epsilon.out\n"})}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/pw.scf.silicon_epsilon.in",showLineNumbers:!0,children:l}),"\n",(0,i.jsx)(n.p,{children:"Especially, notice following changes:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-fortran",children:" nbnd = 20\n nosym = .true.\n noinv = .true.\n"})}),"\n",(0,i.jsxs)(n.p,{children:["We turn off the automatic reduction of k-points that ",(0,i.jsx)(n.code,{children:"pw.x"})," does by using\ncrystal symmetries (",(0,i.jsx)(n.code,{children:"nosym = .true."})," and ",(0,i.jsx)(n.code,{children:"noinv = .true."}),"). This is because\n",(0,i.jsx)(n.code,{children:"epsilon.x"})," does not recognize crystal symmetries, therefore the entire list of\nk-points in the grid is needed. Secondly, we calculate a larger number of bands\n(20), since we are interested in interband transitions. Also, note that\n",(0,i.jsx)(n.code,{children:"epsilon.x"})," doesn't support the reduction of the k-points grid into the\nirreducible Brillouin zone, so the PW runs must be performed with a uniform\nk-points grid and all k-points weights must be equal to each other, i.e. in the\nk-points card the k-points coordinates must be given manually in ",(0,i.jsx)(n.code,{children:"crystal"})," or\n",(0,i.jsx)(n.code,{children:"alat"})," or ",(0,i.jsx)(n.code,{children:"bohr"}),", but not with the ",(0,i.jsx)(n.code,{children:"automatic"})," option. However, the automatic\nk-points option seems to work. If necessary, we can perform ",(0,i.jsx)(n.code,{children:"nscf"})," calculation\nwith finer k-grid."]}),"\n",(0,i.jsxs)(n.p,{children:["Next step is to prepare the input file for ",(0,i.jsx)(n.code,{children:"epsilon.x"}),":"]}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/epsilon.si.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsxs)(n.p,{children:["The variables ",(0,i.jsx)(n.code,{children:"smeartype"})," and ",(0,i.jsx)(n.code,{children:"intersmear"})," define the numerical approximation\nused to represent the Dirac delta functions in the expression for ",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"2"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_2"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"2"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),"\ngiven above. The variables ",(0,i.jsx)(n.code,{children:"wmin"}),", ",(0,i.jsx)(n.code,{children:"wmax"})," and ",(0,i.jsx)(n.code,{children:"nw"})," define the energy grid for\nthe dielectric function. All the energy variables are in eV."]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"mpirun -np 4 epsilon.x -i epsilon.si.in > epsilon.si.out\n"})}),"\n",(0,i.jsxs)(n.p,{children:["We will see the results are saved in separate ",(0,i.jsx)(n.code,{children:".dat"})," files. We can plot the real\n(",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"1"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_1"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"1"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),") and imaginary (",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"\u03f5"}),(0,i.jsx)(n.mn,{children:"2"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon_2"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,i.jsx)(n.span,{className:"pstrut",style:{height:"2.7em"}}),(0,i.jsx)(n.span,{className:"sizing reset-size6 size3 mtight",children:(0,i.jsx)(n.span,{className:"mord mtight",children:"2"})})]})}),(0,i.jsx)(n.span,{className:"vlist-s",children:"\u200b"})]}),(0,i.jsx)(n.span,{className:"vlist-r",children:(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.15em"},children:(0,i.jsx)(n.span,{})})})]})})]})]})})]}),") parts of dielectric constants:"]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-py",children:'import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\nplt.rcParams["figure.dpi"]=150\nplt.rcParams["figure.facecolor"]="white"\n\ndata_r = np.loadtxt(\'../src/silicon/epsr_silicon.dat\')\ndata_i = np.loadtxt(\'../src/silicon/epsi_silicon.dat\')\nenergy_r, epsilon_r = data_r[:, 0], data_r[:, 2]\nenergy_i, epsilon_i = data_i[:, 0], data_i[:, 2]\n\nplt.plot(energy_r, epsilon_r, lw=1, label="$\\\\epsilon_1$")\nplt.plot(energy_i, epsilon_i, lw=1, label="$\\\\epsilon_2$")\nplt.xlim(0, 15)\nplt.xlabel("Energy (eV)")\nplt.ylabel("$\\\\epsilon_1~/~\\\\epsilon_2$")\nplt.legend(frameon=False)\nplt.show()\n'})}),"\n",(0,i.jsxs)("picture",{children:[(0,i.jsx)("source",{type:"image/webp",srcSet:s(1621).A}),(0,i.jsx)("img",{src:s(712).A,alt:"silicon-epsilon"})]}),"\n",(0,i.jsx)(n.admonition,{type:"warning",children:(0,i.jsxs)(n.p,{children:["Ultra-soft pseudopotentials do not work with ",(0,i.jsx)(n.code,{children:"epsilon.x"}),". Also note that the\nabove example is not tested against the k-mesh. We usually need finer k-mesh for\n",(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsx)(n.mi,{children:"\u03f5"})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"\\epsilon"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.4306em"}}),(0,i.jsx)(n.span,{className:"mord mathnormal",children:"\u03f5"})]})})]})," to converge. By default the maximum number of k-points is set to\n40000 in Quantum Espresso, if we need more k-points, we can change\n",(0,i.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/blob/develop/Modules/parameters.f90",children:"Modules/parameters.f90"}),"\nand recompile Quantum Espresso."]})}),"\n",(0,i.jsx)(n.h3,{id:"resources",children:"Resources"}),"\n",(0,i.jsxs)(n.ul,{children:["\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)("a",{target:"_blank",href:s(3402).A,children:"Epsilon.x manual"}),"\n"]}),"\n"]})]})}function x(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,i.jsx)(n,{...e,children:(0,i.jsx)(p,{...e})}):p(e)}},3402:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/files/eps_man-ab3fac19eb366509dd129c37fbf94ac0.pdf"},712:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/images/silicon-epsilon-6e55dab7b29cb772e78678d57ff267f9.png"},1621:(e,n,s)=>{s.d(n,{A:()=>i});const i=s.p+"assets/images/silicon-epsilon-83924adfcef99d6186800decced9800e.webp"}}]); \ No newline at end of file diff --git a/assets/js/1d59910a.6c9983da.js b/assets/js/1d59910a.6c9983da.js deleted file mode 100644 index 325f543d..00000000 --- a/assets/js/1d59910a.6c9983da.js +++ /dev/null @@ -1 +0,0 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4737],{355:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>m,contentTitle:()=>t,default:()=>d,frontMatter:()=>i,metadata:()=>c,toc:()=>r});var l=a(4848),n=a(8453);const i={title:"Hartree-Fock Theory",sidebar_label:"Hartree-Fock"},t=void 0,c={id:"theory/hartree-fock",title:"Hartree-Fock Theory",description:"Hatree-Fock theory is foundational to many subsequent electronic structure",source:"@site/docs/theory/hartree-fock.md",sourceDirName:"theory",slug:"/theory/hartree-fock",permalink:"/espresso/theory/hartree-fock",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/theory/hartree-fock.md",tags:[],version:"current",frontMatter:{title:"Hartree-Fock Theory",sidebar_label:"Hartree-Fock"},sidebar:"docs",previous:{title:"Problem statement",permalink:"/espresso/theory/problem-statement"},next:{title:"DFT overview",permalink:"/espresso/theory/dft"}},m={},r=[{value:"Slater determinant",id:"slater-determinant",level:2},{value:"Resources",id:"resources",level:2}];function h(s){const e={a:"a",annotation:"annotation",h2:"h2",li:"li",math:"math",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mpadded:"mpadded",mrow:"mrow",mspace:"mspace",msqrt:"msqrt",mstyle:"mstyle",msub:"msub",mtable:"mtable",mtd:"mtd",mtext:"mtext",mtr:"mtr",p:"p",path:"path",semantics:"semantics",span:"span",strong:"strong",svg:"svg",ul:"ul",...(0,n.R)(),...s.components};return(0,l.jsxs)(l.Fragment,{children:[(0,l.jsxs)(e.p,{children:["Hatree-Fock theory is foundational to many subsequent electronic structure\ntheories. 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\ No newline at end of file diff --git a/assets/js/279e2484.e8c076b4.js b/assets/js/279e2484.e8c076b4.js new file mode 100644 index 00000000..693eefdc --- /dev/null +++ b/assets/js/279e2484.e8c076b4.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9718],{1230:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>h,contentTitle:()=>c,default:()=>p,frontMatter:()=>t,metadata:()=>r,toc:()=>d});var n=a(4848),l=a(8453),i=a(1432);const m="&PROJWFC\n prefix= 'al',\n outdir= '/tmp/',\n filpdos= 'al_pdos.dat'\n/\n",t={title:"Projected Density of States",sidebar_label:"P-DOS"},c=void 0,r={id:"hands-on/pdos",title:"Projected Density of States",description:"Here we continue with our Aluminum example.",source:"@site/docs/hands-on/pdos.mdx",sourceDirName:"hands-on",slug:"/hands-on/pdos",permalink:"/espresso/hands-on/pdos",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/pdos.mdx",tags:[],version:"current",frontMatter:{title:"Projected Density of States",sidebar_label:"P-DOS"},sidebar:"docs",previous:{title:"Al (metal)",permalink:"/espresso/hands-on/aluminum"},next:{title:"k-resolved DOS",permalink:"/espresso/hands-on/kpdos"}},h={},d=[];function x(s){const e={a:"a",annotation:"annotation",code:"code",li:"li",math:"math",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",msub:"msub",msubsup:"msubsup",msup:"msup",mtext:"mtext",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,l.R)(),...s.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsxs)(e.p,{children:["Here we continue with our Aluminum example.\nOften it is needed to know the contribution from each individual atoms and/or\neach of their orbital contributions. 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First, we must perform the self consistent field calculation followed by\nthe non-self consistent field calculation with denser k-points."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x < al_scf.in > al_scf.out\npw.x < al_nscf.in > al_nscf.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Then we prepare the input file for ",(0,n.jsx)(e.strong,{children:"projwfc.x"}),":"]}),"\n","\n",(0,n.jsx)(i.A,{language:"bash",title:"src/al/al_projwfc.in",showLineNumbers:!0,children:m}),"\n",(0,n.jsx)(e.p,{children:"Perform the calculation:"}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"projwfc.x < al_projwfc.in > al_projwfc.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Output data format:"})," the DOS values are written in the file\n",(0,n.jsx)(e.code,{children:"{filpdos}.pdos_atm#N(X)_wfc#M(l)"}),", where ",(0,n.jsx)(e.code,{children:"N"})," is atom number, ",(0,n.jsx)(e.code,{children:"X"})," is atom\nsymbol, ",(0,n.jsx)(e.code,{children:"M"})," is wfc number, and ",(0,n.jsx)(e.code,{children:"l=s,p,d,f"})," one file for each atomic wavefunction\nread from pseudopotential file. 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",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"m"}),(0,n.jsx)(e.mo,{children:"="}),(0,n.jsx)(e.mo,{children:"\xb1"}),(0,n.jsx)(e.mn,{children:"2"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"m=\\pm 2"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,n.jsx)(e.span,{className:"mord 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Let's\ncreate our plots:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-python",metastring:'title="src/notebooks/al-pdos.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\n\n# load data\ndef data_loader(fname):\n import numpy as np\n\n data = np.loadtxt(fname)\n energy = data[:, 0]\n pdos = data[:, 1] # ldos col, total contribution for a given orbital\n\n return energy, pdos\n\nenergy, pdos_s = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#1(s)')\n_, pdos_p = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#2(p)')\n_, pdos_tot = data_loader('../src/al/al_pdos.dat.pdos_tot')\n\n# make plots\nplt.figure(figsize = (8, 4))\nplt.plot(energy, pdos_s, linewidth=0.75, color='#006699', label='s-orbital')\nplt.plot(energy, pdos_p, linewidth=0.75, color='r', label='p-orbital')\nplt.plot(energy, pdos_tot, linewidth=0.75, color='k', label='total')\nplt.yticks([])\nplt.xlabel('Energy (eV)')\nplt.ylabel('DOS')\nplt.axvline(x= 7.9421, linewidth=0.5, color='k', linestyle=(0, (8, 10)))\nplt.xlim(-5, 27)\nplt.ylim(0, )\nplt.fill_between(energy, 0, pdos_s, where=(energy < 7.9421), facecolor='#006699', alpha=0.25)\nplt.fill_between(energy, 0, pdos_p, where=(energy < 7.9421), facecolor='r', alpha=0.25)\nplt.fill_between(energy, 0, pdos_tot, where=(energy < 7.9421), facecolor='k', alpha=0.25)\n# plt.text(6.5, 0.52, 'Fermi energy', fontsize= small, rotation=90)\nplt.legend(frameon=False)\nplt.show()\n"})}),"\n",(0,n.jsx)(e.p,{children:"Here is how our projected density of states plot looks like:"}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(1457).A}),(0,n.jsx)("img",{src:a(4607).A,alt:"al-pdos"})]}),"\n",(0,n.jsxs)(e.p,{children:["We can perform sums of specific atom or orbital contributions using\n",(0,n.jsx)(e.strong,{children:"sumpdos.x"})," code if there are multiple ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"s"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"s"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"s"})]})})]})," or ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"p"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"p"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"p"})]})})]})," orbitals:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"sumpdos.x *\\(Al\\)* > atom_Al_tot.dat\nsumpdos.x *\\(Al\\)*\\(s\\) > atom_Al_s.dat\nsumpdos.x *\\(Al\\)*\\(p\\) > atom_Al_p.dat\n"})})]})}function p(s={}){const{wrapper:e}={...(0,l.R)(),...s.components};return e?(0,n.jsx)(e,{...s,children:(0,n.jsx)(x,{...s})}):x(s)}},4607:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/al-pdos-ad0dc41d5956164f364eb6f3c9921cda.png"},1457:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/al-pdos-8f11ae8032a200a37d9f9646f4c0be71.webp"}}]); \ No newline at end of file diff --git a/assets/js/282d1385.94990242.js b/assets/js/282d1385.fbe64ed3.js similarity index 98% rename from assets/js/282d1385.94990242.js rename to assets/js/282d1385.fbe64ed3.js index a491c306..8a2372aa 100644 --- a/assets/js/282d1385.94990242.js +++ b/assets/js/282d1385.fbe64ed3.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[8934],{6147:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>p,contentTitle:()=>c,default:()=>m,frontMatter:()=>l,metadata:()=>h,toc:()=>u});var s=t(4848),o=t(8453),i=t(6540);class r extends i.Component{constructor(e){super(e),this.handleChange=e=>{this.setState({ang:e.target.value})},this.handleCopy=()=>{const e=(parseFloat(this.state.ang)/.529177249).toFixed(10);this.setState({showCopied:!0}),setTimeout((()=>{this.setState({showCopied:!1})}),1500),navigator.clipboard.writeText(e)},this.state={ang:1,showCopied:!1}}render(){const e=(parseFloat(this.state.ang)/.529177249).toFixed(10);return(0,s.jsx)(s.Fragment,{children:(0,s.jsxs)("p",{children:[(0,s.jsx)("input",{className:"appInput",type:"number",step:"0.01",value:this.state.ang,onChange:this.handleChange}),"\xa0\u212b\xa0= ",(0,s.jsx)("span",{className:"appOutput",children:e}),"\xa0Bohr.\u2002",(0,s.jsx)("button",{className:"appBtn",onClick:this.handleCopy,children:this.state.showCopied?"Copied":"Copy"})]})})}}const a=r,l={title:"Density Functional Theory using Quantum Espresso",sidebar_label:"Welcome",slug:"/",keywords:["DFT","first principles calculation","Angstrom to Bohr converter"]},c=void 0,h={id:"welcome",title:"Density Functional Theory using Quantum Espresso",description:"This tutorial is result of my personal notes while trying (which I still do) to",source:"@site/docs/welcome.mdx",sourceDirName:".",slug:"/",permalink:"/espresso/",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/welcome.mdx",tags:[],version:"current",frontMatter:{title:"Density Functional Theory using Quantum Espresso",sidebar_label:"Welcome",slug:"/",keywords:["DFT","first principles calculation","Angstrom to Bohr converter"]},sidebar:"docs",next:{title:"Setup",permalink:"/espresso/category/setup"}},p={},u=[{value:"Filename conventions",id:"filename-conventions",level:2},{value:"Unit conversions",id:"unit-conversions",level:2}];function d(e){const n={a:"a",code:"code",em:"em",h2:"h2",li:"li",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,o.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsx)(n.p,{children:"This tutorial is result of my personal notes while trying (which I still do) to\nlearn Density Functional Theory calculations myself. I am no expert in this\nsubject. I am sharing this notes here, just in case it helps you getting\nstarted. I will cite numerous other resources that I am following. Hope you will\nfind this tutorial helpful."}),"\n",(0,s.jsxs)(n.p,{children:["The quantum espresso input files, jupyter notebooks (containing python code for\nvisualizations), and other source files related to this tutorial can be found on\nGitHub: ",(0,s.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/",children:"pranabdas/espresso"}),". You may\nclone the repository to your local machine:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"git clone https://github.com/pranabdas/espresso.git\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Or, if you do not have git installed, download zipped copy of the repository\n",(0,s.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/archive/refs/heads/main.zip",children:"here"}),"."]}),"\n",(0,s.jsx)(n.h2,{id:"filename-conventions",children:"Filename conventions"}),"\n",(0,s.jsx)(n.p,{children:"Lately, I decided to follow specific pattern for the filenames, but you can\nchoose whatever works best for you. Note that all example files in this\ntutorial does not follow this convention yet."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{children:"{program}.{calculation}.{system}.{in, out}\n{program}.{calculation}.{system_description}.{in, out}\n{pw, pp, ...}.{scf, bands, ...}.{silicon, al_slab}.{in, out}\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Example: ",(0,s.jsx)(n.em,{children:"pw.bands.silicon.in"})," \u2192 ",(0,s.jsx)(n.em,{children:"input"})," file for the ",(0,s.jsx)(n.em,{children:"bands"})," calculation using\n",(0,s.jsx)(n.em,{children:"PWscf"})," program for ",(0,s.jsx)(n.em,{children:"silicon"}),"."]}),"\n",(0,s.jsxs)(n.p,{children:["For PWTK scripts, we will use ",(0,s.jsx)(n.code,{children:".pwtk"})," extension (e.g., ",(0,s.jsx)(n.em,{children:"silicon_vc_relax.pwtk"}),")."]}),"\n",(0,s.jsx)(n.h2,{id:"unit-conversions",children:"Unit conversions"}),"\n",(0,s.jsxs)(n.ul,{children:["\n",(0,s.jsx)(n.li,{children:"1 Bohr = 0.529177249 \xc5"}),"\n",(0,s.jsx)(n.li,{children:"1 Rydberg (Ry) = 13.6056981 eV."}),"\n"]}),"\n",(0,s.jsxs)(n.p,{children:[(0,s.jsx)(n.strong,{children:"Angstrom to Bohr converter:"})," lattice constants are often provided in\nangstrom, you can use following utility to convert to Bohr."]}),"\n","\n",(0,s.jsx)(a,{})]})}function m(e={}){const{wrapper:n}={...(0,o.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(d,{...e})}):d(e)}},8453:(e,n,t)=>{t.d(n,{R:()=>r,x:()=>a});var s=t(6540);const o={},i=s.createContext(o);function r(e){const n=s.useContext(i);return s.useMemo((function(){return"function"==typeof e?e(n):{...n,...e}}),[n,e])}function a(e){let n;return n=e.disableParentContext?"function"==typeof e.components?e.components(o):e.components||o:r(e.components),s.createElement(i.Provider,{value:n},e.children)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[8934],{3206:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>p,contentTitle:()=>c,default:()=>m,frontMatter:()=>l,metadata:()=>h,toc:()=>u});var s=t(4848),o=t(8453),i=t(6540);class r extends i.Component{constructor(e){super(e),this.handleChange=e=>{this.setState({ang:e.target.value})},this.handleCopy=()=>{const e=(parseFloat(this.state.ang)/.529177249).toFixed(10);this.setState({showCopied:!0}),setTimeout((()=>{this.setState({showCopied:!1})}),1500),navigator.clipboard.writeText(e)},this.state={ang:1,showCopied:!1}}render(){const e=(parseFloat(this.state.ang)/.529177249).toFixed(10);return(0,s.jsx)(s.Fragment,{children:(0,s.jsxs)("p",{children:[(0,s.jsx)("input",{className:"appInput",type:"number",step:"0.01",value:this.state.ang,onChange:this.handleChange}),"\xa0\u212b\xa0= ",(0,s.jsx)("span",{className:"appOutput",children:e}),"\xa0Bohr.\u2002",(0,s.jsx)("button",{className:"appBtn",onClick:this.handleCopy,children:this.state.showCopied?"Copied":"Copy"})]})})}}const a=r,l={title:"Density Functional Theory using Quantum Espresso",sidebar_label:"Welcome",slug:"/",keywords:["DFT","first principles calculation","Angstrom to Bohr converter"]},c=void 0,h={id:"welcome",title:"Density Functional Theory using Quantum Espresso",description:"This tutorial is result of my personal notes while trying (which I still do) to",source:"@site/docs/welcome.mdx",sourceDirName:".",slug:"/",permalink:"/espresso/",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/welcome.mdx",tags:[],version:"current",frontMatter:{title:"Density Functional Theory using Quantum Espresso",sidebar_label:"Welcome",slug:"/",keywords:["DFT","first principles calculation","Angstrom to Bohr converter"]},sidebar:"docs",next:{title:"Setup",permalink:"/espresso/category/setup"}},p={},u=[{value:"Filename conventions",id:"filename-conventions",level:2},{value:"Unit conversions",id:"unit-conversions",level:2}];function d(e){const n={a:"a",code:"code",em:"em",h2:"h2",li:"li",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,o.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsx)(n.p,{children:"This tutorial is result of my personal notes while trying (which I still do) to\nlearn Density Functional Theory calculations myself. I am no expert in this\nsubject. I am sharing this notes here, just in case it helps you getting\nstarted. I will cite numerous other resources that I am following. Hope you will\nfind this tutorial helpful."}),"\n",(0,s.jsxs)(n.p,{children:["The quantum espresso input files, jupyter notebooks (containing python code for\nvisualizations), and other source files related to this tutorial can be found on\nGitHub: ",(0,s.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/",children:"pranabdas/espresso"}),". You may\nclone the repository to your local machine:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"git clone https://github.com/pranabdas/espresso.git\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Or, if you do not have git installed, download zipped copy of the repository\n",(0,s.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/archive/refs/heads/main.zip",children:"here"}),"."]}),"\n",(0,s.jsx)(n.h2,{id:"filename-conventions",children:"Filename conventions"}),"\n",(0,s.jsx)(n.p,{children:"Lately, I decided to follow specific pattern for the filenames, but you can\nchoose whatever works best for you. Note that all example files in this\ntutorial does not follow this convention yet."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{children:"{program}.{calculation}.{system}.{in, out}\n{program}.{calculation}.{system_description}.{in, out}\n{pw, pp, ...}.{scf, bands, ...}.{silicon, al_slab}.{in, out}\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Example: ",(0,s.jsx)(n.em,{children:"pw.bands.silicon.in"})," \u2192 ",(0,s.jsx)(n.em,{children:"input"})," file for the ",(0,s.jsx)(n.em,{children:"bands"})," calculation using\n",(0,s.jsx)(n.em,{children:"PWscf"})," program for ",(0,s.jsx)(n.em,{children:"silicon"}),"."]}),"\n",(0,s.jsxs)(n.p,{children:["For PWTK scripts, we will use ",(0,s.jsx)(n.code,{children:".pwtk"})," extension (e.g., ",(0,s.jsx)(n.em,{children:"silicon_vc_relax.pwtk"}),")."]}),"\n",(0,s.jsx)(n.h2,{id:"unit-conversions",children:"Unit conversions"}),"\n",(0,s.jsxs)(n.ul,{children:["\n",(0,s.jsx)(n.li,{children:"1 Bohr = 0.529177249 \xc5"}),"\n",(0,s.jsx)(n.li,{children:"1 Rydberg (Ry) = 13.6056981 eV."}),"\n"]}),"\n",(0,s.jsxs)(n.p,{children:[(0,s.jsx)(n.strong,{children:"Angstrom to Bohr converter:"})," lattice constants are often provided in\nangstrom, you can use following utility to convert to Bohr."]}),"\n","\n",(0,s.jsx)(a,{})]})}function m(e={}){const{wrapper:n}={...(0,o.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(d,{...e})}):d(e)}},8453:(e,n,t)=>{t.d(n,{R:()=>r,x:()=>a});var s=t(6540);const o={},i=s.createContext(o);function r(e){const n=s.useContext(i);return s.useMemo((function(){return"function"==typeof e?e(n):{...n,...e}}),[n,e])}function a(e){let n;return n=e.disableParentContext?"function"==typeof e.components?e.components(o):e.components||o:r(e.components),s.createElement(i.Provider,{value:n},e.children)}}}]); \ No newline at end of file diff --git a/assets/js/2aae1fcb.4684b31d.js b/assets/js/2aae1fcb.0e6b223f.js similarity index 97% rename from assets/js/2aae1fcb.4684b31d.js rename to assets/js/2aae1fcb.0e6b223f.js index 874733b3..effad20b 100644 --- a/assets/js/2aae1fcb.4684b31d.js +++ b/assets/js/2aae1fcb.0e6b223f.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[5308],{2256:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>o,contentTitle:()=>c,default:()=>h,frontMatter:()=>d,metadata:()=>p,toc:()=>l});var i=s(4848),a=s(8453),r=s(1432);const t="&BANDS\n outdir='./tmp/',\n prefix='ni',\n filband='ni_bands_up.dat',\n spin_component = 1,\n/\n",d={title:"Spin polarized bandstructure calculation for nickel",sidebar_label:"Ni (spin pol. bands)"},c=void 0,p={id:"hands-on/ni",title:"Spin polarized bandstructure calculation for nickel",description:"We prepare the input file pwscfni.in and run the calculation:",source:"@site/docs/hands-on/ni.mdx",sourceDirName:"hands-on",slug:"/hands-on/ni",permalink:"/espresso/hands-on/ni",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/ni.mdx",tags:[],version:"current",frontMatter:{title:"Spin polarized bandstructure calculation for nickel",sidebar_label:"Ni (spin pol. bands)"},sidebar:"docs",previous:{title:"Fe (magnetic)",permalink:"/espresso/hands-on/fe"},next:{title:"DFT+U calculation",permalink:"/espresso/hands-on/dft-u"}},o={},l=[];function u(n){const e={code:"code",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...n.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(e.p,{children:["We prepare the input file ",(0,i.jsx)(e.code,{children:"pw_scf_ni.in"})," and run the calculation:"]}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw_scf_ni.in > pw_scf_ni.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Prepare the input file for bands calculation ",(0,i.jsx)(e.code,{children:"pw_bands_ni.in"})," with our desired\nk-path and run:"]}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw_bands_ni.in > pw_bands_ni.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Now we perform the ",(0,i.jsx)(e.strong,{children:"bands.x"})," calculation with ",(0,i.jsx)(e.code,{children:"spin_component=1"})," to process\nonly the spin up bands:"]}),"\n","\n",(0,i.jsx)(r.A,{language:"bash",title:"src/ni/bands_ni_up.in",showLineNumbers:!0,children:t}),"\n",(0,i.jsx)(e.p,{children:"Run the calculation:"}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 bands.x -i bands_ni_up.in > bands_ni_up.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Similarly, we process the spin down bands ",(0,i.jsx)(e.code,{children:"spin_component=2"})," and plot them."]}),"\n",(0,i.jsxs)("picture",{children:[(0,i.jsx)("source",{type:"image/webp",srcSet:s(9490).A}),(0,i.jsx)("img",{src:s(8057).A,alt:"ni-spin-bands"})]})]})}function h(n={}){const{wrapper:e}={...(0,a.R)(),...n.components};return e?(0,i.jsx)(e,{...n,children:(0,i.jsx)(u,{...n})}):u(n)}},8057:(n,e,s)=>{s.d(e,{A:()=>i});const i=s.p+"assets/images/ni-spin-bands-28a1f6d047e378e2bda9fd69130c55f7.png"},9490:(n,e,s)=>{s.d(e,{A:()=>i});const i=s.p+"assets/images/ni-spin-bands-2d86482da5664329843fb81d437f8cb0.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[5308],{6443:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>o,contentTitle:()=>c,default:()=>h,frontMatter:()=>d,metadata:()=>p,toc:()=>l});var i=s(4848),a=s(8453),r=s(1432);const t="&BANDS\n outdir='./tmp/',\n prefix='ni',\n filband='ni_bands_up.dat',\n spin_component = 1,\n/\n",d={title:"Spin polarized bandstructure calculation for nickel",sidebar_label:"Ni (spin pol. bands)"},c=void 0,p={id:"hands-on/ni",title:"Spin polarized bandstructure calculation for nickel",description:"We prepare the input file pwscfni.in and run the calculation:",source:"@site/docs/hands-on/ni.mdx",sourceDirName:"hands-on",slug:"/hands-on/ni",permalink:"/espresso/hands-on/ni",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/ni.mdx",tags:[],version:"current",frontMatter:{title:"Spin polarized bandstructure calculation for nickel",sidebar_label:"Ni (spin pol. bands)"},sidebar:"docs",previous:{title:"Fe (magnetic)",permalink:"/espresso/hands-on/fe"},next:{title:"DFT+U calculation",permalink:"/espresso/hands-on/dft-u"}},o={},l=[];function u(n){const e={code:"code",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...n.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(e.p,{children:["We prepare the input file ",(0,i.jsx)(e.code,{children:"pw_scf_ni.in"})," and run the calculation:"]}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw_scf_ni.in > pw_scf_ni.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Prepare the input file for bands calculation ",(0,i.jsx)(e.code,{children:"pw_bands_ni.in"})," with our desired\nk-path and run:"]}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 pw.x -i pw_bands_ni.in > pw_bands_ni.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Now we perform the ",(0,i.jsx)(e.strong,{children:"bands.x"})," calculation with ",(0,i.jsx)(e.code,{children:"spin_component=1"})," to process\nonly the spin up bands:"]}),"\n","\n",(0,i.jsx)(r.A,{language:"bash",title:"src/ni/bands_ni_up.in",showLineNumbers:!0,children:t}),"\n",(0,i.jsx)(e.p,{children:"Run the calculation:"}),"\n",(0,i.jsx)(e.pre,{children:(0,i.jsx)(e.code,{className:"language-bash",children:"mpirun -np 8 bands.x -i bands_ni_up.in > bands_ni_up.out\n"})}),"\n",(0,i.jsxs)(e.p,{children:["Similarly, we process the spin down bands ",(0,i.jsx)(e.code,{children:"spin_component=2"})," and plot them."]}),"\n",(0,i.jsxs)("picture",{children:[(0,i.jsx)("source",{type:"image/webp",srcSet:s(9490).A}),(0,i.jsx)("img",{src:s(8057).A,alt:"ni-spin-bands"})]})]})}function h(n={}){const{wrapper:e}={...(0,a.R)(),...n.components};return e?(0,i.jsx)(e,{...n,children:(0,i.jsx)(u,{...n})}):u(n)}},8057:(n,e,s)=>{s.d(e,{A:()=>i});const i=s.p+"assets/images/ni-spin-bands-28a1f6d047e378e2bda9fd69130c55f7.png"},9490:(n,e,s)=>{s.d(e,{A:()=>i});const i=s.p+"assets/images/ni-spin-bands-2d86482da5664329843fb81d437f8cb0.webp"}}]); \ No newline at end of file diff --git a/assets/js/33273f9d.777881f1.js b/assets/js/33273f9d.6d34a4bb.js similarity index 98% rename from assets/js/33273f9d.777881f1.js rename to assets/js/33273f9d.6d34a4bb.js index 86c109d2..5b9200a4 100644 --- a/assets/js/33273f9d.777881f1.js +++ b/assets/js/33273f9d.6d34a4bb.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4172],{2515:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>c,contentTitle:()=>r,default:()=>p,frontMatter:()=>o,metadata:()=>i,toc:()=>l});var t=s(4848),a=s(8453);const o={title:"Bandstructure of GaAs",sidebar_label:"GaAs"},r=void 0,i={id:"hands-on/GaAs",title:"Bandstructure of GaAs",description:"Now that we have calculated the bandstructure of silicon (semiconductor) and",source:"@site/docs/hands-on/GaAs.md",sourceDirName:"hands-on",slug:"/hands-on/GaAs",permalink:"/espresso/hands-on/GaAs",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/GaAs.md",tags:[],version:"current",frontMatter:{title:"Bandstructure of GaAs",sidebar_label:"GaAs"},sidebar:"docs",previous:{title:"Graphene",permalink:"/espresso/hands-on/graphene"},next:{title:"Fe (magnetic)",permalink:"/espresso/hands-on/fe"}},c={},l=[];function d(e){const n={a:"a",admonition:"admonition",code:"code",p:"p",pre:"pre",...(0,a.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsx)(n.p,{children:"Now that we have calculated the bandstructure of silicon (semiconductor) and\naluminum (metal), let us proceed with a compound which has two different atoms.\nWe follow the steps like before:"}),"\n",(0,t.jsx)(n.p,{children:"First check the lattice constant with cell relaxation according to our chosen\npseudo potential. We use that lattice constant in our next steps. Our lattice\nconstant = 10.6867 * 0.508176602 / 0.5 = 10.861462."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.relax.GaAs.in > pw.relax.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Perform self consistent field calculation:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.scf.GaAs.in > pw.scf.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Give denser k-points and perform non-self consistent calculation. This step is\nonly necessary if you need to obtain density of states."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.nscf.GaAs.in > pw.nscf.GaAs.out\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Perform ",(0,t.jsx)(n.code,{children:"bands"})," calculation"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.bands.GaAs.in > pw.bands.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Post process the data and plot the bandstructure."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"bands.x < pp.bands.GaAs.in > pp.bands.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"If everything goes well, you will get the bandstructure as below:"}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:s(2356).A}),(0,t.jsx)("img",{src:s(5383).A,alt:"GaAs-bands"})]}),"\n",(0,t.jsx)(n.admonition,{title:"Warning",type:"caution",children:(0,t.jsx)(n.p,{children:"Sometimes a calculation with the same inputs converges in one computer, while\nfails in another due to library configuration or even due to floating point\napproximations. The final output numbers will always vary slightly for different\nmachines, or even among different runs in the same machine. Also check the\nQuantum Espresso version for reproducibility."})}),"\n",(0,t.jsxs)(n.p,{children:["Also see the bandstructure of GaAs with ",(0,t.jsx)(n.a,{href:"soc#soc-calculation-for-gaas",children:"SOC"}),"."]})]})}function p(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,t.jsx)(n,{...e,children:(0,t.jsx)(d,{...e})}):d(e)}},5383:(e,n,s)=>{s.d(n,{A:()=>t});const t=s.p+"assets/images/GaAs-bands-3a34f0ae96238317bb703f4c913e41d5.png"},2356:(e,n,s)=>{s.d(n,{A:()=>t});const t=s.p+"assets/images/GaAs-bands-b658e9b11ba890636e2709eb390ef959.webp"},8453:(e,n,s)=>{s.d(n,{R:()=>r,x:()=>i});var t=s(6540);const a={},o=t.createContext(a);function r(e){const n=t.useContext(o);return t.useMemo((function(){return"function"==typeof e?e(n):{...n,...e}}),[n,e])}function i(e){let n;return n=e.disableParentContext?"function"==typeof e.components?e.components(a):e.components||a:r(e.components),t.createElement(o.Provider,{value:n},e.children)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4172],{6704:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>c,contentTitle:()=>r,default:()=>p,frontMatter:()=>o,metadata:()=>i,toc:()=>l});var t=s(4848),a=s(8453);const o={title:"Bandstructure of GaAs",sidebar_label:"GaAs"},r=void 0,i={id:"hands-on/GaAs",title:"Bandstructure of GaAs",description:"Now that we have calculated the bandstructure of silicon (semiconductor) and",source:"@site/docs/hands-on/GaAs.md",sourceDirName:"hands-on",slug:"/hands-on/GaAs",permalink:"/espresso/hands-on/GaAs",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/GaAs.md",tags:[],version:"current",frontMatter:{title:"Bandstructure of GaAs",sidebar_label:"GaAs"},sidebar:"docs",previous:{title:"Graphene",permalink:"/espresso/hands-on/graphene"},next:{title:"Fe (magnetic)",permalink:"/espresso/hands-on/fe"}},c={},l=[];function d(e){const n={a:"a",admonition:"admonition",code:"code",p:"p",pre:"pre",...(0,a.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsx)(n.p,{children:"Now that we have calculated the bandstructure of silicon (semiconductor) and\naluminum (metal), let us proceed with a compound which has two different atoms.\nWe follow the steps like before:"}),"\n",(0,t.jsx)(n.p,{children:"First check the lattice constant with cell relaxation according to our chosen\npseudo potential. We use that lattice constant in our next steps. Our lattice\nconstant = 10.6867 * 0.508176602 / 0.5 = 10.861462."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.relax.GaAs.in > pw.relax.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Perform self consistent field calculation:"}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.scf.GaAs.in > pw.scf.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Give denser k-points and perform non-self consistent calculation. This step is\nonly necessary if you need to obtain density of states."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.nscf.GaAs.in > pw.nscf.GaAs.out\n"})}),"\n",(0,t.jsxs)(n.p,{children:["Perform ",(0,t.jsx)(n.code,{children:"bands"})," calculation"]}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.bands.GaAs.in > pw.bands.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"Post process the data and plot the bandstructure."}),"\n",(0,t.jsx)(n.pre,{children:(0,t.jsx)(n.code,{className:"language-bash",children:"bands.x < pp.bands.GaAs.in > pp.bands.GaAs.out\n"})}),"\n",(0,t.jsx)(n.p,{children:"If everything goes well, you will get the bandstructure as below:"}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:s(2356).A}),(0,t.jsx)("img",{src:s(5383).A,alt:"GaAs-bands"})]}),"\n",(0,t.jsx)(n.admonition,{title:"Warning",type:"caution",children:(0,t.jsx)(n.p,{children:"Sometimes a calculation with the same inputs converges in one computer, while\nfails in another due to library configuration or even due to floating point\napproximations. The final output numbers will always vary slightly for different\nmachines, or even among different runs in the same machine. Also check the\nQuantum Espresso version for reproducibility."})}),"\n",(0,t.jsxs)(n.p,{children:["Also see the bandstructure of GaAs with ",(0,t.jsx)(n.a,{href:"soc#soc-calculation-for-gaas",children:"SOC"}),"."]})]})}function p(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,t.jsx)(n,{...e,children:(0,t.jsx)(d,{...e})}):d(e)}},5383:(e,n,s)=>{s.d(n,{A:()=>t});const t=s.p+"assets/images/GaAs-bands-3a34f0ae96238317bb703f4c913e41d5.png"},2356:(e,n,s)=>{s.d(n,{A:()=>t});const t=s.p+"assets/images/GaAs-bands-b658e9b11ba890636e2709eb390ef959.webp"},8453:(e,n,s)=>{s.d(n,{R:()=>r,x:()=>i});var t=s(6540);const a={},o=t.createContext(a);function r(e){const n=t.useContext(o);return t.useMemo((function(){return"function"==typeof e?e(n):{...n,...e}}),[n,e])}function i(e){let n;return n=e.disableParentContext?"function"==typeof e.components?e.components(a):e.components||a:r(e.components),t.createElement(o.Provider,{value:n},e.children)}}}]); \ No newline at end of file diff --git a/assets/js/33ad165c.19d65811.js b/assets/js/33ad165c.fd3ff922.js similarity index 98% rename from assets/js/33ad165c.19d65811.js rename to assets/js/33ad165c.fd3ff922.js index 1905cc2c..998ff452 100644 --- a/assets/js/33ad165c.19d65811.js +++ b/assets/js/33ad165c.fd3ff922.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[431],{6053:(n,t,e)=>{e.r(t),e.d(t,{assets:()=>u,contentTitle:()=>c,default:()=>h,frontMatter:()=>a,metadata:()=>l,toc:()=>p});var i=e(4848),o=e(8453),s=e(1432);const r="&control\n calculation = 'vc-relax'\n prefix = 'silicon'\n outdir = './tmp/'\n pseudo_dir = './pseudos/'\n etot_conv_thr = 1e-5\n forc_conv_thr = 1e-4\n/\n\n&system\n ibrav=2, celldm(1) =14,\n nat=2, ntyp=1,\n ecutwfc=30\n/\n\n&electrons\n conv_thr=1e-8\n/\n\n&ions\n/\n\n&cell\n cell_dofree='ibrav'\n/\n\nATOMIC_SPECIES\n Si 28.0855 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.00 0.00 0.00 0 0 0\n Si 0.25 0.25 0.25 0 0 0\n\nK_POINTS (automatic)\n 6 6 6 1 1 1\n",a={title:"Structure optimization",keywords:["Structural optimization using DFT","Structural optimization using Density Functional Theory","Structural optimization in Quantum Espresso","Cell relaxation"]},c=void 0,l={id:"hands-on/structure-optimization",title:"Structure optimization",description:"There are two types of structural optimization calculations in Quantum espresso:",source:"@site/docs/hands-on/structure-optimization.mdx",sourceDirName:"hands-on",slug:"/hands-on/structure-optimization",permalink:"/espresso/hands-on/structure-optimization",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/structure-optimization.mdx",tags:[],version:"current",frontMatter:{title:"Structure optimization",keywords:["Structural optimization using DFT","Structural optimization using Density Functional Theory","Structural optimization in Quantum Espresso","Cell relaxation"]},sidebar:"docs",previous:{title:"Convergence testing",permalink:"/espresso/hands-on/convergence"},next:{title:"DOS calculation",permalink:"/espresso/hands-on/dos"}},u={},p=[];function d(n){const t={code:"code",p:"p",pre:"pre",strong:"strong",...(0,o.R)(),...n.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(t.p,{children:["There are two types of structural optimization calculations in Quantum espresso:\n(1) ",(0,i.jsx)(t.strong,{children:"relax"}),": where only the atomic positions are allowed to vary, and (2)\n",(0,i.jsx)(t.strong,{children:"vc-relax"}),": which allows to vary both the atomic positions and lattice\nconstants."]}),"\n","\n",(0,i.jsx)(s.A,{language:"bash",title:"src/silicon/si_relax.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsx)(t.p,{children:"Perform the plane wave calculation:"}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-bash",children:"pw.x -inp si_relax.in > si_relax.out\n"})}),"\n",(0,i.jsxs)(t.p,{children:["This produces following output (see the ",(0,i.jsx)(t.code,{children:"si_relax.out"}),' for more details, look\nfor "Final enthalpy"):']}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-bash",children:" Final enthalpy = -15.8536258868 Ry\nBegin final coordinates\n new unit-cell volume = 265.89380 a.u.^3 ( 39.40140 Ang^3 )\n density = 2.36728 g/cm^3\n\nCELL_PARAMETERS (alat= 14.00000000)\n -0.364556379 0.000000000 0.364556379\n 0.000000000 0.364556379 0.364556379\n -0.364556379 0.364556379 0.000000000\n\nATOMIC_POSITIONS (alat)\nSi 0.0000000000 0.0000000000 0.0000000000 0 0 0\nSi 0.1822781896 0.1822781896 0.1822781896 0 0 0\nEnd final coordinates\n"})}),"\n",(0,i.jsx)(t.p,{children:"Lattice constant = 0.364556379 * 14 / 0.5 = 10.2076 Bohr."})]})}function h(n={}){const{wrapper:t}={...(0,o.R)(),...n.components};return t?(0,i.jsx)(t,{...n,children:(0,i.jsx)(d,{...n})}):d(n)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[431],{4457:(n,t,e)=>{e.r(t),e.d(t,{assets:()=>u,contentTitle:()=>c,default:()=>h,frontMatter:()=>a,metadata:()=>l,toc:()=>p});var i=e(4848),o=e(8453),s=e(1432);const r="&control\n calculation = 'vc-relax'\n prefix = 'silicon'\n outdir = './tmp/'\n pseudo_dir = './pseudos/'\n etot_conv_thr = 1e-5\n forc_conv_thr = 1e-4\n/\n\n&system\n ibrav=2, celldm(1) =14,\n nat=2, ntyp=1,\n ecutwfc=30\n/\n\n&electrons\n conv_thr=1e-8\n/\n\n&ions\n/\n\n&cell\n cell_dofree='ibrav'\n/\n\nATOMIC_SPECIES\n Si 28.0855 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.00 0.00 0.00 0 0 0\n Si 0.25 0.25 0.25 0 0 0\n\nK_POINTS (automatic)\n 6 6 6 1 1 1\n",a={title:"Structure optimization",keywords:["Structural optimization using DFT","Structural optimization using Density Functional Theory","Structural optimization in Quantum Espresso","Cell relaxation"]},c=void 0,l={id:"hands-on/structure-optimization",title:"Structure optimization",description:"There are two types of structural optimization calculations in Quantum espresso:",source:"@site/docs/hands-on/structure-optimization.mdx",sourceDirName:"hands-on",slug:"/hands-on/structure-optimization",permalink:"/espresso/hands-on/structure-optimization",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/structure-optimization.mdx",tags:[],version:"current",frontMatter:{title:"Structure optimization",keywords:["Structural optimization using DFT","Structural optimization using Density Functional Theory","Structural optimization in Quantum Espresso","Cell relaxation"]},sidebar:"docs",previous:{title:"Convergence testing",permalink:"/espresso/hands-on/convergence"},next:{title:"DOS calculation",permalink:"/espresso/hands-on/dos"}},u={},p=[];function d(n){const t={code:"code",p:"p",pre:"pre",strong:"strong",...(0,o.R)(),...n.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(t.p,{children:["There are two types of structural optimization calculations in Quantum espresso:\n(1) ",(0,i.jsx)(t.strong,{children:"relax"}),": where only the atomic positions are allowed to vary, and (2)\n",(0,i.jsx)(t.strong,{children:"vc-relax"}),": which allows to vary both the atomic positions and lattice\nconstants."]}),"\n","\n",(0,i.jsx)(s.A,{language:"bash",title:"src/silicon/si_relax.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsx)(t.p,{children:"Perform the plane wave calculation:"}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-bash",children:"pw.x -inp si_relax.in > si_relax.out\n"})}),"\n",(0,i.jsxs)(t.p,{children:["This produces following output (see the ",(0,i.jsx)(t.code,{children:"si_relax.out"}),' for more details, look\nfor "Final enthalpy"):']}),"\n",(0,i.jsx)(t.pre,{children:(0,i.jsx)(t.code,{className:"language-bash",children:" Final enthalpy = -15.8536258868 Ry\nBegin final coordinates\n new unit-cell volume = 265.89380 a.u.^3 ( 39.40140 Ang^3 )\n density = 2.36728 g/cm^3\n\nCELL_PARAMETERS (alat= 14.00000000)\n -0.364556379 0.000000000 0.364556379\n 0.000000000 0.364556379 0.364556379\n -0.364556379 0.364556379 0.000000000\n\nATOMIC_POSITIONS (alat)\nSi 0.0000000000 0.0000000000 0.0000000000 0 0 0\nSi 0.1822781896 0.1822781896 0.1822781896 0 0 0\nEnd final coordinates\n"})}),"\n",(0,i.jsx)(t.p,{children:"Lattice constant = 0.364556379 * 14 / 0.5 = 10.2076 Bohr."})]})}function h(n={}){const{wrapper:t}={...(0,o.R)(),...n.components};return t?(0,i.jsx)(t,{...n,children:(0,i.jsx)(d,{...n})}):d(n)}}}]); \ No newline at end of file diff --git a/assets/js/34df526f.a44ca76c.js b/assets/js/34df526f.5e6f29be.js similarity index 99% rename from assets/js/34df526f.a44ca76c.js rename to assets/js/34df526f.5e6f29be.js index a7ace416..7dde396f 100644 --- a/assets/js/34df526f.a44ca76c.js +++ b/assets/js/34df526f.5e6f29be.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[8521],{8534:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>r,contentTitle:()=>i,default:()=>d,frontMatter:()=>m,metadata:()=>c,toc:()=>t});var l=a(4848),n=a(8453);const m={title:"Wannier basis"},i=void 0,c={id:"theory/wannier",title:"Wannier basis",description:"Introduction",source:"@site/docs/theory/wannier.md",sourceDirName:"theory",slug:"/theory/wannier",permalink:"/espresso/theory/wannier",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/theory/wannier.md",tags:[],version:"current",frontMatter:{title:"Wannier basis"},sidebar:"docs",previous:{title:"DFT overview",permalink:"/espresso/theory/dft"},next:{title:"Hands-on",permalink:"/espresso/category/hands-on"}},r={},t=[{value:"Introduction",id:"introduction",level:2},{value:"Maximally Localized Wannier Function",id:"maximally-localized-wannier-function",level:2},{value:"Resources",id:"resources",level:2}];function h(s){const e={a:"a",annotation:"annotation",em:"em",h2:"h2",li:"li",math:"math",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mpadded:"mpadded",mrow:"mrow",mspace:"mspace",msqrt:"msqrt",mstyle:"mstyle",msub:"msub",msubsup:"msubsup",msup:"msup",mtable:"mtable",mtd:"mtd",mtext:"mtext",mtr:"mtr",munder:"munder",munderover:"munderover",p:"p",path:"path",semantics:"semantics",span:"span",strong:"strong",svg:"svg",ul:"ul",...(0,n.R)(),...s.components};return(0,l.jsxs)(l.Fragment,{children:[(0,l.jsx)(e.h2,{id:"introduction",children:"Introduction"}),"\n",(0,l.jsxs)(e.p,{children:["Wannier functions are an alternative representation of Bloch states in terms of\na localized basis set. 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",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"t"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"m"}),(0,l.jsx)(e.mi,{children:"n"})]})]})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"t_{mn}"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.7651em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",children:"t"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t 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One such option could be the set\nthat maximizes localization. Two different sets of Wannier basis are connected\nvia unitary transformation. MLWFs can be considered as a generalization of\nlocalized molecular orbitals (LMOs) to periodic systems."}),"\n",(0,l.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.a,{href:"https://youtu.be/_XWIwoE7Pc4",children:"Introduction to Wannier Basis lecture by Vijay A. Singh"})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsxs)(e.a,{href:"https://doi.org/10.1103/PhysRevB.56.12847",children:[(0,l.jsx)(e.em,{children:"Maximally localized generalized Wannier functions for composite energy bands"}),", Marzari and Vanderbilt, Phys. Rev. B ",(0,l.jsx)(e.strong,{children:"56"}),", 12847 (1997)"]})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsxs)(e.a,{href:"https://doi.org/10.1103/PhysRevB.65.035109",children:[(0,l.jsx)(e.em,{children:"Maximally localized Wannier functions for entangled energy bands"}),", Souza, Marzari and Vanderbilt, Phys. Rev. B ",(0,l.jsx)(e.strong,{children:"65"}),", 035109 (2001)"]})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsxs)(e.a,{href:"https://doi.org/10.1103/RevModPhys.84.1419",children:[(0,l.jsx)(e.em,{children:"Maximally localized Wannier functions: Theory and applications"}),", Marzari ",(0,l.jsx)(e.em,{children:"et. al."}),", Rev. Mod. Phys. ",(0,l.jsx)(e.strong,{children:"84"}),", 1419 (2012)"]})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsxs)(e.a,{href:"https://doi.org/10.1002/9781119148739.ch6",children:[(0,l.jsx)(e.em,{children:"Introduction to Maximally Localized Wannier Functions"}),", Ambrosetti and Silvestrelli, Reviews in Computational Chemistry, Ch. 6, pp. 327 (2016)"]})}),"\n"]})]})}function d(s={}){const{wrapper:e}={...(0,n.R)(),...s.components};return e?(0,l.jsx)(e,{...s,children:(0,l.jsx)(h,{...s})}):h(s)}},8453:(s,e,a)=>{a.d(e,{R:()=>i,x:()=>c});var l=a(6540);const n={},m=l.createContext(n);function i(s){const e=l.useContext(m);return l.useMemo((function(){return"function"==typeof s?s(e):{...e,...s}}),[e,s])}function c(s){let e;return e=s.disableParentContext?"function"==typeof s.components?s.components(n):s.components||n:i(s.components),l.createElement(m.Provider,{value:e},s.children)}}}]); \ No newline at end of file diff --git a/assets/js/3608c70f.ad2bc235.js b/assets/js/3608c70f.ad2bc235.js new file mode 100644 index 00000000..b5ca0a2e --- /dev/null +++ b/assets/js/3608c70f.ad2bc235.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4628],{8628:e=>{e.exports=JSON.parse('{"categoryGeneratedIndex":{"title":"Hands-on","slug":"/category/hands-on","permalink":"/espresso/category/hands-on","sidebar":"docs","navigation":{"previous":{"title":"Wannier basis","permalink":"/espresso/theory/wannier"},"next":{"title":"SCF calculation","permalink":"/espresso/hands-on/scf"}}}}')}}]); \ No newline at end of file diff --git a/assets/js/3bbf8d33.37a6e1c7.js b/assets/js/3bbf8d33.3c8fa896.js similarity index 98% rename from assets/js/3bbf8d33.37a6e1c7.js rename to assets/js/3bbf8d33.3c8fa896.js index c9b18a74..2e226dde 100644 --- a/assets/js/3bbf8d33.37a6e1c7.js +++ b/assets/js/3bbf8d33.3c8fa896.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[2518],{8318:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>c,contentTitle:()=>r,default:()=>u,frontMatter:()=>l,metadata:()=>p,toc:()=>d});var i=s(4848),o=s(8453),t=s(1432);const a="&projwfc\n outdir = './tmp/'\n prefix = 'silicon'\n ngauss = 0\n degauss = 0.036748\n DeltaE = 0.005\n kresolveddos = .true.\n filpdos = 'silicon.k'\n/\n",l={title:"k-resolved DOS",keywords:["Density of States"]},r=void 0,p={id:"hands-on/kpdos",title:"k-resolved DOS",description:"Here we will calculate k-resolved density of states for silicon. 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Note that for bands calculation I have\ndoubled the number of k-points compared to our previous bands calculation."}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"pw.x -inp si_bands.in > si_bands.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"Calculate the orbital projections with k-resolved information:"}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/si_projwfc.in",showLineNumbers:!0,children:a}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"projwfc.x -inp si_projwfc.in > si_projwfc.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"This will give separate orbital projections, as well as total sum for k-resolved\nDOS. 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Note that for bands calculation I have\ndoubled the number of k-points compared to our previous bands calculation."}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"pw.x -inp si_bands.in > si_bands.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"Calculate the orbital projections with k-resolved information:"}),"\n","\n",(0,i.jsx)(t.A,{language:"bash",title:"src/silicon/si_projwfc.in",showLineNumbers:!0,children:a}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"projwfc.x -inp si_projwfc.in > si_projwfc.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"This will give separate orbital projections, as well as total sum for k-resolved\nDOS. 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The pseudopotential describes the atomic nucleus and all the\nelectrons except the outermost valence shell. The rapidly changing potential\nfield near the atomic core is replaced by a smoother function that simulates the\npotential field far from the core very well. By doing so, it requires less\nnumber plane wave basis for wavefunction expansion."}),"\n",(0,s.jsx)(n.admonition,{type:"tip",children:(0,s.jsxs)(n.p,{children:["You may try my ",(0,s.jsx)(n.a,{href:"https://pseudos.netlify.app/",children:"Pseudos Web-App"}),", where you can\nlook for pseudopotentials by element name, and download them. Currently,\nStandard Solid State Pseudopotentials (SSSP) and GBRV pseudopotentials are\nincluded."]})}),"\n",(0,s.jsx)(n.p,{children:"We can choose form various pseudopotential libraries. Choice of pseudopotential\ndepends on the problem we are investigating, e.g., if there is a heavy element\npresent in our system and we are interested in the spin-orbit coupling effects,\nwe should choose a full relativistic pseudopotential. 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Choice of pseudopotential\ndepends on the problem we are investigating, e.g., if there is a heavy element\npresent in our system and we are interested in the spin-orbit coupling effects,\nwe should choose a full relativistic pseudopotential. 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You will find the recommended ",(0,s.jsx)(n.code,{children:"ecutwfc"})," in the\nheader of each pseudopotential file. If you choose an ultra-soft\npseudopotential, you will need ",(0,s.jsx)(n.code,{children:"ecutrho"})," about 8 times the value of ",(0,s.jsx)(n.code,{children:"ecutwfc"}),".\nThe default ",(0,s.jsx)(n.code,{children:"ecutrho"})," is 4 times ",(0,s.jsx)(n.code,{children:"ecutwfc"})," in Quantum Espresso code, which is a\ngood choice for norm conserving pseudopotentials. You should check energy\nconvergence against ",(0,s.jsx)(n.code,{children:"ecutwfc"})," for your system."]}),"\n",(0,s.jsx)(n.p,{children:"By using pseudopotential, we want to get rid of the core electrons that do not\nparticipate in the chemical properties of material. This is known also as rigid\ncore approximation. 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'),this.$menu.append(this.$empty),this.$empty.hide()),this.datasets=i.map(t.datasets,(function(e){return function(t,e,n){return new u.Dataset(i.mixin({$menu:t,cssClasses:n},e))}(o.$menu,e,t.cssClasses)})),i.each(this.datasets,(function(t){var e=t.getRoot();e&&0===e.parent().length&&o.$menu.append(e),t.onSync("rendered",o._onRendered,o)})),t.templates&&t.templates.footer&&(this.templates.footer=i.templatify(t.templates.footer),this.$menu.append(this.templates.footer()));var l=this;s.element(window).resize((function(){l._redraw()}))}i.mixin(u.prototype,r,{_onSuggestionClick:function(t){this.trigger("suggestionClicked",s.element(t.currentTarget))},_onSuggestionMouseEnter:function(t){var e=s.element(t.currentTarget);if(!e.hasClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0))){this._removeCursor();var n=this;setTimeout((function(){n._setCursor(e,!1)}),0)}},_onSuggestionMouseLeave:function(t){if(t.relatedTarget&&s.element(t.relatedTarget).closest("."+i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).length>0)return;this._removeCursor(),this.trigger("cursorRemoved")},_onRendered:function(t,e){if(this.isEmpty=i.every(this.datasets,(function(t){return t.isEmpty()})),this.isEmpty)if(e.length>=this.minLength&&this.trigger("empty"),this.$empty)if(e.length=this.minLength?this._show():this._hide());this.trigger("datasetRendered")},_hide:function(){this.$container.hide()},_show:function(){this.$container.css("display","block"),this._redraw(),this.trigger("shown")},_redraw:function(){this.isOpen&&this.appendTo&&this.trigger("redrawn")},_getSuggestions:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.suggestion))},_getCursor:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.cursor)).first()},_setCursor:function(t,e){t.first().addClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).attr("aria-selected","true"),this.trigger("cursorMoved",e)},_removeCursor:function(){this._getCursor().removeClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).removeAttr("aria-selected")},_moveCursor:function(t){var e,n,i,s;this.isOpen&&(n=this._getCursor(),e=this._getSuggestions(),this._removeCursor(),-1!==(i=((i=e.index(n)+t)+1)%(e.length+1)-1)?(i<-1&&(i=e.length-1),this._setCursor(s=e.eq(i),!0),this._ensureVisible(s)):this.trigger("cursorRemoved"))},_ensureVisible:function(t){var e,n,i,s;n=(e=t.position().top)+t.height()+parseInt(t.css("margin-top"),10)+parseInt(t.css("margin-bottom"),10),i=this.$menu.scrollTop(),s=this.$menu.height()+parseInt(this.$menu.css("padding-top"),10)+parseInt(this.$menu.css("padding-bottom"),10),e<0?this.$menu.scrollTop(i+e):s{"use strict";var i=n(6573),s=n(1348);function r(t){t&&t.el||i.error("EventBus initialized without el"),this.$el=s.element(t.el)}i.mixin(r.prototype,{trigger:function(t,e,n,s){var r=i.Event("autocomplete:"+t);return this.$el.trigger(r,[e,n,s]),r}}),t.exports=r},4436:(t,e,n)=>{"use strict";var i=n(874),s=/\s+/;function r(t,e,n,i){var r;if(!n)return this;for(e=e.split(s),n=i?function(t,e){return t.bind?t.bind(e):function(){t.apply(e,[].slice.call(arguments,0))}}(n,i):n,this._callbacks=this._callbacks||{};r=e.shift();)this._callbacks[r]=this._callbacks[r]||{sync:[],async:[]},this._callbacks[r][t].push(n);return this}function o(t,e,n){return function(){for(var i,s=0,r=t.length;!i&&s{"use strict";t.exports={wrapper:'',dropdown:'',dataset:'
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'}},9629:(t,e,n)=>{"use strict";var i;i={9:"tab",27:"esc",37:"left",39:"right",13:"enter",38:"up",40:"down"};var s=n(6573),r=n(1348),o=n(4436);function a(t){var e,n,o,a,u,c=this;(t=t||{}).input||s.error("input is missing"),e=s.bind(this._onBlur,this),n=s.bind(this._onFocus,this),o=s.bind(this._onKeydown,this),a=s.bind(this._onInput,this),this.$hint=r.element(t.hint),this.$input=r.element(t.input).on("blur.aa",e).on("focus.aa",n).on("keydown.aa",o),0===this.$hint.length&&(this.setHint=this.getHint=this.clearHint=this.clearHintIfInvalid=s.noop),s.isMsie()?this.$input.on("keydown.aa keypress.aa cut.aa paste.aa",(function(t){i[t.which||t.keyCode]||s.defer(s.bind(c._onInput,c,t))})):this.$input.on("input.aa",a),this.query=this.$input.val(),this.$overflowHelper=(u=this.$input,r.element('').css({position:"absolute",visibility:"hidden",whiteSpace:"pre",fontFamily:u.css("font-family"),fontSize:u.css("font-size"),fontStyle:u.css("font-style"),fontVariant:u.css("font-variant"),fontWeight:u.css("font-weight"),wordSpacing:u.css("word-spacing"),letterSpacing:u.css("letter-spacing"),textIndent:u.css("text-indent"),textRendering:u.css("text-rendering"),textTransform:u.css("text-transform")}).insertAfter(u))}function u(t){return t.altKey||t.ctrlKey||t.metaKey||t.shiftKey}a.normalizeQuery=function(t){return(t||"").replace(/^\s*/g,"").replace(/\s{2,}/g," ")},s.mixin(a.prototype,o,{_onBlur:function(){this.resetInputValue(),this.$input.removeAttr("aria-activedescendant"),this.trigger("blurred")},_onFocus:function(){this.trigger("focused")},_onKeydown:function(t){var e=i[t.which||t.keyCode];this._managePreventDefault(e,t),e&&this._shouldTrigger(e,t)&&this.trigger(e+"Keyed",t)},_onInput:function(){this._checkInputValue()},_managePreventDefault:function(t,e){var n,i,s;switch(t){case"tab":i=this.getHint(),s=this.getInputValue(),n=i&&i!==s&&!u(e);break;case"up":case"down":n=!u(e);break;default:n=!1}n&&e.preventDefault()},_shouldTrigger:function(t,e){var n;if("tab"===t)n=!u(e);else n=!0;return n},_checkInputValue:function(){var t,e,n,i,s;t=this.getInputValue(),i=t,s=this.query,n=!(!(e=a.normalizeQuery(i)===a.normalizeQuery(s))||!this.query)&&this.query.length!==t.length,this.query=t,e?n&&this.trigger("whitespaceChanged",this.query):this.trigger("queryChanged",this.query)},focus:function(){this.$input.focus()},blur:function(){this.$input.blur()},getQuery:function(){return this.query},setQuery:function(t){this.query=t},getInputValue:function(){return this.$input.val()},setInputValue:function(t,e){void 0===t&&(t=this.query),this.$input.val(t),e?this.clearHint():this._checkInputValue()},expand:function(){this.$input.attr("aria-expanded","true")},collapse:function(){this.$input.attr("aria-expanded","false")},setActiveDescendant:function(t){this.$input.attr("aria-activedescendant",t)},removeActiveDescendant:function(){this.$input.removeAttr("aria-activedescendant")},resetInputValue:function(){this.setInputValue(this.query,!0)},getHint:function(){return this.$hint.val()},setHint:function(t){this.$hint.val(t)},clearHint:function(){this.setHint("")},clearHintIfInvalid:function(){var t,e,n;n=(t=this.getInputValue())!==(e=this.getHint())&&0===e.indexOf(t),""!==t&&n&&!this.hasOverflow()||this.clearHint()},getLanguageDirection:function(){return(this.$input.css("direction")||"ltr").toLowerCase()},hasOverflow:function(){var t=this.$input.width()-2;return this.$overflowHelper.text(this.getInputValue()),this.$overflowHelper.width()>=t},isCursorAtEnd:function(){var t,e,n;return t=this.$input.val().length,e=this.$input[0].selectionStart,s.isNumber(e)?e===t:!document.selection||((n=document.selection.createRange()).moveStart("character",-t),t===n.text.length)},destroy:function(){this.$hint.off(".aa"),this.$input.off(".aa"),this.$hint=this.$input=this.$overflowHelper=null}}),t.exports=a},7360:(t,e,n)=>{"use strict";var i="aaAttrs",s=n(6573),r=n(1348),o=n(2324),a=n(9629),u=n(1540),c=n(9272),l=n(2542);function h(t){var e,n;if((t=t||{}).input||s.error("missing input"),this.isActivated=!1,this.debug=!!t.debug,this.autoselect=!!t.autoselect,this.autoselectOnBlur=!!t.autoselectOnBlur,this.openOnFocus=!!t.openOnFocus,this.minLength=s.isNumber(t.minLength)?t.minLength:1,this.autoWidth=void 0===t.autoWidth||!!t.autoWidth,this.clearOnSelected=!!t.clearOnSelected,this.tabAutocomplete=void 0===t.tabAutocomplete||!!t.tabAutocomplete,t.hint=!!t.hint,t.hint&&t.appendTo)throw new Error("[autocomplete.js] hint and appendTo options can't be used at the same time");this.css=t.css=s.mixin({},l,t.appendTo?l.appendTo:{}),this.cssClasses=t.cssClasses=s.mixin({},l.defaultClasses,t.cssClasses||{}),this.cssClasses.prefix=t.cssClasses.formattedPrefix=s.formatPrefix(this.cssClasses.prefix,this.cssClasses.noPrefix),this.listboxId=t.listboxId=[this.cssClasses.root,"listbox",s.getUniqueId()].join("-");var a=function(t){var e,n,o,a;e=r.element(t.input),n=r.element(c.wrapper.replace("%ROOT%",t.cssClasses.root)).css(t.css.wrapper),t.appendTo||"block"!==e.css("display")||"table"!==e.parent().css("display")||n.css("display","table-cell");var u=c.dropdown.replace("%PREFIX%",t.cssClasses.prefix).replace("%DROPDOWN_MENU%",t.cssClasses.dropdownMenu);o=r.element(u).css(t.css.dropdown).attr({role:"listbox",id:t.listboxId}),t.templates&&t.templates.dropdownMenu&&o.html(s.templatify(t.templates.dropdownMenu)());a=e.clone().css(t.css.hint).css(function(t){return{backgroundAttachment:t.css("background-attachment"),backgroundClip:t.css("background-clip"),backgroundColor:t.css("background-color"),backgroundImage:t.css("background-image"),backgroundOrigin:t.css("background-origin"),backgroundPosition:t.css("background-position"),backgroundRepeat:t.css("background-repeat"),backgroundSize:t.css("background-size")}}(e)),a.val("").addClass(s.className(t.cssClasses.prefix,t.cssClasses.hint,!0)).removeAttr("id name placeholder 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u=this.$input=a.input;e=a.menu,n=a.hint,t.dropdownMenuContainer&&r.element(t.dropdownMenuContainer).css("position","relative").append(e.css("top","0")),u.on("blur.aa",(function(t){var n=document.activeElement;s.isMsie()&&(e[0]===n||e[0].contains(n))&&(t.preventDefault(),t.stopImmediatePropagation(),s.defer((function(){u.focus()})))})),e.on("mousedown.aa",(function(t){t.preventDefault()})),this.eventBus=t.eventBus||new o({el:u}),this.dropdown=new h.Dropdown({appendTo:t.appendTo,wrapper:this.$node,menu:e,datasets:t.datasets,templates:t.templates,cssClasses:t.cssClasses,minLength:this.minLength}).onSync("suggestionClicked",this._onSuggestionClicked,this).onSync("cursorMoved",this._onCursorMoved,this).onSync("cursorRemoved",this._onCursorRemoved,this).onSync("opened",this._onOpened,this).onSync("closed",this._onClosed,this).onSync("shown",this._onShown,this).onSync("empty",this._onEmpty,this).onSync("redrawn",this._onRedrawn,this).onAsync("datasetRendered",this._onDatasetRendered,this),this.input=new h.Input({input:u,hint:n}).onSync("focused",this._onFocused,this).onSync("blurred",this._onBlurred,this).onSync("enterKeyed",this._onEnterKeyed,this).onSync("tabKeyed",this._onTabKeyed,this).onSync("escKeyed",this._onEscKeyed,this).onSync("upKeyed",this._onUpKeyed,this).onSync("downKeyed",this._onDownKeyed,this).onSync("leftKeyed",this._onLeftKeyed,this).onSync("rightKeyed",this._onRightKeyed,this).onSync("queryChanged",this._onQueryChanged,this).onSync("whitespaceChanged",this._onWhitespaceChanged,this),this._bindKeyboardShortcuts(t),this._setLanguageDirection()}s.mixin(h.prototype,{_bindKeyboardShortcuts:function(t){if(t.keyboardShortcuts){var e=this.$input,n=[];s.each(t.keyboardShortcuts,(function(t){"string"==typeof t&&(t=t.toUpperCase().charCodeAt(0)),n.push(t)})),r.element(document).keydown((function(t){var i=t.target||t.srcElement,s=i.tagName;if(!i.isContentEditable&&"INPUT"!==s&&"SELECT"!==s&&"TEXTAREA"!==s){var r=t.which||t.keyCode;-1!==n.indexOf(r)&&(e.focus(),t.stopPropagation(),t.preventDefault())}}))}},_onSuggestionClicked:function(t,e){var n;(n=this.dropdown.getDatumForSuggestion(e))&&this._select(n,{selectionMethod:"click"})},_onCursorMoved:function(t,e){var n=this.dropdown.getDatumForCursor(),i=this.dropdown.getCurrentCursor().attr("id");this.input.setActiveDescendant(i),n&&(e&&this.input.setInputValue(n.value,!0),this.eventBus.trigger("cursorchanged",n.raw,n.datasetName))},_onCursorRemoved:function(){this.input.resetInputValue(),this._updateHint(),this.eventBus.trigger("cursorremoved")},_onDatasetRendered:function(){this._updateHint(),this.eventBus.trigger("updated")},_onOpened:function(){this._updateHint(),this.input.expand(),this.eventBus.trigger("opened")},_onEmpty:function(){this.eventBus.trigger("empty")},_onRedrawn:function(){this.$node.css("top","0px"),this.$node.css("left","0px");var 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of file diff --git a/assets/js/5affa833.ff8be6a5.js b/assets/js/5affa833.a5cc0606.js similarity index 99% rename from assets/js/5affa833.ff8be6a5.js rename to assets/js/5affa833.a5cc0606.js index fba8c4ce..f8a03ddf 100644 --- a/assets/js/5affa833.ff8be6a5.js +++ b/assets/js/5affa833.a5cc0606.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[3536],{4849:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>d,contentTitle:()=>c,default:()=>p,frontMatter:()=>a,metadata:()=>l,toc:()=>h});var i=s(4848),t=s(8453),o=s(1432);const r="&CONTROL\n! we want to perform self consistent field calculation\n calculation = 'scf',\n\n! prefix is reference to the output files\n prefix = 'silicon',\n\n! output directory. Note that it is deprecated.\n outdir = './tmp/'\n\n! directory for the pseudo potential directory\n pseudo_dir = '../pseudos/'\n\n! verbosity high will give more details on the output file\n verbosity = 'high'\n/\n\n&SYSTEM\n! Bravais lattice index, which is 2 for FCC structure\n ibrav = 2,\n\n! Lattice constant in BOHR\n celldm(1) = 10.26,\n\n! number of atoms in an unit cell\n nat = 2,\n\n! number of different types of atom in the cell\n ntyp = 1,\n\n! kinetic energy cutoff for wavefunction in Ry\n ecutwfc = 30\n\n! number of bands to calculate\n nbnd = 8\n/\n\n&ELECTRONS\n! Mixing factor used in the self-consistent method\n mixing_beta = 0.6\n/\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 6 6 6 0 0 0\n",a={title:"Self consistent field calculation for silicon",sidebar_label:"SCF calculation",keywords:["SCF calculation","Self consistent field calculation","Self consistent calculation","SCF calculation using Quantum Espresso","Silicon bandstructure","Quantum Espresso input"]},c=void 0,l={id:"hands-on/scf",title:"Self consistent field calculation for silicon",description:"We need to provide various important parameters for the self consistent",source:"@site/docs/hands-on/scf.mdx",sourceDirName:"hands-on",slug:"/hands-on/scf",permalink:"/espresso/hands-on/scf",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/scf.mdx",tags:[],version:"current",frontMatter:{title:"Self consistent field calculation for silicon",sidebar_label:"SCF calculation",keywords:["SCF calculation","Self consistent field calculation","Self consistent calculation","SCF calculation using Quantum Espresso","Silicon bandstructure","Quantum Espresso input"]},sidebar:"docs",previous:{title:"Hands-on",permalink:"/espresso/category/hands-on"},next:{title:"Convergence testing",permalink:"/espresso/hands-on/convergence"}},d={},h=[{value:"Resources",id:"resources",level:2}];function u(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",li:"li",ol:"ol",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,t.R)(),...e.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(n.p,{children:["We need to provide various important parameters for the self consistent\ncalculation (solves the Kohn-Sham equation self-consistently) via an input file.\nIn QE input files, there are ",(0,i.jsx)(n.code,{children:"NAMELISTS"})," and ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"}),". ",(0,i.jsx)(n.code,{children:"NAMELISTS"}),"\nvariables have default values, and new values can be provided as required for a\nspecific calculation. The variables can be declared in any specific order. On\nthe other hand, the variables in the ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"})," has always to be specified\nand in specific order. Logically independent ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"})," may be organized in\nany order."]}),"\n",(0,i.jsxs)(n.p,{children:["There are three mandatory ",(0,i.jsx)(n.code,{children:"NAMELISTS"})," in ",(0,i.jsx)(n.code,{children:"PWscf"}),": (1) ",(0,i.jsx)(n.code,{children:"&CONTROL"}),": specifies the\nflux of computation, (2) ",(0,i.jsx)(n.code,{children:"&SYSTEM"}),": specifies the system, and (3) ",(0,i.jsx)(n.code,{children:"&ELECTRONS"}),":\nspecifies the algorithms used to solve the Kohn-Sham equation. There are two\nother ",(0,i.jsx)(n.code,{children:"NAMELISTS"}),": ",(0,i.jsx)(n.code,{children:"&IONS"})," and ",(0,i.jsx)(n.code,{children:"&CELLS"}),", which need to be specified depending on\nthe calculation."]}),"\n",(0,i.jsxs)(n.p,{children:["Three ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"}),": ",(0,i.jsx)(n.code,{children:"ATOMIC_SPECIES"}),", ",(0,i.jsx)(n.code,{children:"ATOMIC_POSITIONS"}),", and ",(0,i.jsx)(n.code,{children:"K_POINTS"})," in\n",(0,i.jsx)(n.code,{children:"PWscf"})," are mandatory. There are few others that must be provided in certain\ncalculations."]}),"\n",(0,i.jsxs)(n.p,{children:["Below is our input file ",(0,i.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/tree/main/src/silicon",children:"pw.scf.silicon.in"})," for silicon in\nstandard diamond (FCC) structure. Note that Quantum ESPRESSO uses primitive unit\ncell when ",(0,i.jsx)(n.code,{children:"CELL_PARAMETERS"})," are not provided. One can use any other type of cell\ne.g., conventional unit cell or supercell by specifying corresponding\n",(0,i.jsx)(n.code,{children:"CELL_PARAMETERS"})," and ",(0,i.jsx)(n.code,{children:"ATOMIC_POSITIONS"}),".The input files are typically named\nwith ",(0,i.jsx)(n.code,{children:".in"})," prefix, while output files are named with ",(0,i.jsx)(n.code,{children:".out"})," prefix for their\neasier identification. The input parameters are organized in ",(0,i.jsx)(n.code,{children:"&namelists"}),"\nfollowed by their fields or cards. The ",(0,i.jsx)(n.code,{children:"&control"}),", ",(0,i.jsx)(n.code,{children:"&system"}),", and ",(0,i.jsx)(n.code,{children:"&electrons"}),"\nnamelists are required. There are also optional ",(0,i.jsx)(n.code,{children:"&cell"})," and ",(0,i.jsx)(n.code,{children:"&ions"}),", you must\nprovide them if your calculation require them. Most parameters in the\n",(0,i.jsx)(n.code,{children:"namelists"})," have default values (which may or may not suit your needs), however\nsome variables you must always provide. Comment lines can be added with lines\nstarting with a ",(0,i.jsx)(n.code,{children:"!"})," like in FORTRAN. Also, parameter names are not\ncase-sensitive as in FORTRAN, i.e., ",(0,i.jsx)(n.code,{children:"&control"})," and ",(0,i.jsx)(n.code,{children:"&CONTROL"})," are the same."]}),"\n","\n",(0,i.jsx)(o.A,{language:"bash",title:"src/silicon/pw.scf.silicon.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsxs)(n.p,{children:["I am using the pseudo potential file (",(0,i.jsx)(n.code,{children:"Si.pz-vbc.UPF"}),") downloaded from ",(0,i.jsx)(n.a,{href:"https://www.quantum-espresso.org/pseudopotentials",children:"Quantum\nEspresso Website"}),"."]}),"\n",(0,i.jsxs)(n.p,{children:["You must read the ",(0,i.jsx)(n.strong,{children:"PWscf user manual"})," for in-depth understanding. Check the\n",(0,i.jsx)(n.code,{children:"qe-x.x/PW/Doc/"})," folder under your installation directory. Also see\n",(0,i.jsx)(n.code,{children:"INPUT_PW.html"})," describing various input parameters. PW stands for plane waves."]}),"\n",(0,i.jsxs)(n.p,{children:["Run ",(0,i.jsx)(n.code,{children:"pw.x"})," in self consistent mode for silicon."]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.scf.silicon.in > pw.scf.silicon.out\n# For parallel execution\nmpirun -np 4 pw.x -inp pw.scf.silicon.in > pw.scf.silicon.out\n"})}),"\n",(0,i.jsx)(n.admonition,{type:"note",children:(0,i.jsxs)(n.p,{children:["I have added the Quantum ESPRESSO executable directory to the ",(0,i.jsx)(n.code,{children:"PATH"})," environment\nvariable in bash/zsh profile, otherwise we have to type the full path of ",(0,i.jsx)(n.code,{children:"pw.x"}),"\nexecutable location."]})}),"\n",(0,i.jsxs)(n.p,{children:["Now let's look at the output file ",(0,i.jsx)(n.code,{children:"pw.scf.silicon.out"})," and see how the\nconvergence is reached:"]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"grep -e 'total energy' -e estimate pw.scf.silicon.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"and you should see something like this:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-fortran",children:" total energy = -15.85014573 Ry\n Harris-Foulkes estimate = -15.86899637 Ry\n estimated scf accuracy < 0.06093037 Ry\n total energy = -15.85194177 Ry\n Harris-Foulkes estimate = -15.85292281 Ry\n estimated scf accuracy < 0.00462014 Ry\n total energy = -15.85218359 Ry\n Harris-Foulkes estimate = -15.85220235 Ry\n estimated scf accuracy < 0.00011293 Ry\n! total energy = -15.85219789 Ry\n Harris-Foulkes estimate = -15.85219831 Ry\n estimated scf accuracy < 0.00000099 Ry\n The total energy is the sum of the following terms:\n"})}),"\n",(0,i.jsx)(n.p,{children:"It is important to note that the absolute value of DFT total energy is not with\nrespect to the vacuum reference, and depends on the chosen pseudopotential. The\nmeaningful measure is the difference in total energy, where various offsets\ncancel out."}),"\n",(0,i.jsx)(n.admonition,{type:"note",children:(0,i.jsxs)(n.p,{children:["In the above calculation, if you check the output file ",(0,i.jsx)(n.code,{children:"pw.scf.silicon.out"}),", you\nwill find: highest occupied, lowest unoccupied level (eV): 6.2117 6.8442.\nTherefore, the bandgap is 0.6325 eV, which is an underestimation of actual\nbandgap (1.12 eV)."]})}),"\n",(0,i.jsx)(n.admonition,{title:"Tips on convergence",type:"tip",children:(0,i.jsxs)(n.ol,{children:["\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsxs)(n.p,{children:["Reduce ",(0,i.jsx)(n.code,{children:"mixing_beta"})," value, especially if there is an oscillation around the\nconvergence energy."]}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"If it is a metallic system, use smearing and degauss. In this case, the SCF\naccuracy gradually goes down then suddenly increases (due to slight change in\nFermi energy highest occupied/ lowest unoccupied levels change)."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"Increase energy and charge density cutoffs (make sure they are sufficient)."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"Certain pseudo potential files have issues, you may try with pseudo\npotentials from different libraries."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsxs)(n.p,{children:["Suggested values for the ",(0,i.jsx)(n.code,{children:"conv_thr"}),": for energy and eigenvalues (scf\ncalculation) 1.0d-7, for forces (relax calculation) 1.0d-8, for stress (vc-relax\ncalculation) 1.0d-9 Ry. For certain calculation convergence might be very slow\nfor the first iteration, one can start the calculation with a higher threshold,\nafter few iterations reduce it and restart the calculation."]}),"\n"]}),"\n"]})}),"\n",(0,i.jsx)(n.p,{children:"There are several other important information is printed on the output file.\nExchange correlation used in the calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"Exchange-correlation= SLA PZ NOGX NOGC\n"})}),"\n",(0,i.jsxs)(n.p,{children:["Where ",(0,i.jsx)(n.code,{children:"SLA"})," \u2192 Slater exchange; ",(0,i.jsx)(n.code,{children:"PZ"})," \u2192 Perdew-Zunger parametrization of the LDA;\n",(0,i.jsx)(n.code,{children:"NOGX"})," and ",(0,i.jsx)(n.code,{children:"NOGC"})," indicates that density gradients are not taken into account."]}),"\n",(0,i.jsx)(n.p,{children:"We can see the total number of plane waves (1067) uses in our calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"Parallelization info\n--------------------\nsticks: dense smooth PW G-vecs: dense smooth PW\nMin 108 108 34 1489 1489 266\nMax 109 109 35 1492 1492 267\nSum 433 433 139 5961 5961 1067\n"})}),"\n",(0,i.jsx)(n.p,{children:"Number of Kohn-Sham states:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"number of electrons = 8.00\nnumber of Kohn-Sham states= 8\n"})}),"\n",(0,i.jsx)(n.p,{children:"In our calculation we have specified the number of bands = 8. Otherwise, there\nwould be 4 bands for 8 electrons in case of non spin-polarized systems."}),"\n",(0,i.jsx)(n.h2,{id:"resources",children:"Resources"}),"\n",(0,i.jsxs)(n.ul,{children:["\n",(0,i.jsx)(n.li,{children:(0,i.jsx)(n.a,{href:"https://www.quantum-espresso.org/Doc/pw_user_guide/",children:"https://www.quantum-espresso.org/Doc/pw_user_guide/"})}),"\n",(0,i.jsxs)(n.li,{children:[(0,i.jsx)(n.a,{href:"https://www.materialscloud.org/work/tools/qeinputgenerator",children:"Quantum Espresso Input Generator"})," (can help creating QE input files)"]}),"\n"]})]})}function p(e={}){const{wrapper:n}={...(0,t.R)(),...e.components};return n?(0,i.jsx)(n,{...e,children:(0,i.jsx)(u,{...e})}):u(e)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[3536],{4210:(e,n,s)=>{s.r(n),s.d(n,{assets:()=>d,contentTitle:()=>c,default:()=>p,frontMatter:()=>a,metadata:()=>l,toc:()=>h});var i=s(4848),t=s(8453),o=s(1432);const r="&CONTROL\n! we want to perform self consistent field calculation\n calculation = 'scf',\n\n! prefix is reference to the output files\n prefix = 'silicon',\n\n! output directory. Note that it is deprecated.\n outdir = './tmp/'\n\n! directory for the pseudo potential directory\n pseudo_dir = '../pseudos/'\n\n! verbosity high will give more details on the output file\n verbosity = 'high'\n/\n\n&SYSTEM\n! Bravais lattice index, which is 2 for FCC structure\n ibrav = 2,\n\n! Lattice constant in BOHR\n celldm(1) = 10.26,\n\n! number of atoms in an unit cell\n nat = 2,\n\n! number of different types of atom in the cell\n ntyp = 1,\n\n! kinetic energy cutoff for wavefunction in Ry\n ecutwfc = 30\n\n! number of bands to calculate\n nbnd = 8\n/\n\n&ELECTRONS\n! Mixing factor used in the self-consistent method\n mixing_beta = 0.6\n/\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 6 6 6 0 0 0\n",a={title:"Self consistent field calculation for silicon",sidebar_label:"SCF calculation",keywords:["SCF calculation","Self consistent field calculation","Self consistent calculation","SCF calculation using Quantum Espresso","Silicon bandstructure","Quantum Espresso input"]},c=void 0,l={id:"hands-on/scf",title:"Self consistent field calculation for silicon",description:"We need to provide various important parameters for the self consistent",source:"@site/docs/hands-on/scf.mdx",sourceDirName:"hands-on",slug:"/hands-on/scf",permalink:"/espresso/hands-on/scf",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/scf.mdx",tags:[],version:"current",frontMatter:{title:"Self consistent field calculation for silicon",sidebar_label:"SCF calculation",keywords:["SCF calculation","Self consistent field calculation","Self consistent calculation","SCF calculation using Quantum Espresso","Silicon bandstructure","Quantum Espresso input"]},sidebar:"docs",previous:{title:"Hands-on",permalink:"/espresso/category/hands-on"},next:{title:"Convergence testing",permalink:"/espresso/hands-on/convergence"}},d={},h=[{value:"Resources",id:"resources",level:2}];function u(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",li:"li",ol:"ol",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,t.R)(),...e.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsxs)(n.p,{children:["We need to provide various important parameters for the self consistent\ncalculation (solves the Kohn-Sham equation self-consistently) via an input file.\nIn QE input files, there are ",(0,i.jsx)(n.code,{children:"NAMELISTS"})," and ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"}),". ",(0,i.jsx)(n.code,{children:"NAMELISTS"}),"\nvariables have default values, and new values can be provided as required for a\nspecific calculation. The variables can be declared in any specific order. On\nthe other hand, the variables in the ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"})," has always to be specified\nand in specific order. Logically independent ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"})," may be organized in\nany order."]}),"\n",(0,i.jsxs)(n.p,{children:["There are three mandatory ",(0,i.jsx)(n.code,{children:"NAMELISTS"})," in ",(0,i.jsx)(n.code,{children:"PWscf"}),": (1) ",(0,i.jsx)(n.code,{children:"&CONTROL"}),": specifies the\nflux of computation, (2) ",(0,i.jsx)(n.code,{children:"&SYSTEM"}),": specifies the system, and (3) ",(0,i.jsx)(n.code,{children:"&ELECTRONS"}),":\nspecifies the algorithms used to solve the Kohn-Sham equation. There are two\nother ",(0,i.jsx)(n.code,{children:"NAMELISTS"}),": ",(0,i.jsx)(n.code,{children:"&IONS"})," and ",(0,i.jsx)(n.code,{children:"&CELLS"}),", which need to be specified depending on\nthe calculation."]}),"\n",(0,i.jsxs)(n.p,{children:["Three ",(0,i.jsx)(n.code,{children:"INPUT_CARDS"}),": ",(0,i.jsx)(n.code,{children:"ATOMIC_SPECIES"}),", ",(0,i.jsx)(n.code,{children:"ATOMIC_POSITIONS"}),", and ",(0,i.jsx)(n.code,{children:"K_POINTS"})," in\n",(0,i.jsx)(n.code,{children:"PWscf"})," are mandatory. There are few others that must be provided in certain\ncalculations."]}),"\n",(0,i.jsxs)(n.p,{children:["Below is our input file ",(0,i.jsx)(n.a,{href:"https://github.com/pranabdas/espresso/tree/main/src/silicon",children:"pw.scf.silicon.in"})," for silicon in\nstandard diamond (FCC) structure. Note that Quantum ESPRESSO uses primitive unit\ncell when ",(0,i.jsx)(n.code,{children:"CELL_PARAMETERS"})," are not provided. One can use any other type of cell\ne.g., conventional unit cell or supercell by specifying corresponding\n",(0,i.jsx)(n.code,{children:"CELL_PARAMETERS"})," and ",(0,i.jsx)(n.code,{children:"ATOMIC_POSITIONS"}),".The input files are typically named\nwith ",(0,i.jsx)(n.code,{children:".in"})," prefix, while output files are named with ",(0,i.jsx)(n.code,{children:".out"})," prefix for their\neasier identification. The input parameters are organized in ",(0,i.jsx)(n.code,{children:"&namelists"}),"\nfollowed by their fields or cards. The ",(0,i.jsx)(n.code,{children:"&control"}),", ",(0,i.jsx)(n.code,{children:"&system"}),", and ",(0,i.jsx)(n.code,{children:"&electrons"}),"\nnamelists are required. There are also optional ",(0,i.jsx)(n.code,{children:"&cell"})," and ",(0,i.jsx)(n.code,{children:"&ions"}),", you must\nprovide them if your calculation require them. Most parameters in the\n",(0,i.jsx)(n.code,{children:"namelists"})," have default values (which may or may not suit your needs), however\nsome variables you must always provide. Comment lines can be added with lines\nstarting with a ",(0,i.jsx)(n.code,{children:"!"})," like in FORTRAN. Also, parameter names are not\ncase-sensitive as in FORTRAN, i.e., ",(0,i.jsx)(n.code,{children:"&control"})," and ",(0,i.jsx)(n.code,{children:"&CONTROL"})," are the same."]}),"\n","\n",(0,i.jsx)(o.A,{language:"bash",title:"src/silicon/pw.scf.silicon.in",showLineNumbers:!0,children:r}),"\n",(0,i.jsxs)(n.p,{children:["I am using the pseudo potential file (",(0,i.jsx)(n.code,{children:"Si.pz-vbc.UPF"}),") downloaded from ",(0,i.jsx)(n.a,{href:"https://www.quantum-espresso.org/pseudopotentials",children:"Quantum\nEspresso Website"}),"."]}),"\n",(0,i.jsxs)(n.p,{children:["You must read the ",(0,i.jsx)(n.strong,{children:"PWscf user manual"})," for in-depth understanding. Check the\n",(0,i.jsx)(n.code,{children:"qe-x.x/PW/Doc/"})," folder under your installation directory. Also see\n",(0,i.jsx)(n.code,{children:"INPUT_PW.html"})," describing various input parameters. PW stands for plane waves."]}),"\n",(0,i.jsxs)(n.p,{children:["Run ",(0,i.jsx)(n.code,{children:"pw.x"})," in self consistent mode for silicon."]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"pw.x < pw.scf.silicon.in > pw.scf.silicon.out\n# For parallel execution\nmpirun -np 4 pw.x -inp pw.scf.silicon.in > pw.scf.silicon.out\n"})}),"\n",(0,i.jsx)(n.admonition,{type:"note",children:(0,i.jsxs)(n.p,{children:["I have added the Quantum ESPRESSO executable directory to the ",(0,i.jsx)(n.code,{children:"PATH"})," environment\nvariable in bash/zsh profile, otherwise we have to type the full path of ",(0,i.jsx)(n.code,{children:"pw.x"}),"\nexecutable location."]})}),"\n",(0,i.jsxs)(n.p,{children:["Now let's look at the output file ",(0,i.jsx)(n.code,{children:"pw.scf.silicon.out"})," and see how the\nconvergence is reached:"]}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"grep -e 'total energy' -e estimate pw.scf.silicon.out\n"})}),"\n",(0,i.jsx)(n.p,{children:"and you should see something like this:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-fortran",children:" total energy = -15.85014573 Ry\n Harris-Foulkes estimate = -15.86899637 Ry\n estimated scf accuracy < 0.06093037 Ry\n total energy = -15.85194177 Ry\n Harris-Foulkes estimate = -15.85292281 Ry\n estimated scf accuracy < 0.00462014 Ry\n total energy = -15.85218359 Ry\n Harris-Foulkes estimate = -15.85220235 Ry\n estimated scf accuracy < 0.00011293 Ry\n! total energy = -15.85219789 Ry\n Harris-Foulkes estimate = -15.85219831 Ry\n estimated scf accuracy < 0.00000099 Ry\n The total energy is the sum of the following terms:\n"})}),"\n",(0,i.jsx)(n.p,{children:"It is important to note that the absolute value of DFT total energy is not with\nrespect to the vacuum reference, and depends on the chosen pseudopotential. The\nmeaningful measure is the difference in total energy, where various offsets\ncancel out."}),"\n",(0,i.jsx)(n.admonition,{type:"note",children:(0,i.jsxs)(n.p,{children:["In the above calculation, if you check the output file ",(0,i.jsx)(n.code,{children:"pw.scf.silicon.out"}),", you\nwill find: highest occupied, lowest unoccupied level (eV): 6.2117 6.8442.\nTherefore, the bandgap is 0.6325 eV, which is an underestimation of actual\nbandgap (1.12 eV)."]})}),"\n",(0,i.jsx)(n.admonition,{title:"Tips on convergence",type:"tip",children:(0,i.jsxs)(n.ol,{children:["\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsxs)(n.p,{children:["Reduce ",(0,i.jsx)(n.code,{children:"mixing_beta"})," value, especially if there is an oscillation around the\nconvergence energy."]}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"If it is a metallic system, use smearing and degauss. In this case, the SCF\naccuracy gradually goes down then suddenly increases (due to slight change in\nFermi energy highest occupied/ lowest unoccupied levels change)."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"Increase energy and charge density cutoffs (make sure they are sufficient)."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsx)(n.p,{children:"Certain pseudo potential files have issues, you may try with pseudo\npotentials from different libraries."}),"\n"]}),"\n",(0,i.jsxs)(n.li,{children:["\n",(0,i.jsxs)(n.p,{children:["Suggested values for the ",(0,i.jsx)(n.code,{children:"conv_thr"}),": for energy and eigenvalues (scf\ncalculation) 1.0d-7, for forces (relax calculation) 1.0d-8, for stress (vc-relax\ncalculation) 1.0d-9 Ry. For certain calculation convergence might be very slow\nfor the first iteration, one can start the calculation with a higher threshold,\nafter few iterations reduce it and restart the calculation."]}),"\n"]}),"\n"]})}),"\n",(0,i.jsx)(n.p,{children:"There are several other important information is printed on the output file.\nExchange correlation used in the calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"Exchange-correlation= SLA PZ NOGX NOGC\n"})}),"\n",(0,i.jsxs)(n.p,{children:["Where ",(0,i.jsx)(n.code,{children:"SLA"})," \u2192 Slater exchange; ",(0,i.jsx)(n.code,{children:"PZ"})," \u2192 Perdew-Zunger parametrization of the LDA;\n",(0,i.jsx)(n.code,{children:"NOGX"})," and ",(0,i.jsx)(n.code,{children:"NOGC"})," indicates that density gradients are not taken into account."]}),"\n",(0,i.jsx)(n.p,{children:"We can see the total number of plane waves (1067) uses in our calculation:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"Parallelization info\n--------------------\nsticks: dense smooth PW G-vecs: dense smooth PW\nMin 108 108 34 1489 1489 266\nMax 109 109 35 1492 1492 267\nSum 433 433 139 5961 5961 1067\n"})}),"\n",(0,i.jsx)(n.p,{children:"Number of Kohn-Sham states:"}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-bash",children:"number of electrons = 8.00\nnumber of Kohn-Sham states= 8\n"})}),"\n",(0,i.jsx)(n.p,{children:"In our calculation we have specified the number of bands = 8. Otherwise, there\nwould be 4 bands for 8 electrons in case of non spin-polarized systems."}),"\n",(0,i.jsx)(n.h2,{id:"resources",children:"Resources"}),"\n",(0,i.jsxs)(n.ul,{children:["\n",(0,i.jsx)(n.li,{children:(0,i.jsx)(n.a,{href:"https://www.quantum-espresso.org/Doc/pw_user_guide/",children:"https://www.quantum-espresso.org/Doc/pw_user_guide/"})}),"\n",(0,i.jsxs)(n.li,{children:[(0,i.jsx)(n.a,{href:"https://www.materialscloud.org/work/tools/qeinputgenerator",children:"Quantum Espresso Input Generator"})," (can help creating QE input files)"]}),"\n"]})]})}function p(e={}){const{wrapper:n}={...(0,t.R)(),...e.components};return n?(0,i.jsx)(n,{...e,children:(0,i.jsx)(u,{...e})}):u(e)}}}]); \ No newline at end of file diff --git a/assets/js/6503d134.ed096803.js b/assets/js/6503d134.dc00c97e.js similarity index 99% rename from assets/js/6503d134.ed096803.js rename to assets/js/6503d134.dc00c97e.js index f109c7be..33927040 100644 --- a/assets/js/6503d134.ed096803.js +++ b/assets/js/6503d134.dc00c97e.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9083],{7562:(e,s,t)=>{t.r(s),t.d(s,{assets:()=>a,contentTitle:()=>l,default:()=>h,frontMatter:()=>i,metadata:()=>c,toc:()=>d});var r=t(4848),n=t(8453);const i={title:"Crystal structure",keywords:["Crystal structure","Crystal structure visualization","Vesta","Finding crystal structure","cif2cell","Xcrysdens","QE input generator","Supercell construction"]},l=void 0,c={id:"setup/crystal-structure",title:"Crystal structure",description:"Structure databases",source:"@site/docs/setup/crystal-structure.md",sourceDirName:"setup",slug:"/setup/crystal-structure",permalink:"/espresso/setup/crystal-structure",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/setup/crystal-structure.md",tags:[],version:"current",frontMatter:{title:"Crystal structure",keywords:["Crystal structure","Crystal structure visualization","Vesta","Finding crystal structure","cif2cell","Xcrysdens","QE input generator","Supercell construction"]},sidebar:"docs",previous:{title:"Jupyter notebooks",permalink:"/espresso/setup/jupyter"},next:{title:"Pseudo potentials",permalink:"/espresso/setup/pseudo-potential"}},a={},d=[{value:"Structure databases",id:"structure-databases",level:2},{value:"Useful tools:",id:"useful-tools",level:2},{value:"Xcrysdens",id:"xcrysdens",level:3},{value:"QE Input generator",id:"qe-input-generator",level:3},{value:"Resources",id:"resources",level:2}];function o(e){const s={a:"a",admonition:"admonition",code:"code",em:"em",h2:"h2",h3:"h3",li:"li",p:"p",pre:"pre",strong:"strong",table:"table",tbody:"tbody",td:"td",th:"th",thead:"thead",tr:"tr",ul:"ul",...(0,n.R)(),...e.components};return(0,r.jsxs)(r.Fragment,{children:[(0,r.jsx)(s.h2,{id:"structure-databases",children:"Structure databases"}),"\n",(0,r.jsxs)(s.p,{children:["Density functional theory (DFT) calculations are ",(0,r.jsx)(s.em,{children:"ab-initio"})," meaning the\ncalculation is done from the scratch based on given input parameters. We need to\nprovide the crystal structure in order to calculate DFT. Crystal structures are\nwidely available in Crystallographic Information File (",(0,r.jsx)(s.code,{children:".CIF"}),") format. There are\nseveral databases where you can look for crystal structures."]}),"\n",(0,r.jsxs)(s.ul,{children:["\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://crystallography.net/cod/",children:"http://crystallography.net/cod/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://materialsproject.org",children:"https://materialsproject.org"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://mpds.io/",children:"https://mpds.io/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://icsd.fiz-karlsruhe.de/index.xhtml",children:"https://icsd.fiz-karlsruhe.de/index.xhtml"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://aflowlib.org/CrystalDatabase/",children:"http://aflowlib.org/CrystalDatabase/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://crystdb.nims.go.jp/crystdb/search-materials",children:"http://crystdb.nims.go.jp/crystdb/search-materials"})}),"\n"]}),"\n",(0,r.jsxs)(s.p,{children:["In Quantum Espresso, the structure information is provided by ",(0,r.jsx)(s.code,{children:"ibrav"})," number,\nand corresponding ",(0,r.jsx)(s.code,{children:"celldm"})," values or lattice constants and cosines of angle\nbetween the axes. It is also possible to set ",(0,r.jsx)(s.code,{children:"ibrav=0"})," and provide lattice\nvectors in ",(0,r.jsx)(s.code,{children:"CELL_PARAMETERS"}),"."]}),"\n",(0,r.jsx)(s.admonition,{type:"danger",children:(0,r.jsxs)(s.p,{children:["When set ",(0,r.jsx)(s.code,{children:"ibrav=0"}),", the lattice vectors must be provided with sufficiently large\nnumber of decimal accuracy, otherwise symmetry detection may fail and strange\nproblems may arrise."]})}),"\n",(0,r.jsxs)(s.p,{children:[(0,r.jsx)(s.code,{children:"ibrav"})," numbers for different lattice types:"]}),"\n",(0,r.jsxs)(s.table,{children:[(0,r.jsx)(s.thead,{children:(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.th,{children:(0,r.jsx)(s.code,{children:"ibrav"})}),(0,r.jsx)(s.th,{children:"Lattice type"})]})}),(0,r.jsxs)(s.tbody,{children:[(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"1"}),(0,r.jsx)(s.td,{children:"Simple cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"2"}),(0,r.jsx)(s.td,{children:"Face centered cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"3,-3"}),(0,r.jsx)(s.td,{children:"Body centered cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"4"}),(0,r.jsx)(s.td,{children:"Hexagonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"5"}),(0,r.jsx)(s.td,{children:"Trigonal with c as 3-fold axis"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-5"}),(0,r.jsx)(s.td,{children:"Trigonal with <111> as 3-fold axis"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"6"}),(0,r.jsx)(s.td,{children:"Simple tetragonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"7"}),(0,r.jsx)(s.td,{children:"Centered tetragonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"8"}),(0,r.jsx)(s.td,{children:"Simple orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"9,-9,91"}),(0,r.jsx)(s.td,{children:"One-face centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"10"}),(0,r.jsx)(s.td,{children:"Face centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"11"}),(0,r.jsx)(s.td,{children:"Body centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"12"}),(0,r.jsx)(s.td,{children:"Simple monoclinic, c unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-12"}),(0,r.jsx)(s.td,{children:"Simple monoclinic, b unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"13"}),(0,r.jsx)(s.td,{children:"One base centered monoclinic, c unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-13"}),(0,r.jsx)(s.td,{children:"One base centered monoclinic, b unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"14"}),(0,r.jsx)(s.td,{children:"Triclinic"})]})]})]}),"\n",(0,r.jsx)(s.h2,{id:"useful-tools",children:"Useful tools:"}),"\n",(0,r.jsxs)(s.p,{children:[(0,r.jsx)(s.strong,{children:"Vesta"})," - ",(0,r.jsx)(s.a,{href:"https://jp-minerals.org/vesta/en/",children:"https://jp-minerals.org/vesta/en/"}),". It helps you visualize crystal structure,\ncreate and modify supercells, crystal structures, and many other useful\nfunctionalities."]}),"\n",(0,r.jsxs)(s.p,{children:["We can prepare our Quantum Espresso input file using ",(0,r.jsx)(s.strong,{children:"cif2cell"})," utility. If\nyou do not have ",(0,r.jsx)(s.strong,{children:"cif2cell"})," installed, you can use ",(0,r.jsx)(s.strong,{children:"pip"})," to install:"]}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"sudo pip3 install cif2cell\n"})}),"\n",(0,r.jsxs)(s.p,{children:["You may need to add it to the path in your ",(0,r.jsx)(s.code,{children:".bashrc"})," manually:"]}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:'export PATH="/home/pranab/.local/lib/python3.8/site-packages/:$PATH"\n'})}),"\n",(0,r.jsx)(s.p,{children:"Running cif2cell command:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"cif2cell file.cif -p quantum-espresso -o inputfile.in\n"})}),"\n",(0,r.jsx)(s.h3,{id:"xcrysdens",children:"Xcrysdens"}),"\n",(0,r.jsxs)(s.p,{children:["You can explore the crystal structure, find out k-path and many more using\n",(0,r.jsx)(s.strong,{children:"Xcrysdens"})," application - ",(0,r.jsx)(s.a,{href:"http://www.xcrysden.org",children:"http://www.xcrysden.org"})]}),"\n",(0,r.jsx)(s.p,{children:"For certain functionality, Xcrysdens requires basic calculator program. On\nUbuntu/ Debian:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"sudo apt update\nsudo apt install bc xcrysden\n"})}),"\n",(0,r.jsx)(s.p,{children:"Manual installation:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"# install dependencies\nsudo apt install --no-install-recommends bc tk libglu1-mesa libtogl2 \\\n libfftw3-3 libxmu6 imagemagick openbabel libgfortran5\n\n# download the latest version of xcrysden and extract\nwget http://www.xcrysden.org/download/xcrysden-1.6.2-linux_x86_64-shared.tar.gz\ntar -zxvf xcrysden-1.6.2-linux_x86_64-shared.tar.gz\n\n# launch (provided you extracted under your home directory)\n~/xcrysden-1.6.2-bin-shared/xcrysden\n"})}),"\n",(0,r.jsxs)(s.p,{children:["If you are on WSL, you need to install X-server (X-ming for Windows) on the host\nand set ",(0,r.jsx)(s.code,{children:"export DISPLAY=:0"})," in your WSL instance."]}),"\n",(0,r.jsx)(s.h3,{id:"qe-input-generator",children:"QE Input generator"}),"\n",(0,r.jsxs)(s.p,{children:["You can generate ",(0,r.jsx)(s.strong,{children:"PWscf"})," input files using tools in this website as well\n",(0,r.jsx)(s.a,{href:"https://www.materialscloud.org/work/tools/qeinputgenerator",children:"https://www.materialscloud.org/work/tools/qeinputgenerator"})]}),"\n",(0,r.jsxs)(s.p,{children:["The same website also has a tool for k-path visualization and generation\n",(0,r.jsx)(s.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"https://www.materialscloud.org/work/tools/seekpath"})]}),"\n",(0,r.jsx)(s.h2,{id:"resources",children:"Resources"}),"\n",(0,r.jsxs)(s.ul,{children:["\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://www.youtube.com/watch?v=Jk0QUB1fkMU",children:"Supercell construction using Vesta"})}),"\n"]})]})}function h(e={}){const{wrapper:s}={...(0,n.R)(),...e.components};return s?(0,r.jsx)(s,{...e,children:(0,r.jsx)(o,{...e})}):o(e)}},8453:(e,s,t)=>{t.d(s,{R:()=>l,x:()=>c});var r=t(6540);const n={},i=r.createContext(n);function l(e){const s=r.useContext(i);return r.useMemo((function(){return"function"==typeof e?e(s):{...s,...e}}),[s,e])}function c(e){let s;return s=e.disableParentContext?"function"==typeof e.components?e.components(n):e.components||n:l(e.components),r.createElement(i.Provider,{value:s},e.children)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9083],{7665:(e,s,t)=>{t.r(s),t.d(s,{assets:()=>a,contentTitle:()=>l,default:()=>h,frontMatter:()=>i,metadata:()=>c,toc:()=>d});var r=t(4848),n=t(8453);const i={title:"Crystal structure",keywords:["Crystal structure","Crystal structure visualization","Vesta","Finding crystal structure","cif2cell","Xcrysdens","QE input generator","Supercell construction"]},l=void 0,c={id:"setup/crystal-structure",title:"Crystal structure",description:"Structure databases",source:"@site/docs/setup/crystal-structure.md",sourceDirName:"setup",slug:"/setup/crystal-structure",permalink:"/espresso/setup/crystal-structure",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/setup/crystal-structure.md",tags:[],version:"current",frontMatter:{title:"Crystal structure",keywords:["Crystal structure","Crystal structure visualization","Vesta","Finding crystal structure","cif2cell","Xcrysdens","QE input generator","Supercell construction"]},sidebar:"docs",previous:{title:"Jupyter notebooks",permalink:"/espresso/setup/jupyter"},next:{title:"Pseudo potentials",permalink:"/espresso/setup/pseudo-potential"}},a={},d=[{value:"Structure databases",id:"structure-databases",level:2},{value:"Useful tools:",id:"useful-tools",level:2},{value:"Xcrysdens",id:"xcrysdens",level:3},{value:"QE Input generator",id:"qe-input-generator",level:3},{value:"Resources",id:"resources",level:2}];function o(e){const s={a:"a",admonition:"admonition",code:"code",em:"em",h2:"h2",h3:"h3",li:"li",p:"p",pre:"pre",strong:"strong",table:"table",tbody:"tbody",td:"td",th:"th",thead:"thead",tr:"tr",ul:"ul",...(0,n.R)(),...e.components};return(0,r.jsxs)(r.Fragment,{children:[(0,r.jsx)(s.h2,{id:"structure-databases",children:"Structure databases"}),"\n",(0,r.jsxs)(s.p,{children:["Density functional theory (DFT) calculations are ",(0,r.jsx)(s.em,{children:"ab-initio"})," meaning the\ncalculation is done from the scratch based on given input parameters. We need to\nprovide the crystal structure in order to calculate DFT. Crystal structures are\nwidely available in Crystallographic Information File (",(0,r.jsx)(s.code,{children:".CIF"}),") format. There are\nseveral databases where you can look for crystal structures."]}),"\n",(0,r.jsxs)(s.ul,{children:["\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://crystallography.net/cod/",children:"http://crystallography.net/cod/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://materialsproject.org",children:"https://materialsproject.org"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://mpds.io/",children:"https://mpds.io/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://icsd.fiz-karlsruhe.de/index.xhtml",children:"https://icsd.fiz-karlsruhe.de/index.xhtml"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://aflowlib.org/CrystalDatabase/",children:"http://aflowlib.org/CrystalDatabase/"})}),"\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"http://crystdb.nims.go.jp/crystdb/search-materials",children:"http://crystdb.nims.go.jp/crystdb/search-materials"})}),"\n"]}),"\n",(0,r.jsxs)(s.p,{children:["In Quantum Espresso, the structure information is provided by ",(0,r.jsx)(s.code,{children:"ibrav"})," number,\nand corresponding ",(0,r.jsx)(s.code,{children:"celldm"})," values or lattice constants and cosines of angle\nbetween the axes. It is also possible to set ",(0,r.jsx)(s.code,{children:"ibrav=0"})," and provide lattice\nvectors in ",(0,r.jsx)(s.code,{children:"CELL_PARAMETERS"}),"."]}),"\n",(0,r.jsx)(s.admonition,{type:"danger",children:(0,r.jsxs)(s.p,{children:["When set ",(0,r.jsx)(s.code,{children:"ibrav=0"}),", the lattice vectors must be provided with sufficiently large\nnumber of decimal accuracy, otherwise symmetry detection may fail and strange\nproblems may arrise."]})}),"\n",(0,r.jsxs)(s.p,{children:[(0,r.jsx)(s.code,{children:"ibrav"})," numbers for different lattice types:"]}),"\n",(0,r.jsxs)(s.table,{children:[(0,r.jsx)(s.thead,{children:(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.th,{children:(0,r.jsx)(s.code,{children:"ibrav"})}),(0,r.jsx)(s.th,{children:"Lattice type"})]})}),(0,r.jsxs)(s.tbody,{children:[(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"1"}),(0,r.jsx)(s.td,{children:"Simple cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"2"}),(0,r.jsx)(s.td,{children:"Face centered cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"3,-3"}),(0,r.jsx)(s.td,{children:"Body centered cubic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"4"}),(0,r.jsx)(s.td,{children:"Hexagonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"5"}),(0,r.jsx)(s.td,{children:"Trigonal with c as 3-fold axis"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-5"}),(0,r.jsx)(s.td,{children:"Trigonal with <111> as 3-fold axis"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"6"}),(0,r.jsx)(s.td,{children:"Simple tetragonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"7"}),(0,r.jsx)(s.td,{children:"Centered tetragonal"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"8"}),(0,r.jsx)(s.td,{children:"Simple orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"9,-9,91"}),(0,r.jsx)(s.td,{children:"One-face centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"10"}),(0,r.jsx)(s.td,{children:"Face centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"11"}),(0,r.jsx)(s.td,{children:"Body centered orthorhombic"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"12"}),(0,r.jsx)(s.td,{children:"Simple monoclinic, c unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-12"}),(0,r.jsx)(s.td,{children:"Simple monoclinic, b unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"13"}),(0,r.jsx)(s.td,{children:"One base centered monoclinic, c unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"-13"}),(0,r.jsx)(s.td,{children:"One base centered monoclinic, b unique"})]}),(0,r.jsxs)(s.tr,{children:[(0,r.jsx)(s.td,{children:"14"}),(0,r.jsx)(s.td,{children:"Triclinic"})]})]})]}),"\n",(0,r.jsx)(s.h2,{id:"useful-tools",children:"Useful tools:"}),"\n",(0,r.jsxs)(s.p,{children:[(0,r.jsx)(s.strong,{children:"Vesta"})," - ",(0,r.jsx)(s.a,{href:"https://jp-minerals.org/vesta/en/",children:"https://jp-minerals.org/vesta/en/"}),". It helps you visualize crystal structure,\ncreate and modify supercells, crystal structures, and many other useful\nfunctionalities."]}),"\n",(0,r.jsxs)(s.p,{children:["We can prepare our Quantum Espresso input file using ",(0,r.jsx)(s.strong,{children:"cif2cell"})," utility. If\nyou do not have ",(0,r.jsx)(s.strong,{children:"cif2cell"})," installed, you can use ",(0,r.jsx)(s.strong,{children:"pip"})," to install:"]}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"sudo pip3 install cif2cell\n"})}),"\n",(0,r.jsxs)(s.p,{children:["You may need to add it to the path in your ",(0,r.jsx)(s.code,{children:".bashrc"})," manually:"]}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:'export PATH="/home/pranab/.local/lib/python3.8/site-packages/:$PATH"\n'})}),"\n",(0,r.jsx)(s.p,{children:"Running cif2cell command:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"cif2cell file.cif -p quantum-espresso -o inputfile.in\n"})}),"\n",(0,r.jsx)(s.h3,{id:"xcrysdens",children:"Xcrysdens"}),"\n",(0,r.jsxs)(s.p,{children:["You can explore the crystal structure, find out k-path and many more using\n",(0,r.jsx)(s.strong,{children:"Xcrysdens"})," application - ",(0,r.jsx)(s.a,{href:"http://www.xcrysden.org",children:"http://www.xcrysden.org"})]}),"\n",(0,r.jsx)(s.p,{children:"For certain functionality, Xcrysdens requires basic calculator program. On\nUbuntu/ Debian:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"sudo apt update\nsudo apt install bc xcrysden\n"})}),"\n",(0,r.jsx)(s.p,{children:"Manual installation:"}),"\n",(0,r.jsx)(s.pre,{children:(0,r.jsx)(s.code,{className:"language-bash",children:"# install dependencies\nsudo apt install --no-install-recommends bc tk libglu1-mesa libtogl2 \\\n libfftw3-3 libxmu6 imagemagick openbabel libgfortran5\n\n# download the latest version of xcrysden and extract\nwget http://www.xcrysden.org/download/xcrysden-1.6.2-linux_x86_64-shared.tar.gz\ntar -zxvf xcrysden-1.6.2-linux_x86_64-shared.tar.gz\n\n# launch (provided you extracted under your home directory)\n~/xcrysden-1.6.2-bin-shared/xcrysden\n"})}),"\n",(0,r.jsxs)(s.p,{children:["If you are on WSL, you need to install X-server (X-ming for Windows) on the host\nand set ",(0,r.jsx)(s.code,{children:"export DISPLAY=:0"})," in your WSL instance."]}),"\n",(0,r.jsx)(s.h3,{id:"qe-input-generator",children:"QE Input generator"}),"\n",(0,r.jsxs)(s.p,{children:["You can generate ",(0,r.jsx)(s.strong,{children:"PWscf"})," input files using tools in this website as well\n",(0,r.jsx)(s.a,{href:"https://www.materialscloud.org/work/tools/qeinputgenerator",children:"https://www.materialscloud.org/work/tools/qeinputgenerator"})]}),"\n",(0,r.jsxs)(s.p,{children:["The same website also has a tool for k-path visualization and generation\n",(0,r.jsx)(s.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"https://www.materialscloud.org/work/tools/seekpath"})]}),"\n",(0,r.jsx)(s.h2,{id:"resources",children:"Resources"}),"\n",(0,r.jsxs)(s.ul,{children:["\n",(0,r.jsx)(s.li,{children:(0,r.jsx)(s.a,{href:"https://www.youtube.com/watch?v=Jk0QUB1fkMU",children:"Supercell construction using Vesta"})}),"\n"]})]})}function h(e={}){const{wrapper:s}={...(0,n.R)(),...e.components};return s?(0,r.jsx)(s,{...e,children:(0,r.jsx)(o,{...e})}):o(e)}},8453:(e,s,t)=>{t.d(s,{R:()=>l,x:()=>c});var r=t(6540);const n={},i=r.createContext(n);function l(e){const s=r.useContext(i);return r.useMemo((function(){return"function"==typeof e?e(s):{...s,...e}}),[s,e])}function c(e){let s;return s=e.disableParentContext?"function"==typeof e.components?e.components(n):e.components||n:l(e.components),r.createElement(i.Provider,{value:s},e.children)}}}]); \ No newline at end of file diff --git a/assets/js/682b01ab.b1415993.js b/assets/js/682b01ab.b1415993.js deleted file mode 100644 index ed6b094e..00000000 --- a/assets/js/682b01ab.b1415993.js +++ /dev/null @@ -1 +0,0 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[5377],{1698:s=>{s.exports=JSON.parse('{"title":"Hands-on","slug":"/category/hands-on","permalink":"/espresso/category/hands-on","navigation":{"previous":{"title":"Wannier basis","permalink":"/espresso/theory/wannier"},"next":{"title":"SCF calculation","permalink":"/espresso/hands-on/scf"}}}')}}]); \ No newline at end of file diff --git a/assets/js/803d9898.cea8d9c6.js b/assets/js/803d9898.c02b4529.js similarity index 99% rename from assets/js/803d9898.cea8d9c6.js rename to assets/js/803d9898.c02b4529.js index 322c7f14..0c908abe 100644 --- a/assets/js/803d9898.cea8d9c6.js +++ b/assets/js/803d9898.c02b4529.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4366],{5578:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>p,contentTitle:()=>d,default:()=>f,frontMatter:()=>c,metadata:()=>h,toc:()=>u});var t=s(4848),a=s(8453),i=s(1432);const o="&CONTROL\n calculation = 'scf',\n restart_mode = 'from_scratch',\n prefix = 'silicon',\n outdir = './tmp/'\n pseudo_dir = '../pseudos/'\n verbosity = 'high'\n/\n\n&SYSTEM\n ibrav = 2,\n celldm(1) = 10.2076,\n nat = 2,\n ntyp = 1,\n ecutwfc = 50,\n ecutrho = 400,\n nbnd = 8,\n! occupations = 'smearing',\n! smearing = 'gaussian',\n! degauss = 0.005\n/\n\n&ELECTRONS\n conv_thr = 1e-8,\n mixing_beta = 0.6\n/\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 8 8 8 0 0 0\n",r="&control\n calculation = 'bands',\n restart_mode = 'from_scratch',\n prefix = 'silicon',\n outdir = './tmp/'\n pseudo_dir = '../pseudos/'\n verbosity = 'high'\n/\n\n&system\n ibrav = 2,\n celldm(1) = 10.2076,\n nat = 2,\n ntyp = 1,\n ecutwfc = 50,\n ecutrho = 400,\n nbnd = 8\n /\n\n&electrons\n conv_thr = 1e-8,\n mixing_beta = 0.6\n /\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.00 0.00 0.00\n Si 0.25 0.25 0.25\n\nK_POINTS {crystal_b}\n5\n 0.0000 0.5000 0.0000 20 !L\n 0.0000 0.0000 0.0000 30 !G\n -0.500 0.0000 -0.500 10 !X\n -0.375 0.2500 -0.375 30 !U\n 0.0000 0.0000 0.0000 20 !G\n",l="&BANDS\n prefix = 'silicon'\n outdir = './tmp/'\n filband = 'si_bands.dat'\n/\n",c={title:"Bandstructure Calculation",sidebar_label:"Bandstructure"},d=void 0,h={id:"hands-on/bands",title:"Bandstructure Calculation",description:"Before we can run bands calculation, we need to perform single-point [self",source:"@site/docs/hands-on/bands.mdx",sourceDirName:"hands-on",slug:"/hands-on/bands",permalink:"/espresso/hands-on/bands",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/bands.mdx",tags:[],version:"current",frontMatter:{title:"Bandstructure Calculation",sidebar_label:"Bandstructure"},sidebar:"docs",previous:{title:"DOS calculation",permalink:"/espresso/hands-on/dos"},next:{title:"Al (metal)",permalink:"/espresso/hands-on/aluminum"}},p={},u=[{value:"Note on bandgap",id:"note-on-bandgap",level:2},{value:"Resources",id:"resources",level:2}];function m(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",ol:"ol",p:"p",pre:"pre",section:"section",semantics:"semantics",span:"span",strong:"strong",sup:"sup",ul:"ul",...(0,a.R)(),...n.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsxs)(e.p,{children:["Before we can run ",(0,t.jsx)(e.code,{children:"bands"})," calculation, we need to perform single-point ",(0,t.jsx)(e.a,{href:"scf",children:"self\nconsistent field calculation"}),". We have our input ",(0,t.jsx)(e.code,{children:"scf"})," file with some new\nparameters:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pw.scf.silicon_bands.in",showLineNumbers:!0,children:o}),"\n",(0,t.jsxs)(e.p,{children:["Run the ",(0,t.jsx)(e.code,{children:"scf"})," calculation:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.scf.silicon_bands.in > pw.scf.silicon_bands.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["Next step is our band calculation (non-self consistent field) calculation. The\n",(0,t.jsx)(e.code,{children:"bands"})," calculation is ",(0,t.jsx)(e.em,{children:"non self-consistent"})," and reads/uses the ground state\nelectron density, Hartree, exchange and correlation potentials obtained in the\nprevious step (scf calculation). In case of non self-consistent calculation, the\n",(0,t.jsx)(e.strong,{children:"pw.x"})," program determines the Kohn-Sham eigenfunction and eigenvalues without\nupdating Kohn-Sham Hamiltonian at every iteration. We need to specify the\nk-points for which we want to calculate the eigenvalues. You may use the\n",(0,t.jsx)(e.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"See-K-path tool by materials cloud"})," to visualize the K-path. We\ncan specify ",(0,t.jsx)(e.code,{children:"nbnd"}),", by default it calculates half the number of valence\nelectrons, i.e., only the occupied ground state bands. Usually we are interested\nalso in the unoccupied bands above the Fermi energy. Number of occupied bands\ncan be found in the ",(0,t.jsx)(e.code,{children:"scf"})," output as number of Kohn-Sham states. Below is a\nsample input file for the band calculation:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pw.bands.silicon.in",showLineNumbers:!0,children:r}),"\n",(0,t.jsxs)(e.p,{children:["Run ",(0,t.jsx)(e.code,{children:"pw.x"})," with ",(0,t.jsx)(e.code,{children:"bands"})," calculation input file:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.bands.silicon.in > pw.bands.silicon.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["After the bands calculation is performed, we need some postprocessing using\n",(0,t.jsx)(e.code,{children:"bands.x"})," utility in order to obtain the data in more usable format. Input file\nfor ",(0,t.jsx)(e.code,{children:"bands.x"})," postprocessing:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pp.bands.silicon.in",showLineNumbers:!0,children:l}),"\n",(0,t.jsxs)(e.p,{children:["Run ",(0,t.jsx)(e.code,{children:"bands.x"})," from post processing (PP) module:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"bands.x < pp.bands.silicon.in > pp.bands.silicon.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["Finally, we run ",(0,t.jsx)(e.code,{children:"plotband.x"})," to visualize bandstructure. We can either run it\ninteractively (as described below) or provide an input file. In order to run\ninteractively, type ",(0,t.jsx)(e.code,{children:"plotband.x"})," in your terminal."]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:" Input file > si_bands.dat\nReading 8 bands at 91 k-points\nRange: -5.8300 16.3420eV Emin, Emax > -6, 16\nhigh-symmetry point: 0.5000 0.5000 0.5000 x coordinate 0.0000\nhigh-symmetry point: 0.0000 0.0000 0.0000 x coordinate 0.8660\nhigh-symmetry point: 1.0000 0.0000 0.0000 x coordinate 1.8660\nhigh-symmetry point: 1.0000 0.2500 0.2500 x coordinate 2.2196\nhigh-symmetry point: 0.0000 0.0000 0.0000 x coordinate 3.2802\noutput file (gnuplot/xmgr) > si_bands.gnuplot\nbands in gnuplot/xmgr format written to file si_bands.gnuplot\n\n\noutput file (ps) > si_bands.ps\nEfermi > 6.6416\ndeltaE, reference E (for tics) 4, 0\nbands in PostScript format written to file si_bands.ps\n"})}),"\n",(0,t.jsxs)(e.p,{children:["You will have ",(0,t.jsx)(e.code,{children:"si_bands.ps"})," with band diagram. Alternatively, you can use your\nfavorite plotting program to make the plots. Below is an example of using Python\nmatplotlib."]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-python",metastring:'title="notebooks/si-bands.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\n\nplt.rcParams[\"figure.dpi\"]=150\nplt.rcParams[\"figure.facecolor\"]=\"white\"\nplt.rcParams[\"figure.figsize\"]=(8, 6)\n\n# load data\ndata = np.loadtxt('../src/silicon/si_bands.dat.gnu')\n\nk = np.unique(data[:, 0])\nbands = np.reshape(data[:, 1], (-1, len(k)))\n\nfor band in range(len(bands)):\n plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k')\nplt.xlim(min(k), max(k))\n\n# Fermi energy\nplt.axhline(6.6416, linestyle=(0, (5, 5)), linewidth=0.75, color='k', alpha=0.5)\n# High symmetry k-points (check bands_pp.out)\nplt.axvline(0.8660, linewidth=0.75, color='k', alpha=0.5)\nplt.axvline(1.8660, linewidth=0.75, color='k', alpha=0.5)\nplt.axvline(2.2196, linewidth=0.75, color='k', alpha=0.5)\n# text labels\nplt.xticks(ticks= [0, 0.8660, 1.8660, 2.2196, 3.2802], \\\n labels=['L', '$\\Gamma$', 'X', 'U', '$\\Gamma$'])\nplt.ylabel(\"Energy (eV)\")\nplt.text(2.3, 5.6, 'Fermi energy', fontsize= small)\nplt.show()\n"})}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:s(6275).A}),(0,t.jsx)("img",{src:s(5234).A,alt:"silicon-bands"})]}),"\n",(0,t.jsxs)(e.admonition,{type:"info",children:[(0,t.jsxs)(e.p,{children:["The ",(0,t.jsx)(e.code,{children:"k"})," values corresponding to high symmetry points (such as ",(0,t.jsxs)(e.span,{className:"katex",children:[(0,t.jsx)(e.span,{className:"katex-mathml",children:(0,t.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,t.jsxs)(e.semantics,{children:[(0,t.jsx)(e.mrow,{children:(0,t.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,t.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,t.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,t.jsxs)(e.span,{className:"base",children:[(0,t.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,t.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]}),", X, U, L)\nwhich we need to label in our band diagram, can be found in the post-processing\noutput file (",(0,t.jsx)(e.code,{children:"si_bands_pp.out"}),")."]}),(0,t.jsxs)(e.p,{children:["Bandgap value can be determined from the highest occupied, lowest unoccupied\nlevel values printed in ",(0,t.jsx)(e.code,{children:"scf"})," calculation output."]})]}),"\n",(0,t.jsx)(e.h2,{id:"note-on-bandgap",children:"Note on bandgap"}),"\n",(0,t.jsx)(e.p,{children:"Usually, band gaps computed using common exchange-correction functionals such as\nLDA or GGA are severely underestimated compared to actual experimental values.\nThis discrepancy is mainly due to (1) approximations used in the exchange\ncorrection functional and (2) a derivative discontinuity term, originating from\nthe density functional being discontinuous with the total number of electrons in\nthe system. The second contribution is larger contributor to the error. It can\nbe partly addressed by a variety of techniques such as the GW approximation."}),"\n",(0,t.jsxs)(e.p,{children:["Strategies to improve band gap prediction at moderate to low computational cost\nnow been developed by several groups, including Chan and Ceder (delta-sol)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-1",id:"user-content-fnref-1","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"1"})}),",\nHeyd et al. (hybrid functionals)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-2",id:"user-content-fnref-2","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"2"})}),", and Setyawan et al. (empirical fits)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-3",id:"user-content-fnref-3","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"3"})}),"."]}),"\n",(0,t.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,t.jsxs)(e.ul,{children:["\n",(0,t.jsx)(e.li,{children:(0,t.jsx)(e.a,{href:"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures",children:"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures"})}),"\n",(0,t.jsx)(e.li,{children:(0,t.jsx)(e.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"See K-pat online tool"})}),"\n"]}),"\n","\n",(0,t.jsxs)(e.section,{"data-footnotes":!0,className:"footnotes",children:[(0,t.jsx)(e.h2,{className:"sr-only",id:"footnote-label",children:"Footnotes"}),"\n",(0,t.jsxs)(e.ol,{children:["\n",(0,t.jsxs)(e.li,{id:"user-content-fn-1",children:["\n",(0,t.jsxs)(e.p,{children:["M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical\nReview Letters 19 (2010) ",(0,t.jsx)(e.a,{href:"https://doi.org/10.1103/PhysRevLett.105.196403",children:"https://doi.org/10.1103/PhysRevLett.105.196403"})," ",(0,t.jsx)(e.a,{href:"#user-content-fnref-1","data-footnote-backref":"","aria-label":"Back to reference 1",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n",(0,t.jsxs)(e.li,{id:"user-content-fn-2",children:["\n",(0,t.jsxs)(e.p,{children:["J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and\nlattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid\nfunctional, Journal of Chemical Physics 123 (2005)\n",(0,t.jsx)(e.a,{href:"https://doi.org/10.1063/1.2085170",children:"https://doi.org/10.1063/1.2085170"})," ",(0,t.jsx)(e.a,{href:"#user-content-fnref-2","data-footnote-backref":"","aria-label":"Back to reference 2",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n",(0,t.jsxs)(e.li,{id:"user-content-fn-3",children:["\n",(0,t.jsxs)(e.p,{children:["W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo,\nHigh-throughput combinatorial database of electronic band structures for\ninorganic scintillator materials., ACS Combinatorial Science. (2011)\n",(0,t.jsx)(e.a,{href:"https://doi.org/10.1021/co200012w",children:"https://doi.org/10.1021/co200012w"}),". ",(0,t.jsx)(e.a,{href:"#user-content-fnref-3","data-footnote-backref":"","aria-label":"Back to reference 3",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n"]}),"\n"]})]})}function f(n={}){const{wrapper:e}={...(0,a.R)(),...n.components};return e?(0,t.jsx)(e,{...n,children:(0,t.jsx)(m,{...n})}):m(n)}},5234:(n,e,s)=>{s.d(e,{A:()=>t});const t=s.p+"assets/images/silicon-bands-56f3d9af6b5d86ba5da780cbf6801b4a.png"},6275:(n,e,s)=>{s.d(e,{A:()=>t});const t=s.p+"assets/images/silicon-bands-a1a2786319101829eb5f78f018f412a4.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[4366],{6649:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>p,contentTitle:()=>d,default:()=>f,frontMatter:()=>c,metadata:()=>h,toc:()=>u});var t=s(4848),a=s(8453),i=s(1432);const o="&CONTROL\n calculation = 'scf',\n restart_mode = 'from_scratch',\n prefix = 'silicon',\n outdir = './tmp/'\n pseudo_dir = '../pseudos/'\n verbosity = 'high'\n/\n\n&SYSTEM\n ibrav = 2,\n celldm(1) = 10.2076,\n nat = 2,\n ntyp = 1,\n ecutwfc = 50,\n ecutrho = 400,\n nbnd = 8,\n! occupations = 'smearing',\n! smearing = 'gaussian',\n! degauss = 0.005\n/\n\n&ELECTRONS\n conv_thr = 1e-8,\n mixing_beta = 0.6\n/\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 8 8 8 0 0 0\n",r="&control\n calculation = 'bands',\n restart_mode = 'from_scratch',\n prefix = 'silicon',\n outdir = './tmp/'\n pseudo_dir = '../pseudos/'\n verbosity = 'high'\n/\n\n&system\n ibrav = 2,\n celldm(1) = 10.2076,\n nat = 2,\n ntyp = 1,\n ecutwfc = 50,\n ecutrho = 400,\n nbnd = 8\n /\n\n&electrons\n conv_thr = 1e-8,\n mixing_beta = 0.6\n /\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.00 0.00 0.00\n Si 0.25 0.25 0.25\n\nK_POINTS {crystal_b}\n5\n 0.0000 0.5000 0.0000 20 !L\n 0.0000 0.0000 0.0000 30 !G\n -0.500 0.0000 -0.500 10 !X\n -0.375 0.2500 -0.375 30 !U\n 0.0000 0.0000 0.0000 20 !G\n",l="&BANDS\n prefix = 'silicon'\n outdir = './tmp/'\n filband = 'si_bands.dat'\n/\n",c={title:"Bandstructure Calculation",sidebar_label:"Bandstructure"},d=void 0,h={id:"hands-on/bands",title:"Bandstructure Calculation",description:"Before we can run bands calculation, we need to perform single-point [self",source:"@site/docs/hands-on/bands.mdx",sourceDirName:"hands-on",slug:"/hands-on/bands",permalink:"/espresso/hands-on/bands",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/bands.mdx",tags:[],version:"current",frontMatter:{title:"Bandstructure Calculation",sidebar_label:"Bandstructure"},sidebar:"docs",previous:{title:"DOS calculation",permalink:"/espresso/hands-on/dos"},next:{title:"Al (metal)",permalink:"/espresso/hands-on/aluminum"}},p={},u=[{value:"Note on bandgap",id:"note-on-bandgap",level:2},{value:"Resources",id:"resources",level:2}];function m(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",ol:"ol",p:"p",pre:"pre",section:"section",semantics:"semantics",span:"span",strong:"strong",sup:"sup",ul:"ul",...(0,a.R)(),...n.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsxs)(e.p,{children:["Before we can run ",(0,t.jsx)(e.code,{children:"bands"})," calculation, we need to perform single-point ",(0,t.jsx)(e.a,{href:"scf",children:"self\nconsistent field calculation"}),". We have our input ",(0,t.jsx)(e.code,{children:"scf"})," file with some new\nparameters:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pw.scf.silicon_bands.in",showLineNumbers:!0,children:o}),"\n",(0,t.jsxs)(e.p,{children:["Run the ",(0,t.jsx)(e.code,{children:"scf"})," calculation:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.scf.silicon_bands.in > pw.scf.silicon_bands.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["Next step is our band calculation (non-self consistent field) calculation. The\n",(0,t.jsx)(e.code,{children:"bands"})," calculation is ",(0,t.jsx)(e.em,{children:"non self-consistent"})," and reads/uses the ground state\nelectron density, Hartree, exchange and correlation potentials obtained in the\nprevious step (scf calculation). In case of non self-consistent calculation, the\n",(0,t.jsx)(e.strong,{children:"pw.x"})," program determines the Kohn-Sham eigenfunction and eigenvalues without\nupdating Kohn-Sham Hamiltonian at every iteration. We need to specify the\nk-points for which we want to calculate the eigenvalues. You may use the\n",(0,t.jsx)(e.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"See-K-path tool by materials cloud"})," to visualize the K-path. We\ncan specify ",(0,t.jsx)(e.code,{children:"nbnd"}),", by default it calculates half the number of valence\nelectrons, i.e., only the occupied ground state bands. Usually we are interested\nalso in the unoccupied bands above the Fermi energy. Number of occupied bands\ncan be found in the ",(0,t.jsx)(e.code,{children:"scf"})," output as number of Kohn-Sham states. Below is a\nsample input file for the band calculation:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pw.bands.silicon.in",showLineNumbers:!0,children:r}),"\n",(0,t.jsxs)(e.p,{children:["Run ",(0,t.jsx)(e.code,{children:"pw.x"})," with ",(0,t.jsx)(e.code,{children:"bands"})," calculation input file:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.bands.silicon.in > pw.bands.silicon.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["After the bands calculation is performed, we need some postprocessing using\n",(0,t.jsx)(e.code,{children:"bands.x"})," utility in order to obtain the data in more usable format. Input file\nfor ",(0,t.jsx)(e.code,{children:"bands.x"})," postprocessing:"]}),"\n","\n",(0,t.jsx)(i.A,{language:"bash",title:"src/silicon/pp.bands.silicon.in",showLineNumbers:!0,children:l}),"\n",(0,t.jsxs)(e.p,{children:["Run ",(0,t.jsx)(e.code,{children:"bands.x"})," from post processing (PP) module:"]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:"bands.x < pp.bands.silicon.in > pp.bands.silicon.out\n"})}),"\n",(0,t.jsxs)(e.p,{children:["Finally, we run ",(0,t.jsx)(e.code,{children:"plotband.x"})," to visualize bandstructure. We can either run it\ninteractively (as described below) or provide an input file. In order to run\ninteractively, type ",(0,t.jsx)(e.code,{children:"plotband.x"})," in your terminal."]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-bash",children:" Input file > si_bands.dat\nReading 8 bands at 91 k-points\nRange: -5.8300 16.3420eV Emin, Emax > -6, 16\nhigh-symmetry point: 0.5000 0.5000 0.5000 x coordinate 0.0000\nhigh-symmetry point: 0.0000 0.0000 0.0000 x coordinate 0.8660\nhigh-symmetry point: 1.0000 0.0000 0.0000 x coordinate 1.8660\nhigh-symmetry point: 1.0000 0.2500 0.2500 x coordinate 2.2196\nhigh-symmetry point: 0.0000 0.0000 0.0000 x coordinate 3.2802\noutput file (gnuplot/xmgr) > si_bands.gnuplot\nbands in gnuplot/xmgr format written to file si_bands.gnuplot\n\n\noutput file (ps) > si_bands.ps\nEfermi > 6.6416\ndeltaE, reference E (for tics) 4, 0\nbands in PostScript format written to file si_bands.ps\n"})}),"\n",(0,t.jsxs)(e.p,{children:["You will have ",(0,t.jsx)(e.code,{children:"si_bands.ps"})," with band diagram. Alternatively, you can use your\nfavorite plotting program to make the plots. Below is an example of using Python\nmatplotlib."]}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-python",metastring:'title="notebooks/si-bands.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\n\nplt.rcParams[\"figure.dpi\"]=150\nplt.rcParams[\"figure.facecolor\"]=\"white\"\nplt.rcParams[\"figure.figsize\"]=(8, 6)\n\n# load data\ndata = np.loadtxt('../src/silicon/si_bands.dat.gnu')\n\nk = np.unique(data[:, 0])\nbands = np.reshape(data[:, 1], (-1, len(k)))\n\nfor band in range(len(bands)):\n plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k')\nplt.xlim(min(k), max(k))\n\n# Fermi energy\nplt.axhline(6.6416, linestyle=(0, (5, 5)), linewidth=0.75, color='k', alpha=0.5)\n# High symmetry k-points (check bands_pp.out)\nplt.axvline(0.8660, linewidth=0.75, color='k', alpha=0.5)\nplt.axvline(1.8660, linewidth=0.75, color='k', alpha=0.5)\nplt.axvline(2.2196, linewidth=0.75, color='k', alpha=0.5)\n# text labels\nplt.xticks(ticks= [0, 0.8660, 1.8660, 2.2196, 3.2802], \\\n labels=['L', '$\\Gamma$', 'X', 'U', '$\\Gamma$'])\nplt.ylabel(\"Energy (eV)\")\nplt.text(2.3, 5.6, 'Fermi energy', fontsize= small)\nplt.show()\n"})}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:s(6275).A}),(0,t.jsx)("img",{src:s(5234).A,alt:"silicon-bands"})]}),"\n",(0,t.jsxs)(e.admonition,{type:"info",children:[(0,t.jsxs)(e.p,{children:["The ",(0,t.jsx)(e.code,{children:"k"})," values corresponding to high symmetry points (such as ",(0,t.jsxs)(e.span,{className:"katex",children:[(0,t.jsx)(e.span,{className:"katex-mathml",children:(0,t.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,t.jsxs)(e.semantics,{children:[(0,t.jsx)(e.mrow,{children:(0,t.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,t.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,t.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,t.jsxs)(e.span,{className:"base",children:[(0,t.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,t.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]}),", X, U, L)\nwhich we need to label in our band diagram, can be found in the post-processing\noutput file (",(0,t.jsx)(e.code,{children:"si_bands_pp.out"}),")."]}),(0,t.jsxs)(e.p,{children:["Bandgap value can be determined from the highest occupied, lowest unoccupied\nlevel values printed in ",(0,t.jsx)(e.code,{children:"scf"})," calculation output."]})]}),"\n",(0,t.jsx)(e.h2,{id:"note-on-bandgap",children:"Note on bandgap"}),"\n",(0,t.jsx)(e.p,{children:"Usually, band gaps computed using common exchange-correction functionals such as\nLDA or GGA are severely underestimated compared to actual experimental values.\nThis discrepancy is mainly due to (1) approximations used in the exchange\ncorrection functional and (2) a derivative discontinuity term, originating from\nthe density functional being discontinuous with the total number of electrons in\nthe system. The second contribution is larger contributor to the error. It can\nbe partly addressed by a variety of techniques such as the GW approximation."}),"\n",(0,t.jsxs)(e.p,{children:["Strategies to improve band gap prediction at moderate to low computational cost\nnow been developed by several groups, including Chan and Ceder (delta-sol)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-1",id:"user-content-fnref-1","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"1"})}),",\nHeyd et al. (hybrid functionals)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-2",id:"user-content-fnref-2","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"2"})}),", and Setyawan et al. (empirical fits)",(0,t.jsx)(e.sup,{children:(0,t.jsx)(e.a,{href:"#user-content-fn-3",id:"user-content-fnref-3","data-footnote-ref":!0,"aria-describedby":"footnote-label",children:"3"})}),"."]}),"\n",(0,t.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,t.jsxs)(e.ul,{children:["\n",(0,t.jsx)(e.li,{children:(0,t.jsx)(e.a,{href:"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures",children:"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures"})}),"\n",(0,t.jsx)(e.li,{children:(0,t.jsx)(e.a,{href:"https://www.materialscloud.org/work/tools/seekpath",children:"See K-pat online tool"})}),"\n"]}),"\n","\n",(0,t.jsxs)(e.section,{"data-footnotes":!0,className:"footnotes",children:[(0,t.jsx)(e.h2,{className:"sr-only",id:"footnote-label",children:"Footnotes"}),"\n",(0,t.jsxs)(e.ol,{children:["\n",(0,t.jsxs)(e.li,{id:"user-content-fn-1",children:["\n",(0,t.jsxs)(e.p,{children:["M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical\nReview Letters 19 (2010) ",(0,t.jsx)(e.a,{href:"https://doi.org/10.1103/PhysRevLett.105.196403",children:"https://doi.org/10.1103/PhysRevLett.105.196403"})," ",(0,t.jsx)(e.a,{href:"#user-content-fnref-1","data-footnote-backref":"","aria-label":"Back to reference 1",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n",(0,t.jsxs)(e.li,{id:"user-content-fn-2",children:["\n",(0,t.jsxs)(e.p,{children:["J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and\nlattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid\nfunctional, Journal of Chemical Physics 123 (2005)\n",(0,t.jsx)(e.a,{href:"https://doi.org/10.1063/1.2085170",children:"https://doi.org/10.1063/1.2085170"})," ",(0,t.jsx)(e.a,{href:"#user-content-fnref-2","data-footnote-backref":"","aria-label":"Back to reference 2",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n",(0,t.jsxs)(e.li,{id:"user-content-fn-3",children:["\n",(0,t.jsxs)(e.p,{children:["W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo,\nHigh-throughput combinatorial database of electronic band structures for\ninorganic scintillator materials., ACS Combinatorial Science. (2011)\n",(0,t.jsx)(e.a,{href:"https://doi.org/10.1021/co200012w",children:"https://doi.org/10.1021/co200012w"}),". ",(0,t.jsx)(e.a,{href:"#user-content-fnref-3","data-footnote-backref":"","aria-label":"Back to reference 3",className:"data-footnote-backref",children:"\u21a9"})]}),"\n"]}),"\n"]}),"\n"]})]})}function f(n={}){const{wrapper:e}={...(0,a.R)(),...n.components};return e?(0,t.jsx)(e,{...n,children:(0,t.jsx)(m,{...n})}):m(n)}},5234:(n,e,s)=>{s.d(e,{A:()=>t});const t=s.p+"assets/images/silicon-bands-56f3d9af6b5d86ba5da780cbf6801b4a.png"},6275:(n,e,s)=>{s.d(e,{A:()=>t});const t=s.p+"assets/images/silicon-bands-a1a2786319101829eb5f78f018f412a4.webp"}}]); \ No newline at end of file diff --git a/assets/js/8d13118e.ba344cb2.js b/assets/js/8d13118e.8adda61d.js similarity index 99% rename from assets/js/8d13118e.ba344cb2.js rename to assets/js/8d13118e.8adda61d.js index 40d16150..0509e226 100644 --- a/assets/js/8d13118e.ba344cb2.js +++ b/assets/js/8d13118e.8adda61d.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[7844],{8764:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>f,contentTitle:()=>h,default:()=>x,frontMatter:()=>p,metadata:()=>m,toc:()=>g});var a=s(4848),t=s(8453),i=s(1432);const l="&CONTROL\n calculation= 'vc-relax',\n prefix= 'al',\n outdir= '/tmp/'\n pseudo_dir = '../pseudos/'\n etot_conv_thr= 1e-6,\n forc_conv_thr= 1e-5\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1)= 7.652,\n nat= 1,\n ntyp= 1,\n ecutwfc = 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\n&IONS\n/\n\n&CELL\n cell_dofree= 'ibrav'\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 10 10 10 0 0 0\n",r="&CONTROL\n calculation= 'scf',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 10 10 10 0 0 0\n",c="&CONTROL\n calculation= 'nscf',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 40 40 40 0 0 0\n",o="&DOS\n prefix= 'al',\n outdir= '/tmp/',\n fildos= 'al_dos.dat',\n emin= -10,\n emax= 35\n/\n",d="&CONTROL\n calculation= 'bands',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS {crystal_b}\n5\n 00.000 0.500 00.000 20 !L\n 00.000 0.000 00.000 30 !G\n -0.500 0.000 -0.500 10 !X\n -0.375 0.250 -0.375 30 !U\n 00.000 0.000 00.000 20 !G\n",u="&BANDS\n prefix = 'al'\n outdir = '/tmp/'\n filband = 'al_bands.dat'\n/\n",p={title:"DOS and bandstructure for Aluminum (metal)",sidebar_label:"Al (metal)"},h=void 0,m={id:"hands-on/aluminum",title:"DOS and bandstructure for Aluminum (metal)",description:"Variable cell relaxation",source:"@site/docs/hands-on/aluminum.mdx",sourceDirName:"hands-on",slug:"/hands-on/aluminum",permalink:"/espresso/hands-on/aluminum",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/aluminum.mdx",tags:[],version:"current",frontMatter:{title:"DOS and bandstructure for Aluminum (metal)",sidebar_label:"Al (metal)"},sidebar:"docs",previous:{title:"Bandstructure",permalink:"/espresso/hands-on/bands"},next:{title:"P-DOS",permalink:"/espresso/hands-on/pdos"}},f={},g=[{value:"Variable cell relaxation",id:"variable-cell-relaxation",level:2},{value:"Self consistent field (SCF) calculation",id:"self-consistent-field-scf-calculation",level:2},{value:"Non-self consistent field calculation",id:"non-self-consistent-field-calculation",level:2},{value:"Density of states",id:"density-of-states",level:2},{value:"Bandstructure calculation",id:"bandstructure-calculation",level:2},{value:"Importance of smearing in convergence",id:"importance-of-smearing-in-convergence",level:2}];function b(n){const e={code:"code",em:"em",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,t.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsx)(e.h2,{id:"variable-cell-relaxation",children:"Variable cell relaxation"}),"\n",(0,a.jsx)(e.p,{children:"First we are going to relax the cell and choose appropriate lattice constant for\nour chosen pseudo potential. In case of metals, it is important to provide\nsmearing parameters in the input file."}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_vc_relax.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsxs)(e.p,{children:["We run ",(0,a.jsx)(e.code,{children:"pw.x"})," to perform variable cell relaxation calculation:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_vc_relax.in > al_vc_relax.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Now you may open the output file in ",(0,a.jsx)(e.strong,{children:"vi"})," editor and invoke search by pressing\n",(0,a.jsx)(e.code,{children:"/"})," and type ",(0,a.jsx)(e.em,{children:"Final enthalpy"})," You will find the final lattice parameters below\nit."]}),"\n",(0,a.jsx)(e.h2,{id:"self-consistent-field-scf-calculation",children:"Self consistent field (SCF) calculation"}),"\n",(0,a.jsx)(e.p,{children:"We obtain relaxed lattice constant = 7.652 * 0.498611683 / 0.5 = 7.63075 Bohr.\nWe will use this value for our next step, self consistent calculation."}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_scf.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsx)(e.p,{children:"We run our self consistent calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_scf.in > al_scf.out\n"})}),"\n",(0,a.jsx)(e.h2,{id:"non-self-consistent-field-calculation",children:"Non-self consistent field calculation"}),"\n",(0,a.jsx)(e.p,{children:"Inspect the output file, and let's proceed to next step non-self consistent\ncalculation:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_nscf.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsxs)(e.p,{children:["Note the changes in input file. The calculation changed to ",(0,a.jsx)(e.code,{children:"nscf"})," and we are now\nusing a higher number of k-points grid."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_nscf.in > al_nscf.out\n"})}),"\n",(0,a.jsx)(e.h2,{id:"density-of-states",children:"Density of states"}),"\n",(0,a.jsx)(e.p,{children:"Next we go ahead with our density of states calculation:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_dos.in",showLineNumbers:!0,children:o}),"\n",(0,a.jsxs)(e.p,{children:["We run ",(0,a.jsx)(e.code,{children:"dos.x"})," with DOS inputs:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"dos.x < al_dos.in > al_dos.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Note from our ",(0,a.jsx)(e.code,{children:"al_nscf.out"})," that our Fermi energy is at 7.9421 eV. We plot our\ndensity of states:"]}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(8251).A}),(0,a.jsx)("img",{src:s(9962).A,alt:"al-dos"})]}),"\n",(0,a.jsx)(e.h2,{id:"bandstructure-calculation",children:"Bandstructure calculation"}),"\n",(0,a.jsx)(e.p,{children:"We prepare the input file the same as the case of our previous example silicon:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_bands.in",showLineNumbers:!0,children:d}),"\n",(0,a.jsxs)(e.p,{children:["Followed by run ",(0,a.jsx)(e.code,{children:"pw.x"}),":"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_bands.in > al_bands.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"Now we proceed with post-processing:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_bands_pp.in",showLineNumbers:!0,children:u}),"\n",(0,a.jsxs)(e.p,{children:["And run ",(0,a.jsx)(e.code,{children:"bands.x"}),":"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"bands.x < al_bands_pp.in > al_bands_pp.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"We obtain the following bandstructure:"}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(5581).A}),(0,a.jsx)("img",{src:s(1360).A,alt:"al-bands"})]}),"\n",(0,a.jsx)(e.h2,{id:"importance-of-smearing-in-convergence",children:"Importance of smearing in convergence"}),"\n",(0,a.jsx)(e.p,{children:"Smearing is a technique used for suppressing unstable electron density in the\ncalculation of metals. Such a problem occurs in metals (and semimetals) because\nthe valence bands that cross Fermi level are partially occupied. Due to\nnumerical accuracy, the electrons may occupy the unoccupied states during some\niterations, making the algorithm unstable. In order to stablize the algorithm\nwithout using excessive number of k-points, smearing technique is used, which\nreplaces the occupation number (either 0 or 1) is replaced by a smoothly varying\nfunction of energy. Such a smearing function could be Fermi Dirac distribution,\ninstead of a step function (T = 0 K), we can use the finite temperature form."}),"\n",(0,a.jsx)(e.p,{children:"Below we will test the convergence using PWTK against the number of k-points,\nthree different smearing functions (Gauss, Methfessel-Paxton, and\nMarzari-Vanderbilt), and for various smearing values."}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pwtk al.degauss.pwtk\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(3079).A}),(0,a.jsx)("img",{src:s(8734).A,alt:"al-smearing"})]}),"\n",(0,a.jsxs)(e.p,{children:["We see that the ",(0,a.jsx)(e.code,{children:"m-v"})," and ",(0,a.jsx)(e.code,{children:"m-p"})," broadening allow for faster and smother\nconvergence while depending less on ",(0,a.jsx)(e.code,{children:"degauss"})," value than Gaussian broadening.\nThe number suffix next to the legend labels are number of uniform k-points in\nMonkhorst-Plank grid."]})]})}function x(n={}){const{wrapper:e}={...(0,t.R)(),...n.components};return e?(0,a.jsx)(e,{...n,children:(0,a.jsx)(b,{...n})}):b(n)}},1360:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-bands-80a59f979dc76cc93a8a3f0098e552db.png"},5581:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-bands-263ee17f888fd759e02a3ccd0fb26952.webp"},9962:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-dos-1a1a20854f28a36239168339111e6b9e.png"},8251:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-dos-2de0749d0dfd3663a87c46f12a56f226.webp"},8734:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-smearing-5ed252d6a01bf986d7bbebf6226b6feb.png"},3079:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/al-smearing-b0cd82054a83bde2e60e5d7f57866f10.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[7844],{8340:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>f,contentTitle:()=>h,default:()=>x,frontMatter:()=>p,metadata:()=>m,toc:()=>g});var a=s(4848),t=s(8453),i=s(1432);const l="&CONTROL\n calculation= 'vc-relax',\n prefix= 'al',\n outdir= '/tmp/'\n pseudo_dir = '../pseudos/'\n etot_conv_thr= 1e-6,\n forc_conv_thr= 1e-5\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1)= 7.652,\n nat= 1,\n ntyp= 1,\n ecutwfc = 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\n&IONS\n/\n\n&CELL\n cell_dofree= 'ibrav'\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 10 10 10 0 0 0\n",r="&CONTROL\n calculation= 'scf',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 10 10 10 0 0 0\n",c="&CONTROL\n calculation= 'nscf',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS (automatic)\n 40 40 40 0 0 0\n",o="&DOS\n prefix= 'al',\n outdir= '/tmp/',\n fildos= 'al_dos.dat',\n emin= -10,\n emax= 35\n/\n",d="&CONTROL\n calculation= 'bands',\n restart_mode= 'from_scratch',\n prefix= 'al',\n outdir= '/tmp/',\n pseudo_dir= '../pseudos/'\n/\n\n&SYSTEM\n ibrav= 2,\n celldm(1) = 7.63075,\n nat= 1,\n ntyp= 1,\n ecutwfc= 50,\n ecutrho= 500,\n occupations= 'smearing',\n smearing= 'gaussian',\n degauss= 0.01\n/\n\n&ELECTRONS\n conv_thr= 1e-8\n/\n\nATOMIC_SPECIES\n Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF\n\nATOMIC_POSITIONS (alat)\n Al 0.00 0.00 0.00\n\nK_POINTS {crystal_b}\n5\n 00.000 0.500 00.000 20 !L\n 00.000 0.000 00.000 30 !G\n -0.500 0.000 -0.500 10 !X\n -0.375 0.250 -0.375 30 !U\n 00.000 0.000 00.000 20 !G\n",u="&BANDS\n prefix = 'al'\n outdir = '/tmp/'\n filband = 'al_bands.dat'\n/\n",p={title:"DOS and bandstructure for Aluminum (metal)",sidebar_label:"Al (metal)"},h=void 0,m={id:"hands-on/aluminum",title:"DOS and bandstructure for Aluminum (metal)",description:"Variable cell relaxation",source:"@site/docs/hands-on/aluminum.mdx",sourceDirName:"hands-on",slug:"/hands-on/aluminum",permalink:"/espresso/hands-on/aluminum",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/aluminum.mdx",tags:[],version:"current",frontMatter:{title:"DOS and bandstructure for Aluminum (metal)",sidebar_label:"Al (metal)"},sidebar:"docs",previous:{title:"Bandstructure",permalink:"/espresso/hands-on/bands"},next:{title:"P-DOS",permalink:"/espresso/hands-on/pdos"}},f={},g=[{value:"Variable cell relaxation",id:"variable-cell-relaxation",level:2},{value:"Self consistent field (SCF) calculation",id:"self-consistent-field-scf-calculation",level:2},{value:"Non-self consistent field calculation",id:"non-self-consistent-field-calculation",level:2},{value:"Density of states",id:"density-of-states",level:2},{value:"Bandstructure calculation",id:"bandstructure-calculation",level:2},{value:"Importance of smearing in convergence",id:"importance-of-smearing-in-convergence",level:2}];function b(n){const e={code:"code",em:"em",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,t.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsx)(e.h2,{id:"variable-cell-relaxation",children:"Variable cell relaxation"}),"\n",(0,a.jsx)(e.p,{children:"First we are going to relax the cell and choose appropriate lattice constant for\nour chosen pseudo potential. In case of metals, it is important to provide\nsmearing parameters in the input file."}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_vc_relax.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsxs)(e.p,{children:["We run ",(0,a.jsx)(e.code,{children:"pw.x"})," to perform variable cell relaxation calculation:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_vc_relax.in > al_vc_relax.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Now you may open the output file in ",(0,a.jsx)(e.strong,{children:"vi"})," editor and invoke search by pressing\n",(0,a.jsx)(e.code,{children:"/"})," and type ",(0,a.jsx)(e.em,{children:"Final enthalpy"})," You will find the final lattice parameters below\nit."]}),"\n",(0,a.jsx)(e.h2,{id:"self-consistent-field-scf-calculation",children:"Self consistent field (SCF) calculation"}),"\n",(0,a.jsx)(e.p,{children:"We obtain relaxed lattice constant = 7.652 * 0.498611683 / 0.5 = 7.63075 Bohr.\nWe will use this value for our next step, self consistent calculation."}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_scf.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsx)(e.p,{children:"We run our self consistent calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_scf.in > al_scf.out\n"})}),"\n",(0,a.jsx)(e.h2,{id:"non-self-consistent-field-calculation",children:"Non-self consistent field calculation"}),"\n",(0,a.jsx)(e.p,{children:"Inspect the output file, and let's proceed to next step non-self consistent\ncalculation:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_nscf.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsxs)(e.p,{children:["Note the changes in input file. The calculation changed to ",(0,a.jsx)(e.code,{children:"nscf"})," and we are now\nusing a higher number of k-points grid."]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pw.x < al_nscf.in > al_nscf.out\n"})}),"\n",(0,a.jsx)(e.h2,{id:"density-of-states",children:"Density of states"}),"\n",(0,a.jsx)(e.p,{children:"Next we go ahead with our density of states calculation:"}),"\n","\n",(0,a.jsx)(i.A,{language:"bash",title:"src/al/al_dos.in",showLineNumbers:!0,children:o}),"\n",(0,a.jsxs)(e.p,{children:["We run ",(0,a.jsx)(e.code,{children:"dos.x"})," with DOS inputs:"]}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"dos.x < al_dos.in > al_dos.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["Note from our ",(0,a.jsx)(e.code,{children:"al_nscf.out"})," that our Fermi energy is at 7.9421 eV. 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Such a problem occurs in metals (and semimetals) because\nthe valence bands that cross Fermi level are partially occupied. Due to\nnumerical accuracy, the electrons may occupy the unoccupied states during some\niterations, making the algorithm unstable. In order to stablize the algorithm\nwithout using excessive number of k-points, smearing technique is used, which\nreplaces the occupation number (either 0 or 1) is replaced by a smoothly varying\nfunction of energy. Such a smearing function could be Fermi Dirac distribution,\ninstead of a step function (T = 0 K), we can use the finite temperature form."}),"\n",(0,a.jsx)(e.p,{children:"Below we will test the convergence using PWTK against the number of k-points,\nthree different smearing functions (Gauss, Methfessel-Paxton, and\nMarzari-Vanderbilt), and for various smearing values."}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"pwtk al.degauss.pwtk\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(3079).A}),(0,a.jsx)("img",{src:s(8734).A,alt:"al-smearing"})]}),"\n",(0,a.jsxs)(e.p,{children:["We see that the ",(0,a.jsx)(e.code,{children:"m-v"})," and ",(0,a.jsx)(e.code,{children:"m-p"})," broadening allow for faster and smother\nconvergence while depending less on ",(0,a.jsx)(e.code,{children:"degauss"})," value than Gaussian broadening.\nThe number suffix next to the legend labels are number of uniform k-points 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",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"J"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"J"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.09618em"},children:"J"})]})})]})," represents on-site\nexchange interaction. Number of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"J"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"J"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.09618em"},children:"J"})]})})]})," terms depends on the manifold of localized\nelectrons. For ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"p"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"p"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"p"})]})})]}),", we have 1; for ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"d"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"d"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"d"})]})})]}),", we have 2; and for ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"f"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"f"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10764em"},children:"f"})]})})]}),", we have 3\nterms."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-fortran",children:" ...\n lda_plus_u = .TRUE.\n lda_plus_u_kind = 1\n Hubbard_u(i) = U\n Hubbard_J(k, i) = J_{ki}\n ...\n"})}),"\n",(0,n.jsx)(e.admonition,{title:"COMMON ERRORS",type:"danger",children:(0,n.jsxs)(e.p,{children:["If you add ",(0,n.jsx)(e.code,{children:"Hubbard_u"})," for elements that is not implemented to have ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]}),' term\nin QE, you might see a "pseudopotential not yet inserted" error.']})}),"\n",(0,n.jsx)(e.h2,{id:"changes-to-input-syntax-in-v71",children:"Changes to input syntax in v7.1"}),"\n",(0,n.jsxs)(e.p,{children:["Starting from Quantum Espresso version ",(0,n.jsx)(e.code,{children:"7.1"}),", there are changes to input syntax\nfor DFT+U calculations. In the new version, instead of defining the necessary\nDFT+U parameters, now there is a new Hubbard card."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-diff",children:"&system\n...\n- lda_plus_u = .true.,\n- lda_plus_u_kind = 0,\n- U_projection_type = 'atomic',\n- Hubbard_U(1) = 4.6\n- Hubbard_U(2) = 4.6\n...\n/\n\n+ HUBBARD (ortho-atomic)\n+ U Fe1-3d 4.6\n+ U Fe2-3d 4.6\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Please refer to the ",(0,n.jsx)("a",{target:"_blank",href:a(3668).A,children:"\nqe-x.x/Doc/Hubbard_input.pdf"})," for details."]}),"\n",(0,n.jsx)(e.h2,{id:"dft-calculation-for-feo",children:"DFT calculation for FeO"}),"\n",(0,n.jsx)(e.p,{children:"We will first perform the standard DFT calculation."}),"\n",(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsx)(e.li,{children:"Perform the SCF calculation:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x -in feo_scf.in > feo_scf.out\n"})}),"\n",(0,n.jsxs)(e.ol,{start:"2",children:["\n",(0,n.jsx)(e.li,{children:"Perform NSCF calculation with denser k-grid:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x -in feo_nscf.in > feo_nscf.out\n"})}),"\n",(0,n.jsxs)(e.ol,{start:"3",children:["\n",(0,n.jsx)(e.li,{children:"Perform P-DOS calculation:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"projwfc.x -in feo_projwfc.in > feo_projwfc.out\n"})}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(6901).A}),(0,n.jsx)("img",{src:a(3352).A,alt:"feo-pdos-dft"})]}),"\n",(0,n.jsx)(e.p,{children:"This gives us metallic density of states. In practice we get insulating FeO."}),"\n",(0,n.jsx)(e.h2,{id:"calculating-hubbard-u",children:"Calculating Hubbard U"}),"\n","\n",(0,n.jsx)(i.A,{language:"bash",title:"src/FeO/feo_hp.in",showLineNumbers:!0,children:t}),"\n",(0,n.jsxs)(e.p,{children:["Perform a linear-response calculation using ",(0,n.jsx)(e.code,{children:"hp.x"})," program:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"hp.x -in feo_hp.in > feo_hp.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Check the file ",(0,n.jsx)(e.code,{children:"FeO.Hubbard_parameters.dat"}),"."]}),"\n",(0,n.jsx)(e.admonition,{type:"info",children:(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["We need to check the convergence against q-mesh (as well as k-mesh in SCF\ncalculation). Here ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mn,{children:"1"}),(0,n.jsx)(e.mo,{children:"\xd7"}),(0,n.jsx)(e.mn,{children:"1"}),(0,n.jsx)(e.mo,{children:"\xd7"}),(0,n.jsx)(e.mn,{children:"1"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"1\\times 1\\times 1"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\xd7"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\xd7"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6444em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"})]})]})]})," mesh is used. ",(0,n.jsx)(e.strong,{children:"Important:"})," ",(0,n.jsx)(e.code,{children:"lda_plus_u"}),"\nmust be set to ",(0,n.jsx)(e.code,{children:".true."})," during the SCF calculation, ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," may be set to zero."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["We can update the obtained ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value in our SCF calculation, and repeat\nlinear response calculation until we have reached self consistency in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["To go even further one can check the convergence of geometry during ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]}),"\nupdates."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["There is also inter-site Hubbard correction DFT+U+V calculation. The results\ncould be more closer to hybrid functionals like GW. The ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"V"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"V"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.22222em"},children:"V"})]})})]})," can also be\ncalculated using Quantum Espresso ",(0,n.jsx)(e.strong,{children:"hp.x"})," code."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Obtained value of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," depends on pseudopotential, Hubbard manifold (whether\natomic, ortho-atomic etc.)."]}),"\n"]}),"\n"]})}),"\n",(0,n.jsx)(e.admonition,{type:"danger",children:(0,n.jsxs)(e.p,{children:["The above ",(0,n.jsx)(e.strong,{children:"hp.x"})," code is not suitable for closed cell systems (e.g., fully\noccupied d-shell element), in such cases this linear response method gives\nunrealistically large ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value."]})}),"\n",(0,n.jsx)(e.h2,{id:"dftu-calculation",children:"DFT+U calculation"}),"\n",(0,n.jsxs)(e.p,{children:["We repeat the calculation after setting in the ",(0,n.jsx)(e.code,{children:"&SYSTEM"})," card:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"Hubbard_U(1) = 4.6\nHubbard_U(2) = 4.6\n"})}),"\n",(0,n.jsx)(e.p,{children:"We repeat the above calculation and plot the results. Now we find insulating\nground state."}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(6035).A}),(0,n.jsx)("img",{src:a(9746).A,alt:"feo-pdos-dft-u"})]}),"\n",(0,n.jsxs)(e.admonition,{type:"info",children:[(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.code,{children:"U_projection_type = 'ortho-atomic'"})," might give more realistic result than the\ndefault 'atomic'."]}),(0,n.jsxs)(e.p,{children:["When performing ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"D"}),(0,n.jsx)(e.mi,{children:"F"}),(0,n.jsx)(e.mi,{children:"T"}),(0,n.jsx)(e.mo,{children:"+"}),(0,n.jsx)(e.mi,{children:"U"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"DFT+U"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7667em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.02778em"},children:"D"}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"FT"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"+"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})]})]})," calculation, the ground state might get stuck in a\n",(0,n.jsx)(e.strong,{children:"local minimum"}),", in such cases we need to provide ",(0,n.jsx)(e.code,{children:"starting_ns_eigenvalue"})," to\nhelp calculation reach desired/actual ground state. Please see ",(0,n.jsx)("a",{target:"_blank",href:a(9028).A,children:"these slides"})," by\nDr. Iurii Timrov for a relevant example."]})]}),"\n",(0,n.jsx)(e.admonition,{type:"tip",children:(0,n.jsxs)(e.p,{children:["Here we have plotted the ",(0,n.jsx)(e.code,{children:"lpdos"})," (local density of states). If we want to know\nthe contribution of 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Also there arise important Lowdin charges information in the\n",(0,n.jsx)(e.code,{children:"feo_projwfc.out"})," file."]})}),"\n",(0,n.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,n.jsxs)(e.ul,{children:["\n",(0,n.jsx)(e.li,{children:(0,n.jsx)(e.a,{href:"https://youtu.be/34mHl0Iw2_E",children:"Hands-on DFT+U by Iurii Timrov and Matteo Cococcioni"})}),"\n",(0,n.jsx)(e.li,{children:(0,n.jsx)(e.a,{href:"https://youtu.be/64JKOF5lh2U",children:"Hubbard parameter calculation"})}),"\n"]})]})}function o(s={}){const{wrapper:e}={...(0,l.R)(),...s.components};return e?(0,n.jsx)(e,{...s,children:(0,n.jsx)(x,{...s})}):x(s)}},3668:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/files/Hubbard_input-63017ccb804e1b466d256baa695b3730.pdf"},9028:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/files/dft+u-Iurii-Timrov-5f6cc931c153910b3ba506e9f5f1b9d5.pdf"},9746:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/feo-pdos-dft-u-d58210bd11d47b5ecc4438af8e4f9edc.png"},6035:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/feo-pdos-dft-u-fdfc57f36bbc5581362a80ebe5cbfd13.webp"},3352:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/feo-pdos-dft-60b42000630f74847b2a7c07177f2f71.png"},6901:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/feo-pdos-dft-fe155af55cbcf7fc4b13ad54fd26b627.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[6605],{5253:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>m,contentTitle:()=>r,default:()=>o,frontMatter:()=>c,metadata:()=>h,toc:()=>d});var n=a(4848),l=a(8453),i=a(1432);const t="&inputhp\n prefix = 'FeO'\n outdir = './tmp/'\n nq1 = 1, nq2 = 1, nq3 = 1\n/\n",c={title:"DFT+U calculation",keywords:["DFT+U","Hubbard U calculation","DFT+U calculation in Quantum Espresso","LDA+U"]},r=void 0,h={id:"hands-on/dft-u",title:"DFT+U calculation",description:"Electronic structure for transition metals (with localized $$d$$ or $$f$$",source:"@site/docs/hands-on/dft-u.mdx",sourceDirName:"hands-on",slug:"/hands-on/dft-u",permalink:"/espresso/hands-on/dft-u",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/dft-u.mdx",tags:[],version:"current",frontMatter:{title:"DFT+U calculation",keywords:["DFT+U","Hubbard U calculation","DFT+U calculation in Quantum Espresso","LDA+U"]},sidebar:"docs",previous:{title:"Ni (spin pol. bands)",permalink:"/espresso/hands-on/ni"},next:{title:"Spin-Orbit Coupling",permalink:"/espresso/hands-on/soc"}},m={},d=[{value:"Changes to input syntax in v7.1",id:"changes-to-input-syntax-in-v71",level:2},{value:"DFT calculation for FeO",id:"dft-calculation-for-feo",level:2},{value:"Calculating Hubbard U",id:"calculating-hubbard-u",level:2},{value:"DFT+U calculation",id:"dftu-calculation",level:2},{value:"Resources",id:"resources",level:2}];function x(s){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h2:"h2",li:"li",math:"math",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",msub:"msub",msup:"msup",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,l.R)(),...s.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsxs)(e.p,{children:["Electronic structure for transition metals (with localized ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"d"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"d"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"d"})]})})]})," or ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"f"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"f"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10764em"},children:"f"})]})})]}),"\nelectrons) is not accurately described by standard DFT, and therefore the need\nfor DFT+U formulation."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-fortran",children:"&SYSTEM\n ...\n lda_plus_u = .TRUE.\n Hubbard_u(i) = 2.0\n ...\n/\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Here ",(0,n.jsx)(e.code,{children:"i"})," refers to the atomic index in the ",(0,n.jsx)(e.code,{children:"&ATOMIC_SPECIES"})," card corresponding\nto each ",(0,n.jsx)(e.code,{children:"ntyp"}),". 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",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"J"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"J"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.09618em"},children:"J"})]})})]})," represents on-site\nexchange interaction. Number of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"J"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"J"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.09618em"},children:"J"})]})})]})," terms depends on the manifold of localized\nelectrons. For ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"p"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"p"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"p"})]})})]}),", we have 1; for ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"d"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"d"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"d"})]})})]}),", we have 2; and for ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"f"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"f"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10764em"},children:"f"})]})})]}),", we have 3\nterms."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-fortran",children:" ...\n lda_plus_u = .TRUE.\n lda_plus_u_kind = 1\n Hubbard_u(i) = U\n Hubbard_J(k, i) = J_{ki}\n ...\n"})}),"\n",(0,n.jsx)(e.admonition,{title:"COMMON ERRORS",type:"danger",children:(0,n.jsxs)(e.p,{children:["If you add ",(0,n.jsx)(e.code,{children:"Hubbard_u"})," for elements that is not implemented to have ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]}),' term\nin QE, you might see a "pseudopotential not yet inserted" error.']})}),"\n",(0,n.jsx)(e.h2,{id:"changes-to-input-syntax-in-v71",children:"Changes to input syntax in v7.1"}),"\n",(0,n.jsxs)(e.p,{children:["Starting from Quantum Espresso version ",(0,n.jsx)(e.code,{children:"7.1"}),", there are changes to input syntax\nfor DFT+U calculations. In the new version, instead of defining the necessary\nDFT+U parameters, now there is a new Hubbard card."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-diff",children:"&system\n...\n- lda_plus_u = .true.,\n- lda_plus_u_kind = 0,\n- U_projection_type = 'atomic',\n- Hubbard_U(1) = 4.6\n- Hubbard_U(2) = 4.6\n...\n/\n\n+ HUBBARD (ortho-atomic)\n+ U Fe1-3d 4.6\n+ U Fe2-3d 4.6\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Please refer to the ",(0,n.jsx)("a",{target:"_blank",href:a(3668).A,children:"\nqe-x.x/Doc/Hubbard_input.pdf"})," for details."]}),"\n",(0,n.jsx)(e.h2,{id:"dft-calculation-for-feo",children:"DFT calculation for FeO"}),"\n",(0,n.jsx)(e.p,{children:"We will first perform the standard DFT calculation."}),"\n",(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsx)(e.li,{children:"Perform the SCF calculation:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x -in feo_scf.in > feo_scf.out\n"})}),"\n",(0,n.jsxs)(e.ol,{start:"2",children:["\n",(0,n.jsx)(e.li,{children:"Perform NSCF calculation with denser k-grid:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x -in feo_nscf.in > feo_nscf.out\n"})}),"\n",(0,n.jsxs)(e.ol,{start:"3",children:["\n",(0,n.jsx)(e.li,{children:"Perform P-DOS calculation:"}),"\n"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"projwfc.x -in feo_projwfc.in > feo_projwfc.out\n"})}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(6901).A}),(0,n.jsx)("img",{src:a(3352).A,alt:"feo-pdos-dft"})]}),"\n",(0,n.jsx)(e.p,{children:"This gives us metallic density of states. In practice we get insulating FeO."}),"\n",(0,n.jsx)(e.h2,{id:"calculating-hubbard-u",children:"Calculating Hubbard U"}),"\n","\n",(0,n.jsx)(i.A,{language:"bash",title:"src/FeO/feo_hp.in",showLineNumbers:!0,children:t}),"\n",(0,n.jsxs)(e.p,{children:["Perform a linear-response calculation using ",(0,n.jsx)(e.code,{children:"hp.x"})," program:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"hp.x -in feo_hp.in > feo_hp.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Check the file ",(0,n.jsx)(e.code,{children:"FeO.Hubbard_parameters.dat"}),"."]}),"\n",(0,n.jsx)(e.admonition,{type:"info",children:(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["We need to check the convergence against q-mesh (as well as k-mesh in SCF\ncalculation). Here ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mn,{children:"1"}),(0,n.jsx)(e.mo,{children:"\xd7"}),(0,n.jsx)(e.mn,{children:"1"}),(0,n.jsx)(e.mo,{children:"\xd7"}),(0,n.jsx)(e.mn,{children:"1"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"1\\times 1\\times 1"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\xd7"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\xd7"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6444em"}}),(0,n.jsx)(e.span,{className:"mord",children:"1"})]})]})]})," mesh is used. ",(0,n.jsx)(e.strong,{children:"Important:"})," ",(0,n.jsx)(e.code,{children:"lda_plus_u"}),"\nmust be set to ",(0,n.jsx)(e.code,{children:".true."})," during the SCF calculation, ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," may be set to zero."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["We can update the obtained ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value in our SCF calculation, and repeat\nlinear response calculation until we have reached self consistency in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["To go even further one can check the convergence of geometry during ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]}),"\nupdates."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["There is also inter-site Hubbard correction DFT+U+V calculation. The results\ncould be more closer to hybrid functionals like GW. The ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"V"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"V"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.22222em"},children:"V"})]})})]})," can also be\ncalculated using Quantum Espresso ",(0,n.jsx)(e.strong,{children:"hp.x"})," code."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Obtained value of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," depends on pseudopotential, Hubbard manifold (whether\natomic, ortho-atomic etc.)."]}),"\n"]}),"\n"]})}),"\n",(0,n.jsx)(e.admonition,{type:"danger",children:(0,n.jsxs)(e.p,{children:["The above ",(0,n.jsx)(e.strong,{children:"hp.x"})," code is not suitable for closed cell systems (e.g., fully\noccupied d-shell element), in such cases this linear response method gives\nunrealistically large ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"U"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"U"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})})]})," value."]})}),"\n",(0,n.jsx)(e.h2,{id:"dftu-calculation",children:"DFT+U calculation"}),"\n",(0,n.jsxs)(e.p,{children:["We repeat the calculation after setting in the ",(0,n.jsx)(e.code,{children:"&SYSTEM"})," card:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"Hubbard_U(1) = 4.6\nHubbard_U(2) = 4.6\n"})}),"\n",(0,n.jsx)(e.p,{children:"We repeat the above calculation and plot the results. Now we find insulating\nground state."}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(6035).A}),(0,n.jsx)("img",{src:a(9746).A,alt:"feo-pdos-dft-u"})]}),"\n",(0,n.jsxs)(e.admonition,{type:"info",children:[(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.code,{children:"U_projection_type = 'ortho-atomic'"})," might give more realistic result than the\ndefault 'atomic'."]}),(0,n.jsxs)(e.p,{children:["When performing ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"D"}),(0,n.jsx)(e.mi,{children:"F"}),(0,n.jsx)(e.mi,{children:"T"}),(0,n.jsx)(e.mo,{children:"+"}),(0,n.jsx)(e.mi,{children:"U"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"DFT+U"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.7667em",verticalAlign:"-0.0833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.02778em"},children:"D"}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"FT"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"+"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"U"})]})]})]})," calculation, the ground state might get stuck in a\n",(0,n.jsx)(e.strong,{children:"local minimum"}),", in such cases we need to provide ",(0,n.jsx)(e.code,{children:"starting_ns_eigenvalue"})," to\nhelp calculation reach desired/actual ground state. Please see ",(0,n.jsx)("a",{target:"_blank",href:a(9028).A,children:"these slides"})," by\nDr. Iurii Timrov for a relevant example."]})]}),"\n",(0,n.jsx)(e.admonition,{type:"tip",children:(0,n.jsxs)(e.p,{children:["Here we have plotted the ",(0,n.jsx)(e.code,{children:"lpdos"})," (local density of states). If we want to know\nthe contribution of 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G\n",d="&INPUT\n asr = 'crystal'\n flfrc = 'GaAs.fc'\n flfrq = 'GaAs.dos.freq'\n flvec = 'GaAs.dos.modes'\n dos = .true.\n fldos = 'GaAs.dos'\n nk1 = 25\n nk2 = 25\n nk3 = 25\n/\n",p={title:"Phonon dispersion",keywords:["phonon dispersion calculation in Quantum Espresso","Raman spectra"]},h=void 0,m={id:"hands-on/phonon",title:"Phonon dispersion",description:"In Quantum Espresso, phonon dispersion is calculated using ph.x program, which",source:"@site/docs/hands-on/phonon.mdx",sourceDirName:"hands-on",slug:"/hands-on/phonon",permalink:"/espresso/hands-on/phonon",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/phonon.mdx",tags:[],version:"current",frontMatter:{title:"Phonon dispersion",keywords:["phonon dispersion calculation in Quantum Espresso","Raman spectra"]},sidebar:"docs",previous:{title:"Fermi Surface",permalink:"/espresso/hands-on/fermi-surface"},next:{title:"Wannier method",permalink:"/espresso/hands-on/wannier"}},u={},x=[{value:"Phonon Density of States",id:"phonon-density-of-states",level:3},{value:"Resources",id:"resources",level:2}];function f(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h2:"h2",h3:"h3",li:"li",math:"math",mi:"mi",mrow:"mrow",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,o.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsxs)(e.p,{children:["In Quantum Espresso, phonon dispersion is calculated using ",(0,a.jsx)(e.code,{children:"ph.x"})," program, which\nis implementation of ",(0,a.jsx)(e.a,{href:"https://doi.org/10.1103/RevModPhys.73.515",children:"density functional perturbation theory (DFPT)"}),"."]}),"\n",(0,a.jsx)(e.p,{children:"Here are the steps for calculating phonon dispersion:"}),"\n",(0,a.jsxs)(e.p,{children:["(1) perform SCF calculation using ",(0,a.jsx)(e.code,{children:"pw.x"})]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/pw.scf.GaAs.in",showLineNumbers:!0,children:i}),"\n",(0,a.jsx)(e.p,{children:"We perform the SCF calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 pw.x -i pw.scf.GaAs.in > pw.scf.GaAs.out\n"})}),"\n",(0,a.jsx)(e.admonition,{type:"info",children:(0,a.jsxs)(e.ol,{children:["\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsx)(e.p,{children:"Usually higher energy cutoff values are used for phonon calculation to get\nbetter accuracy."}),"\n"]}),"\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:["In case of two dimensional systems, use ",(0,a.jsx)(e.code,{children:"assume_isolated = '2D'"})," in the\n",(0,a.jsx)(e.code,{children:"SYSTEM"})," namelist to avoid negative or imaginary acoustic frequencies near\n",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,a.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]})," point. Read more ",(0,a.jsx)(e.a,{href:"https://doi.org/10.1103/PhysRevB.96.075448",children:"here"}),"."]}),"\n"]}),"\n"]})}),"\n",(0,a.jsxs)(e.p,{children:["(2) calculate the dynamical matrix on a uniform mesh of q-points using ",(0,a.jsx)(e.code,{children:"ph.x"})]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/ph.GaAs.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsx)(e.p,{children:"Run the calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 ph.x -i ph.GaAs.in > ph.GaAs.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"The above calculation is computationally demanding. Our example calculation took\nabout a whole day on a 2.6 GHz quad core processor."}),"\n",(0,a.jsx)(e.admonition,{type:"info",children:(0,a.jsxs)(e.p,{children:["You can restart an interrupted ",(0,a.jsx)(e.code,{children:"ph.x"})," calculation with ",(0,a.jsx)(e.code,{children:"recover = .true."})," in the\n",(0,a.jsx)(e.code,{children:"INPUTPH"})," namelist. You can cleanly exit an ongoing calculation by creating an\nempty file with name ",(0,a.jsx)(e.code,{children:"{prefix}.EXIT"}),"."]})}),"\n",(0,a.jsxs)(e.p,{children:["(3) perform inverse Fourier transform of the dynamical matrix to obtain inverse\nFourier components in real space using ",(0,a.jsx)(e.code,{children:"q2r.x"}),". Below is our input file:"]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/q2r.GaAs.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 q2r.x -i q2r.GaAs.in > q2r.GaAs.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["(4) Finally, perform Fourier transformation of the real space components to get\nthe dynamical matrix at any q by using ",(0,a.jsx)(e.code,{children:"matdyn.x"}),"."]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/matdyn.GaAs.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"We can now plot the phonon dispersion of GaAs:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-py",metastring:'title="notebooks/GaAs-phonon.ipynb"',children:"import numpy as np\nimport matplotlib.pyplot as plt\n\ndata = np.loadtxt(\"../src/GaAs-phonon/GaAs.freq.gp\")\n\nnbands = data.shape[1] - 1\nfor band in range(nbands):\n plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k')\n# High symmetry k-points (check matdyn.GaAs.in)\nplt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \\\n labels=['L', '$\\Gamma$', 'X', 'U,K', '$\\Gamma$'])\nplt.ylabel(\"Frequency (cm$^{-1}$)\")\nplt.xlim(data[0, 0], data[-1, 0])\nplt.ylim(0, )\nplt.show()\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(9764).A}),(0,a.jsx)("img",{src:s(9431).A,alt:"GaAs-phonon",width:"600px"})]}),"\n",(0,a.jsx)(e.admonition,{type:"tip",children:(0,a.jsxs)(e.p,{children:["We may need to lower the value of ",(0,a.jsx)(e.code,{children:"conv_thr"})," in ",(0,a.jsx)(e.code,{children:"scf"})," calculation for more\naccurate result."]})}),"\n",(0,a.jsx)(e.h3,{id:"phonon-density-of-states",children:"Phonon Density of States"}),"\n",(0,a.jsx)(e.p,{children:"Input file for phonon DOS calculation:"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/matdyn.dos.GaAs.in",showLineNumbers:!0,children:d}),"\n",(0,a.jsx)(e.p,{children:"Plot phonon DOS:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-py",metastring:'title="notebooks/GaAs-phonon.ipynb"',children:"freq, dos, pdos_Ga, pdos_As = np.loadtxt(\"../src/GaAs-phonon/GaAs.dos\", unpack=True)\n\nplt.plot(freq, dos, c='k', lw=0.5, label='Total')\nplt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga')\nplt.plot(freq, pdos_As, c='r', lw=0.5, label='As')\nplt.xlabel('$\\\\Omega~(cm^{-1}$)')\nplt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)')\nplt.legend(frameon=False, loc='upper left')\nplt.xlim(freq[0], freq[-1])\nplt.show()\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(7111).A}),(0,a.jsx)("img",{src:s(2222).A,alt:"GaAs-phonon-dos",width:"600px"})]}),"\n",(0,a.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.a,{href:"https://indico.ictp.it/event/8301/other-view?view=ictptimetable",children:"School on Electron-Phonon Physics from First Principles (2018)"})," (",(0,a.jsx)(e.a,{href:"https://www.youtube.com/playlist?list=PLYc-eBoIpXTIboem6dKTYD1-1m0sMYnYz",children:"Video lectures on YouTube"}),")"]}),"\n",(0,a.jsx)(e.li,{children:(0,a.jsx)(e.a,{href:"https://github.com/nguyen-group/QE-SSP",children:"https://github.com/nguyen-group/QE-SSP"})}),"\n"]})]})}function j(n={}){const{wrapper:e}={...(0,o.R)(),...n.components};return e?(0,a.jsx)(e,{...n,children:(0,a.jsx)(f,{...n})}):f(n)}},2222:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-dos-5d5b89c131eaa671e47e9c22d45a5150.png"},7111:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-dos-28bb2abdbdc46635a19e09e6a68e08a3.webp"},9431:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-aca5fff6fe3b4fa9dbf8248d0076ba6d.png"},9764:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-2ef384622642cf14574a0f41201bd329.webp"}}]); \ No newline at end of file diff --git a/assets/js/ab8358d7.faa4cf76.js b/assets/js/ab8358d7.faa4cf76.js deleted file mode 100644 index 72bd83ab..00000000 --- a/assets/js/ab8358d7.faa4cf76.js +++ /dev/null @@ -1 +0,0 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[9501],{5241:(n,e,s)=>{s.r(e),s.d(e,{assets:()=>u,contentTitle:()=>h,default:()=>j,frontMatter:()=>p,metadata:()=>m,toc:()=>x});var a=s(4848),o=s(8453),t=s(1432);const i="&control\n calculation = 'scf'\n prefix = 'GaAs'\n pseudo_dir = '../pseudos/'\n outdir = './tmp/'\n verbosity = 'high'\n wf_collect = .true.\n/\n\n&system\n ibrav = 2\n celldm(1) = 10.861462\n nat = 2\n ntyp = 2\n ecutwfc = 80\n ecutrho = 640\n/\n\n&electrons\n mixing_mode = 'plain'\n mixing_beta = 0.7\n conv_thr = 1.0e-8\n/\n\nATOMIC_SPECIES\n Ga 69.723 Ga.pbe-dn-kjpaw_psl.1.0.0.UPF\n As 74.921595 As.nc.z_15.oncvpsp3.dojo.v4-std.upf\n\nATOMIC_POSITIONS\n Ga 0.00 0.00 0.00\n As 0.25 0.25 0.25\n\nK_POINTS {automatic}\n 8 8 8 0 0 0\n",r="&INPUTPH\n outdir = './tmp/'\n prefix = 'GaAs'\n tr2_ph = 1d-14\n ldisp = .true.\n! recover = .true.\n nq1 = 6\n nq2 = 6\n nq3 = 6\n fildyn = 'GaAs.dyn'\n/\n",l="&INPUT\n fildyn = 'GaAs.dyn'\n zasr = 'crystal'\n flfrc = 'GaAs.fc'\n/\n",c="&INPUT\n asr = 'crystal'\n flfrc = 'GaAs.fc'\n flfrq = 'GaAs.freq'\n flvec = 'GaAs.modes'\n! loto_2d = .true.\n q_in_band_form = .true.\n/\n5\n0.500 0.500 0.500 20 ! L\n0.000 0.000 0.000 20 ! G\n0.500 0.000 0.500 20 ! X\n0.375 0.375 0.750 20 ! K\n0.000 0.000 0.000 1 ! G\n",d="&INPUT\n asr = 'crystal'\n flfrc = 'GaAs.fc'\n flfrq = 'GaAs.dos.freq'\n flvec = 'GaAs.dos.modes'\n dos = .true.\n fldos = 'GaAs.dos'\n nk1 = 25\n nk2 = 25\n nk3 = 25\n/\n",p={title:"Phonon dispersion",keywords:["phonon dispersion calculation in Quantum Espresso","Raman spectra"]},h=void 0,m={id:"hands-on/phonon",title:"Phonon dispersion",description:"In Quantum Espresso, phonon dispersion is calculated using ph.x program, which",source:"@site/docs/hands-on/phonon.mdx",sourceDirName:"hands-on",slug:"/hands-on/phonon",permalink:"/espresso/hands-on/phonon",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/phonon.mdx",tags:[],version:"current",frontMatter:{title:"Phonon dispersion",keywords:["phonon dispersion calculation in Quantum Espresso","Raman spectra"]},sidebar:"docs",previous:{title:"Fermi Surface",permalink:"/espresso/hands-on/fermi-surface"},next:{title:"Wannier method",permalink:"/espresso/hands-on/wannier"}},u={},x=[{value:"Phonon Density of States",id:"phonon-density-of-states",level:3},{value:"Resources",id:"resources",level:2}];function f(n){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",h2:"h2",h3:"h3",li:"li",math:"math",mi:"mi",mrow:"mrow",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,o.R)(),...n.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsxs)(e.p,{children:["In Quantum Espresso, phonon dispersion is calculated using ",(0,a.jsx)(e.code,{children:"ph.x"})," program, which\nis implementation of ",(0,a.jsx)(e.a,{href:"https://doi.org/10.1103/RevModPhys.73.515",children:"density functional perturbation theory (DFPT)"}),"."]}),"\n",(0,a.jsx)(e.p,{children:"Here are the steps for calculating phonon dispersion:"}),"\n",(0,a.jsxs)(e.p,{children:["(1) perform SCF calculation using ",(0,a.jsx)(e.code,{children:"pw.x"})]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/pw.scf.GaAs.in",showLineNumbers:!0,children:i}),"\n",(0,a.jsx)(e.p,{children:"We perform the SCF calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 pw.x -i pw.scf.GaAs.in > pw.scf.GaAs.out\n"})}),"\n",(0,a.jsx)(e.admonition,{type:"info",children:(0,a.jsxs)(e.ol,{children:["\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsx)(e.p,{children:"Usually higher energy cutoff values are used for phonon calculation to get\nbetter accuracy."}),"\n"]}),"\n",(0,a.jsxs)(e.li,{children:["\n",(0,a.jsxs)(e.p,{children:["In case of two dimensional systems, use ",(0,a.jsx)(e.code,{children:"assume_isolated = '2D'"})," in the\n",(0,a.jsx)(e.code,{children:"SYSTEM"})," namelist to avoid negative or imaginary acoustic frequencies near\n",(0,a.jsxs)(e.span,{className:"katex",children:[(0,a.jsx)(e.span,{className:"katex-mathml",children:(0,a.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,a.jsxs)(e.semantics,{children:[(0,a.jsx)(e.mrow,{children:(0,a.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,a.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,a.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,a.jsxs)(e.span,{className:"base",children:[(0,a.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,a.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]})," point. Read more ",(0,a.jsx)(e.a,{href:"https://doi.org/10.1103/PhysRevB.96.075448",children:"here"}),"."]}),"\n"]}),"\n"]})}),"\n",(0,a.jsxs)(e.p,{children:["(2) calculate the dynamical matrix on a uniform mesh of q-points using ",(0,a.jsx)(e.code,{children:"ph.x"})]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/ph.GaAs.in",showLineNumbers:!0,children:r}),"\n",(0,a.jsx)(e.p,{children:"Run the calculation:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 ph.x -i ph.GaAs.in > ph.GaAs.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"The above calculation is computationally demanding. Our example calculation took\nabout a whole day on a 2.6 GHz quad core processor."}),"\n",(0,a.jsx)(e.admonition,{type:"info",children:(0,a.jsxs)(e.p,{children:["You can restart an interrupted ",(0,a.jsx)(e.code,{children:"ph.x"})," calculation with ",(0,a.jsx)(e.code,{children:"recover = .true."})," in the\n",(0,a.jsx)(e.code,{children:"INPUTPH"})," namelist. You can cleanly exit an ongoing calculation by creating an\nempty file with name ",(0,a.jsx)(e.code,{children:"{prefix}.EXIT"}),"."]})}),"\n",(0,a.jsxs)(e.p,{children:["(3) perform inverse Fourier transform of the dynamical matrix to obtain inverse\nFourier components in real space using ",(0,a.jsx)(e.code,{children:"q2r.x"}),". Below is our input file:"]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/q2r.GaAs.in",showLineNumbers:!0,children:l}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 q2r.x -i q2r.GaAs.in > q2r.GaAs.out\n"})}),"\n",(0,a.jsxs)(e.p,{children:["(4) Finally, perform Fourier transformation of the real space components to get\nthe dynamical matrix at any q by using ",(0,a.jsx)(e.code,{children:"matdyn.x"}),"."]}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/matdyn.GaAs.in",showLineNumbers:!0,children:c}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-bash",children:"mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out\n"})}),"\n",(0,a.jsx)(e.p,{children:"We can now plot the phonon dispersion of GaAs:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-py",metastring:'title="notebooks/GaAs-phonon.ipynb"',children:"import numpy as np\nimport matplotlib.pyplot as plt\n\ndata = np.loadtxt(\"../src/GaAs-phonon/GaAs.freq.gp\")\n\nnbands = data.shape[1] - 1\nfor band in range(nbands):\n plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k')\n# High symmetry k-points (check matdyn.GaAs.in)\nplt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5)\nplt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \\\n labels=['L', '$\\Gamma$', 'X', 'U,K', '$\\Gamma$'])\nplt.ylabel(\"Frequency (cm$^{-1}$)\")\nplt.xlim(data[0, 0], data[-1, 0])\nplt.ylim(0, )\nplt.show()\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(9764).A}),(0,a.jsx)("img",{src:s(9431).A,alt:"GaAs-phonon",width:"600px"})]}),"\n",(0,a.jsx)(e.admonition,{type:"tip",children:(0,a.jsxs)(e.p,{children:["We may need to lower the value of ",(0,a.jsx)(e.code,{children:"conv_thr"})," in ",(0,a.jsx)(e.code,{children:"scf"})," calculation for more\naccurate result."]})}),"\n",(0,a.jsx)(e.h3,{id:"phonon-density-of-states",children:"Phonon Density of States"}),"\n",(0,a.jsx)(e.p,{children:"Input file for phonon DOS calculation:"}),"\n","\n",(0,a.jsx)(t.A,{language:"bash",title:"src/GaAs-phonon/matdyn.dos.GaAs.in",showLineNumbers:!0,children:d}),"\n",(0,a.jsx)(e.p,{children:"Plot phonon DOS:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{className:"language-py",metastring:'title="notebooks/GaAs-phonon.ipynb"',children:"freq, dos, pdos_Ga, pdos_As = np.loadtxt(\"../src/GaAs-phonon/GaAs.dos\", unpack=True)\n\nplt.plot(freq, dos, c='k', lw=0.5, label='Total')\nplt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga')\nplt.plot(freq, pdos_As, c='r', lw=0.5, label='As')\nplt.xlabel('$\\\\Omega~(cm^{-1}$)')\nplt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)')\nplt.legend(frameon=False, loc='upper left')\nplt.xlim(freq[0], freq[-1])\nplt.show()\n"})}),"\n",(0,a.jsxs)("picture",{children:[(0,a.jsx)("source",{type:"image/webp",srcSet:s(7111).A}),(0,a.jsx)("img",{src:s(2222).A,alt:"GaAs-phonon-dos",width:"600px"})]}),"\n",(0,a.jsx)(e.h2,{id:"resources",children:"Resources"}),"\n",(0,a.jsxs)(e.ul,{children:["\n",(0,a.jsxs)(e.li,{children:[(0,a.jsx)(e.a,{href:"https://indico.ictp.it/event/8301/other-view?view=ictptimetable",children:"School on Electron-Phonon Physics from First Principles (2018)"})," (",(0,a.jsx)(e.a,{href:"https://www.youtube.com/playlist?list=PLYc-eBoIpXTIboem6dKTYD1-1m0sMYnYz",children:"Video lectures on YouTube"}),")"]}),"\n",(0,a.jsx)(e.li,{children:(0,a.jsx)(e.a,{href:"https://github.com/nguyen-group/QE-SSP",children:"https://github.com/nguyen-group/QE-SSP"})}),"\n"]})]})}function j(n={}){const{wrapper:e}={...(0,o.R)(),...n.components};return e?(0,a.jsx)(e,{...n,children:(0,a.jsx)(f,{...n})}):f(n)}},2222:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-dos-5d5b89c131eaa671e47e9c22d45a5150.png"},7111:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-dos-28bb2abdbdc46635a19e09e6a68e08a3.webp"},9431:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-c72a2335477e9d01eb3902649b18815e.png"},9764:(n,e,s)=>{s.d(e,{A:()=>a});const a=s.p+"assets/images/GaAs-phonon-c3ba40a21b539b8e25e519642369cedb.webp"}}]); 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Any third party materials in this work are not included in the\narticle\u2019s Creative Commons license, and users will need to obtain permission\nfrom the respective license holder to reproduce such materials."}),"\n",(0,j.jsxs)(N.p,{children:["You are free to: ",(0,j.jsx)("br",{}),"\n",(0,j.jsx)(N.strong,{children:"Share"})," \u2014 copy and redistribute the material in any medium or format. ",(0,j.jsx)("br",{}),"\n",(0,j.jsx)(N.strong,{children:"Adapt"})," \u2014 remix, transform, and build upon the material for any purpose, even\ncommercially."]}),"\n",(0,j.jsxs)(N.p,{children:["Under the following terms: ",(0,j.jsx)("br",{}),"\n",(0,j.jsx)(N.strong,{children:"Attribution"})," \u2014 You must give appropriate credit, provide a link to the\nlicense, and indicate if changes were made. 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\ No newline at end of file diff --git a/assets/js/cfda1d21.f6290cc9.js b/assets/js/cfda1d21.c8c16dde.js similarity index 99% rename from assets/js/cfda1d21.f6290cc9.js rename to assets/js/cfda1d21.c8c16dde.js index 1bbd2996..ee34f12a 100644 --- a/assets/js/cfda1d21.f6290cc9.js +++ b/assets/js/cfda1d21.c8c16dde.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[2317],{4853:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>r,contentTitle:()=>i,default:()=>d,frontMatter:()=>m,metadata:()=>t,toc:()=>c});var l=a(4848),n=a(8453);const m={title:"What problem are we trying to solve?",sidebar_label:"Problem statement"},i=void 0,t={id:"theory/problem-statement",title:"What problem are we trying to solve?",description:"We want to calculate the electronic structure of real materials and their",source:"@site/docs/theory/problem-statement.md",sourceDirName:"theory",slug:"/theory/problem-statement",permalink:"/espresso/theory/problem-statement",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/theory/problem-statement.md",tags:[],version:"current",frontMatter:{title:"What problem are we trying to solve?",sidebar_label:"Problem statement"},sidebar:"docs",previous:{title:"Theory",permalink:"/espresso/category/theory"},next:{title:"Hartree-Fock",permalink:"/espresso/theory/hartree-fock"}},r={},c=[];function h(s){const e={annotation:"annotation",em:"em",math:"math",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mover:"mover",mpadded:"mpadded",mrow:"mrow",msub:"msub",msubsup:"msubsup",msup:"msup",mtext:"mtext",munder:"munder",munderover:"munderover",p:"p",semantics:"semantics",span:"span",...(0,n.R)(),...s.components};return(0,l.jsxs)(l.Fragment,{children:[(0,l.jsxs)(e.p,{children:["We want to calculate the electronic structure of real materials and their\nphysical properties by ",(0,l.jsx)(e.em,{children:"ab-initio"})," method. 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Quantum\nparticles are described by the wave function."]}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"\u03bb"}),(0,l.jsx)(e.mo,{children:"\u22c5"}),(0,l.jsx)(e.mi,{children:"p"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mi,{children:"h"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\lambda \\cdot p = h"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"\u03bb"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,l.jsx)(e.span,{className:"mbin",children:"\u22c5"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"p"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"h"})]})]})]})}),"\n",(0,l.jsxs)(e.p,{children:["where ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"h"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"h"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"h"})]})})]})," is the Plank constant. 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For example, the electrons\ninside a material are subjected to the Coulomb field of the nucleus. The nucleus\nis heavy and their motion is much slower than the motion of the electrons. 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Quantum\nparticles are described by the wave function."]}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"\u03bb"}),(0,l.jsx)(e.mo,{children:"\u22c5"}),(0,l.jsx)(e.mi,{children:"p"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mi,{children:"h"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\lambda \\cdot p = h"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"\u03bb"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,l.jsx)(e.span,{className:"mbin",children:"\u22c5"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"p"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"h"})]})]})]})}),"\n",(0,l.jsxs)(e.p,{children:["where ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"h"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"h"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"h"})]})})]})," is the Plank constant. The Wavefunction of an electron in a potential\nfiled ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"V"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"(V)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.22222em"},children:"V"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is calculated by solving the Schr\xf6dinger 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strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[81],{2539:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>u,contentTitle:()=>d,default:()=>g,frontMatter:()=>p,metadata:()=>h,toc:()=>m});var s=t(4848),i=t(8453),o=t(1432);const c='# load the pw.x input from file\nload_fromPWI pw.scf.silicon.in\n\n# open a file for writing resulting total energies\nset fid [open etot_vs_ecutwfc.dat w]\n\n# loop over different "ecut" values\nforeach ecut { 12 16 20 24 28 32 } {\n\n # name of I/O files: $name.in & $name.out\n set name si_scf_ecutwfc-$ecut\n\n # set the pw.x "ecutwfc" variable\n SYSTEM "ecutwfc = $ecut"\n\n # run the pw.x calculation\n runPW $name.in\n\n # extract the "total energy" and write it to file\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$ecut $Etot"\n}\n\nclose $fid\n',a="#!/bin/sh\nNAME=\"ecut\"\n\nfor CUTOFF in 10 15 20 25 30 35 40\ndo\ncat > ${NAME}_${CUTOFF}.in << EOF\n &control\n calculation = 'scf',\n prefix = 'silicon'\n outdir = './tmp/'\n pseudo_dir = './pseudos/'\n /\n &system\n ibrav = 2,\n celldm(1) = 10.0,\n nat = 2,\n ntyp = 1,\n ecutwfc = $CUTOFF\n /\n &electrons\n mixing_beta = 0.6\n /\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 6 6 6 1 1 1\nEOF\n\npw.x < ${NAME}_${CUTOFF}.in > ${NAME}_${CUTOFF}.out\necho ${NAME}_${CUTOFF}\ngrep ! ${NAME}_${CUTOFF}.out\n\ndone\n",r='load_fromPWI pw.scf.silicon.in\n\nset fid [open etot-vs-kpoint.dat w]\n\nforeach k { 2 4 6 8 } {\n\n set name si_scf_kpoints-$k\n\n K_POINTS automatic "$k $k $k 1 1 1"\n runPW $name.in\n\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$k $Etot"\n}\n\nclose $fid\n',l='load_fromPWI pw.scf.silicon.in\n\n# please uncomment & insert value as determined in the "ecutwfc" exercise\nSYSTEM { ecutwfc = 30 }\n\n# please uncomment & insert values as determined in the "kpoints" exercise\nK_POINTS automatic { 6 6 6 1 1 1 }\n\n\nset fid [open etot-vs-alat.dat w]\n\nforeach alat { 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 } {\n\n set name si_scf_alat-$alat\n\n SYSTEM "celldm(1) = $alat"\n runPW $name.in\n\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$alat $Etot"\n}\n\nclose $fid\n',p={title:"Convergence testing"},d=void 0,h={id:"hands-on/convergence",title:"Convergence testing",description:"Convergence with cutoff energy using PWTK",source:"@site/docs/hands-on/convergence.mdx",sourceDirName:"hands-on",slug:"/hands-on/convergence",permalink:"/espresso/hands-on/convergence",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/convergence.mdx",tags:[],version:"current",frontMatter:{title:"Convergence testing"},sidebar:"docs",previous:{title:"SCF calculation",permalink:"/espresso/hands-on/scf"},next:{title:"Structure optimization",permalink:"/espresso/hands-on/structure-optimization"}},u={},m=[{value:"Convergence with cutoff energy using PWTK",id:"convergence-with-cutoff-energy-using-pwtk",level:2},{value:"Convergence test using UNIX shell script",id:"convergence-test-using-unix-shell-script",level:2},{value:"Convergence test against the number of k-points",id:"convergence-test-against-the-number-of-k-points",level:2},{value:"Convergence against lattice constant",id:"convergence-against-lattice-constant",level:2},{value:"Note on CPU time",id:"note-on-cpu-time",level:2}];function f(e){const n={admonition:"admonition",code:"code",h2:"h2",li:"li",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,i.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsx)(n.h2,{id:"convergence-with-cutoff-energy-using-pwtk",children:"Convergence with cutoff energy using PWTK"}),"\n",(0,s.jsxs)(n.p,{children:["We can automate the previous self consistent calculation by varying a certain\nparameter. Say we want to check the total energy of the system for various\nvalues of ",(0,s.jsx)(n.code,{children:"ecutwfc"}),". We can do that by using ",(0,s.jsx)(n.code,{children:"pwtk"})," script."]}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_scf_ecutoff.pwtk",showLineNumbers:!0,children:c}),"\n",(0,s.jsx)(n.p,{children:"To run the above script:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pwtk si_scf_ecutoff.pwtk\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Now we can plot the total energy with respect to ecutwfc. The data is in\n",(0,s.jsx)(n.code,{children:"etot-vs-ecutwfc.dat"})]}),"\n",(0,s.jsx)(n.p,{children:"We will use matplotlib to make the plots. Here is the python code for plotting:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-python",metastring:'title="notebooks/silicon-scf.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\nplt.rcParams[\"figure.dpi\"]=150\nplt.rcParams[\"figure.facecolor\"]=\"white\"\n\nx, y = np.loadtxt('../src/silicon/etot-vs-ecutwfc.dat', delimiter=' ', unpack=True)\nplt.plot(x, y, \"o-\", markersize=5, label='Etot vs ecutwfc')\nplt.xlabel('ecutwfc (Ry)')\nplt.ylabel('Etot (Ry)')\nplt.legend(frameon=False)\nplt.show()\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5721).A}),(0,s.jsx)("img",{src:t(708).A,alt:"etot-vs-ecutwfc"})]}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-using-unix-shell-script",children:"Convergence test using UNIX shell script"}),"\n",(0,s.jsx)(n.p,{children:"We can do the convergence test with various parameters. We can calculate the\ntotal energy of the system by varying various parameters. We will use the shell\nscript to automate the process with different cutoff energy values."}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_script.sh",showLineNumbers:!0,children:a}),"\n",(0,s.jsx)(n.p,{children:"Make sure the file has executable permission for the user:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"chmod 700 si_script.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"Run the script file:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"./si_script.sh\n# or\nsh si_script.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"We can plot the energy vs cutoff energy, and choose a reasonable value."}),"\n",(0,s.jsxs)(n.admonition,{type:"caution",children:[(0,s.jsx)(n.p,{children:"Initially, I had problem in running the script in macOS. The problem occurred\nbecause the script file format was set to DOS. The file format can be checked in\nfollowing way:"}),(0,s.jsxs)(n.p,{children:["Open the file in ",(0,s.jsx)(n.strong,{children:"vi"})," editor. ",(0,s.jsx)(n.code,{children:"vi si_script.sh"})," Now in ",(0,s.jsx)(n.strong,{children:"vi"})," editor command\nmode (ESC key), type ",(0,s.jsx)(n.code,{children:":set ff?"})," This would tell you the file format. Now to\nchange file format, use the command ",(0,s.jsx)(n.code,{children:":set fileformat=unix"})]})]}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-against-the-number-of-k-points",children:"Convergence test against the number of k-points"}),"\n",(0,s.jsx)(n.p,{children:"We can run similar convergence test against another parameter, and choose the\nbest value of that particular parameter. Here we will try to calculate the\nnumber of k-points in the Monkhorst-Pack mesh."}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_scf_kpoints.pwtk",showLineNumbers:!0,children:r}),"\n",(0,s.jsx)(n.p,{children:"Run pwtk program:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pwtk si_scf_kpoints.pwtk\n"})}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-python",metastring:'title="notebooks/silicon-scf.ipynb" showLineNumbers',children:"x, y = np.loadtxt('../src/silicon/etot-vs-kpoint.dat', delimiter=' ', unpack=True)\nplt.plot(x, y, \"o-\", markersize=5, label='Etot vs kpoints')\nplt.xlabel('# kpoints')\nplt.ylabel('Etot (Ry)')\nplt.legend(frameon=False)\nplt.show()\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(9786).A}),(0,s.jsx)("img",{src:t(6497).A,alt:"etot-vs-kpoints"})]}),"\n",(0,s.jsx)(n.h2,{id:"convergence-against-lattice-constant",children:"Convergence against lattice constant"}),"\n",(0,s.jsx)(n.p,{children:"Calculating total energy with respect to varying lattice constant."}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_scf_alat.pwtk",showLineNumbers:!0,children:l}),"\n",(0,s.jsx)(n.p,{children:"Run the above code:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{children:"pwtk si_scf_alat.pwtk\n"})}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-python",metastring:'title="notebooks/silicon-scf.ipynb" showLineNumbers',children:"x, y = np.loadtxt('../src/silicon/etot-vs-alat.dat', delimiter=' ', unpack=True)\nplt.plot(x, y, \"o-\", markersize=5, label='Etot vs alat')\nplt.xlabel('alat (Bohr)')\nplt.ylabel('Etot (Ry)')\nplt.legend(frameon=False)\nplt.show()\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(2444).A}),(0,s.jsx)("img",{src:t(1087).A,alt:"etot-vs-alat"})]}),"\n",(0,s.jsx)(n.h2,{id:"note-on-cpu-time",children:"Note on CPU time"}),"\n",(0,s.jsxs)(n.ul,{children:["\n",(0,s.jsxs)(n.li,{children:["\n",(0,s.jsxs)(n.p,{children:["CPU time is proportional to the number of plane waves used for the\ncalculation. Number of plane wave is proportional to the (ecutwfc)",(0,s.jsx)("sup",{children:"3/2"})]}),"\n"]}),"\n",(0,s.jsxs)(n.li,{children:["\n",(0,s.jsx)(n.p,{children:"CPU time is proportional to the number if inequivalent k-points"}),"\n"]}),"\n",(0,s.jsxs)(n.li,{children:["\n",(0,s.jsxs)(n.p,{children:["CPU time increases as N",(0,s.jsx)("sup",{children:"3"}),", where N is the number of atoms in the\nsystem."]}),"\n"]}),"\n"]})]})}function g(e={}){const{wrapper:n}={...(0,i.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(f,{...e})}):f(e)}},1087:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-alat-7c9003bf8d492a4ce692a57260181a9b.png"},2444:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-alat-5491930b9380c877f6f3ee7e8630d735.webp"},708:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-ecutwfc-b7408d04175ded7a80e8070b2466faa3.png"},5721:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-ecutwfc-952592f51ad4594a8e4f0caf8050c5b2.webp"},6497:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-kpoints-70be9122fc1dc1613ee4b46a8733fb1f.png"},9786:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/etot-vs-kpoints-f63a8b6dc81ea6f91e4cabbc02686315.webp"}}]); \ No newline at end of file diff --git a/assets/js/d4c90dae.ada90cc3.js b/assets/js/d4c90dae.ada90cc3.js new file mode 100644 index 00000000..33bbfa66 --- /dev/null +++ b/assets/js/d4c90dae.ada90cc3.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[81],{665:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>u,contentTitle:()=>d,default:()=>g,frontMatter:()=>p,metadata:()=>h,toc:()=>m});var s=t(4848),i=t(8453),o=t(1432);const c='# load the pw.x input from file\nload_fromPWI pw.scf.silicon.in\n\n# open a file for writing resulting total energies\nset fid [open etot_vs_ecutwfc.dat w]\n\n# loop over different "ecut" values\nforeach ecut { 12 16 20 24 28 32 } {\n\n # name of I/O files: $name.in & $name.out\n set name si_scf_ecutwfc-$ecut\n\n # set the pw.x "ecutwfc" variable\n SYSTEM "ecutwfc = $ecut"\n\n # run the pw.x calculation\n runPW $name.in\n\n # extract the "total energy" and write it to file\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$ecut $Etot"\n}\n\nclose $fid\n',a="#!/bin/sh\nNAME=\"ecut\"\n\nfor CUTOFF in 10 15 20 25 30 35 40\ndo\ncat > ${NAME}_${CUTOFF}.in << EOF\n &control\n calculation = 'scf',\n prefix = 'silicon'\n outdir = './tmp/'\n pseudo_dir = './pseudos/'\n /\n &system\n ibrav = 2,\n celldm(1) = 10.0,\n nat = 2,\n ntyp = 1,\n ecutwfc = $CUTOFF\n /\n &electrons\n mixing_beta = 0.6\n /\n\nATOMIC_SPECIES\n Si 28.086 Si.pz-vbc.UPF\n\nATOMIC_POSITIONS (alat)\n Si 0.0 0.0 0.0\n Si 0.25 0.25 0.25\n\nK_POINTS (automatic)\n 6 6 6 1 1 1\nEOF\n\npw.x < ${NAME}_${CUTOFF}.in > ${NAME}_${CUTOFF}.out\necho ${NAME}_${CUTOFF}\ngrep ! ${NAME}_${CUTOFF}.out\n\ndone\n",r='load_fromPWI pw.scf.silicon.in\n\nset fid [open etot-vs-kpoint.dat w]\n\nforeach k { 2 4 6 8 } {\n\n set name si_scf_kpoints-$k\n\n K_POINTS automatic "$k $k $k 1 1 1"\n runPW $name.in\n\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$k $Etot"\n}\n\nclose $fid\n',l='load_fromPWI pw.scf.silicon.in\n\n# please uncomment & insert value as determined in the "ecutwfc" exercise\nSYSTEM { ecutwfc = 30 }\n\n# please uncomment & insert values as determined in the "kpoints" exercise\nK_POINTS automatic { 6 6 6 1 1 1 }\n\n\nset fid [open etot-vs-alat.dat w]\n\nforeach alat { 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 } {\n\n set name si_scf_alat-$alat\n\n SYSTEM "celldm(1) = $alat"\n runPW $name.in\n\n set Etot [::pwtk::pwo::totene $name.out]\n puts $fid "$alat $Etot"\n}\n\nclose $fid\n',p={title:"Convergence testing"},d=void 0,h={id:"hands-on/convergence",title:"Convergence testing",description:"Convergence with cutoff energy using PWTK",source:"@site/docs/hands-on/convergence.mdx",sourceDirName:"hands-on",slug:"/hands-on/convergence",permalink:"/espresso/hands-on/convergence",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/convergence.mdx",tags:[],version:"current",frontMatter:{title:"Convergence testing"},sidebar:"docs",previous:{title:"SCF calculation",permalink:"/espresso/hands-on/scf"},next:{title:"Structure optimization",permalink:"/espresso/hands-on/structure-optimization"}},u={},m=[{value:"Convergence with cutoff energy using PWTK",id:"convergence-with-cutoff-energy-using-pwtk",level:2},{value:"Convergence test using UNIX shell script",id:"convergence-test-using-unix-shell-script",level:2},{value:"Convergence test against the number of k-points",id:"convergence-test-against-the-number-of-k-points",level:2},{value:"Convergence against lattice constant",id:"convergence-against-lattice-constant",level:2},{value:"Note on CPU time",id:"note-on-cpu-time",level:2}];function f(e){const n={admonition:"admonition",code:"code",h2:"h2",li:"li",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,i.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsx)(n.h2,{id:"convergence-with-cutoff-energy-using-pwtk",children:"Convergence with cutoff energy using PWTK"}),"\n",(0,s.jsxs)(n.p,{children:["We can automate the previous self consistent calculation by varying a certain\nparameter. Say we want to check the total energy of the system for various\nvalues of ",(0,s.jsx)(n.code,{children:"ecutwfc"}),". We can do that by using ",(0,s.jsx)(n.code,{children:"pwtk"})," script."]}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_scf_ecutoff.pwtk",showLineNumbers:!0,children:c}),"\n",(0,s.jsx)(n.p,{children:"To run the above script:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pwtk si_scf_ecutoff.pwtk\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Now we can plot the total energy with respect to ecutwfc. The data is in\n",(0,s.jsx)(n.code,{children:"etot-vs-ecutwfc.dat"})]}),"\n",(0,s.jsx)(n.p,{children:"We will use matplotlib to make the plots. Here is the python code for plotting:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-python",metastring:'title="notebooks/silicon-scf.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\nplt.rcParams[\"figure.dpi\"]=150\nplt.rcParams[\"figure.facecolor\"]=\"white\"\n\nx, y = np.loadtxt('../src/silicon/etot-vs-ecutwfc.dat', delimiter=' ', unpack=True)\nplt.plot(x, y, \"o-\", markersize=5, label='Etot vs ecutwfc')\nplt.xlabel('ecutwfc (Ry)')\nplt.ylabel('Etot (Ry)')\nplt.legend(frameon=False)\nplt.show()\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5721).A}),(0,s.jsx)("img",{src:t(708).A,alt:"etot-vs-ecutwfc"})]}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-using-unix-shell-script",children:"Convergence test using UNIX shell script"}),"\n",(0,s.jsx)(n.p,{children:"We can do the convergence test with various parameters. We can calculate the\ntotal energy of the system by varying various parameters. We will use the shell\nscript to automate the process with different cutoff energy values."}),"\n","\n",(0,s.jsx)(o.A,{language:"bash",title:"src/silicon/si_script.sh",showLineNumbers:!0,children:a}),"\n",(0,s.jsx)(n.p,{children:"Make sure the file has executable permission for the user:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"chmod 700 si_script.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"Run the script file:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"./si_script.sh\n# or\nsh si_script.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"We can plot the energy vs cutoff energy, and choose a reasonable value."}),"\n",(0,s.jsxs)(n.admonition,{type:"caution",children:[(0,s.jsx)(n.p,{children:"Initially, I had problem in running the script in macOS. The problem occurred\nbecause the script file format was set to DOS. The file format can be checked in\nfollowing way:"}),(0,s.jsxs)(n.p,{children:["Open the file in ",(0,s.jsx)(n.strong,{children:"vi"})," editor. ",(0,s.jsx)(n.code,{children:"vi si_script.sh"})," Now in ",(0,s.jsx)(n.strong,{children:"vi"})," editor command\nmode (ESC key), type ",(0,s.jsx)(n.code,{children:":set ff?"})," This would tell you the file format. Now to\nchange file format, use the command ",(0,s.jsx)(n.code,{children:":set fileformat=unix"})]})]}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-against-the-number-of-k-points",children:"Convergence test against the number of k-points"}),"\n",(0,s.jsx)(n.p,{children:"We can run similar convergence test against another parameter, and choose the\nbest value of that particular parameter. 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the external potential\nenergy ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"v"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"v(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"v"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord 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Schr\xf6dinger\nequation says how we can get the wavefunction from a given potential. Once\nsolved the wavefunction (which could be difficult), we can determine the density\nor any other properties. Now Hohenberg and Kohn theorem says the opposite is\nalso true. For a given density, the potential can be uniquely determined. For\nnon-degenerate ground states, two different Hamiltonian cannot have the same\nground-state electron density. It is possible to define the ground-state energy\nas a function of electronic density."}),"\n",(0,l.jsx)(e.h2,{id:"hohenberg-kohn-theorem-2",children:"Hohenberg-Kohn Theorem 2"}),"\n",(0,l.jsxs)(e.blockquote,{children:["\n",(0,l.jsxs)(e.p,{children:["Total energy of the system ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is minimal when ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is the\nactual ground-state density, among all possible electron densities."]}),"\n"]}),"\n",(0,l.jsxs)(e.p,{children:["The ground state energy can therefore be found by minimizing ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," instead of\nsolving for the many-electron wavefunction. However, note that HK theorems do\nnot tell us how the energy depends on the electron density. In reality, apart\nfrom some special cases, the exact ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is 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Therefore\nthe problem is non-linear. It is usually solved computationally by starting from\na trial potential and iterate to self-consistency. Also note that we have not\nincluded the kinetic energy term for the nucleus. 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There are also more advanced\nfunctionals: Meta-GGA (e.g., SCAN), hybrids (e.g., B3LYP), nonlocal functionals\nfor van der Waals forces, Grimme's DFT+D (a semi-empirical correction to GGA).\nThey usually produces more accurate result, but computationally more expensive\nand sometimes numerically unstable."}),"\n",(0,l.jsx)(e.h2,{id:"algorithmic-implementation",children:"Algorithmic implementation"}),"\n",(0,l.jsx)(e.p,{children:"We can write our Schr\xf6dinger in Dirac Bra-Ket notation:"}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.mover,{accent:"true",children:[(0,l.jsx)(e.mi,{children:"H"}),(0,l.jsx)(e.mo,{children:"^"})]}),(0,l.jsxs)(e.mpadded,{children:[(0,l.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"}),(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"\u27e9"})]}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsxs)(e.mpadded,{children:[(0,l.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"}),(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"\u27e9"})]})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\hat{H} \\ket{\\psi} = E\\ket{\\psi}"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1.1968em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord accent",children:(0,l.jsx)(e.span,{className:"vlist-t",children:(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsxs)(e.span,{className:"vlist",style:{height:"0.9468em"},children:[(0,l.jsxs)(e.span,{style:{top:"-3em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.08125em"},children:"H"})]}),(0,l.jsxs)(e.span,{style:{top:"-3.2523em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"accent-body",style:{left:"-0.1944em"},children:(0,l.jsx)(e.span,{className:"mord",children:"^"})})]})]})})})}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"minner",children:[(0,l.jsx)(e.span,{className:"mord",children:"\u2223"}),(0,l.jsx)(e.span,{className:"mord",children:(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"})}),(0,l.jsx)(e.span,{className:"mclose",children:"\u27e9"})]}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"minner",children:[(0,l.jsx)(e.span,{className:"mord",children:"\u2223"}),(0,l.jsx)(e.span,{className:"mord",children:(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"})}),(0,l.jsx)(e.span,{className:"mclose",children:"\u27e9"})]})]})]})]})}),"\n",(0,l.jsxs)(e.p,{children:["we are going to solve non-interacting single particle Hamiltonian in terms of\nknown basis functions (plane waves) with unknown coefficients. We start with an\ninitial guess for the electron density ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", and construct a pseudo\npotential for the nuclear potential. In turn, we have the Hamiltonian. Solve for\n",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mi,{children:"i"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\psi_i(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3117em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"i"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200b"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", subsequently ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", and iterate until self\nconsistency is achieved."]}),"\n",(0,l.jsxs)("picture",{children:[(0,l.jsx)("source",{type:"image/webp",srcSet:a(7814).A}),(0,l.jsx)("img",{src:a(5525).A,alt:"self-consistent-solution"})]}),"\n",(0,l.jsxs)("p",{className:"fig-caption",children:["Self consistency loop in DFT calculation. The above screenshot was taken from lecture slide of Professor Ralph Gevauer from ",(0,l.jsx)("a",{href:"http://indico.ictp.it/event/9616/other-view?view=ictptimetable",children:" ICTP MAX School 2021"}),"."]}),"\n",(0,l.jsx)(e.p,{children:"The potential due to the ions is replaced by the pseudo potentials which removes\nthe oscillations near the atomic core (reducing number of required plane wave\nbasis vectors) and simulates the exact behavior elsewhere. The pseudo potential\nis also different for different exchange correlation functional, and it is\nspecified in the pseudo potential file. If a system had more than one type of\natom, always choose the pseudo potentials with same exchange correlation (e.g.,\nPBE)."}),"\n",(0,l.jsxs)(e.p,{children:["It is important to note that DFT is calculations are not exact solution to the\nreal systems because exact functional (",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"v"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mi,{children:"c"})]})]})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"v_{xc}"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"v"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.1514em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"x"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"c"})]})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200b"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})})]}),") we need to solve the Kohn-Sham\nequation is not known. Therefore, we have to compare the results with\nexperimental observations. The Kohn-Sham wavefunction of orbitals is not an\napproximation to the exact wavefunction. Rather it is precisely defined property\nof any electronic system, which is uniquely determined by the density. The\nin-exactness of DFT results come from the fact that we do not know the exact\ncorrelation functional that truly describes real systems."]}),"\n",(0,l.jsx)(e.h2,{id:"plane-wave-expansion",children:"Plane-wave expansion"}),"\n",(0,l.jsx)(e.p,{children:"The wavefunctions are expanded in terms of a basis set. In quantum espresso, the\nthe basis function is plane waves. There exists other DFT codes that use\nlocalized basis function as well. Plane waves are simpler but generally requires\nmuch large number of them compared to other localized basis sets."}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mi,{children:"i"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsxs)(e.munderover,{children:[(0,l.jsx)(e.mo,{children:"\u2211"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"\u03b1"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mn,{children:"1"})]}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"N"}),(0,l.jsx)(e.mi,{children:"b"})]})]}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"c"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"i"}),(0,l.jsx)(e.mi,{children:"\u03b1"})]})]}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"f"}),(0,l.jsx)(e.mi,{children:"\u03b1"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\psi_i(\\textbf{r}) 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the external potential\nenergy ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"v"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"v(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"v"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," to within a trivial additive constant."]}),"\n"]}),"\n",(0,l.jsx)(e.p,{children:"So what Hohenberg-Kohn theorem says, may not sound very trivial. Schr\xf6dinger\nequation says how we can get the wavefunction from a given potential. Once\nsolved the wavefunction (which could be difficult), we can determine the density\nor any other properties. Now Hohenberg and Kohn theorem says the opposite is\nalso true. For a given density, the potential can be uniquely determined. For\nnon-degenerate ground states, two different Hamiltonian cannot have the same\nground-state electron density. It is possible to define the ground-state energy\nas a function of electronic density."}),"\n",(0,l.jsx)(e.h2,{id:"hohenberg-kohn-theorem-2",children:"Hohenberg-Kohn Theorem 2"}),"\n",(0,l.jsxs)(e.blockquote,{children:["\n",(0,l.jsxs)(e.p,{children:["Total energy of the system ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is minimal when ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is the\nactual ground-state density, among all possible electron densities."]}),"\n"]}),"\n",(0,l.jsxs)(e.p,{children:["The ground state energy can therefore be found by minimizing ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," instead of\nsolving for the many-electron wavefunction. However, note that HK theorems do\nnot tell us how the energy depends on the electron density. In reality, apart\nfrom some special cases, the exact ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"E(n)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," is 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Therefore\nthe problem is non-linear. It is usually solved computationally by starting from\na trial potential and iterate to self-consistency. Also note that we have not\nincluded the kinetic energy term for the nucleus. This is because the nuclear\nmass is about three orders of magnitude heavier than the electronic mass\n(",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"M"}),(0,l.jsx)(e.mo,{children:"\u226b"}),(0,l.jsx)(e.mi,{children:"m"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"M \\gg m"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.7224em",verticalAlign:"-0.0391em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.10903em"},children:"M"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"\u226b"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"m"})]})]})]}),"), so essentially electronic dynamics is much faster than the nuclear\ndynamics (see Born-Oppenheimer approximation). 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that depends on the local density and the\nlocal gradient of the 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There are also more advanced\nfunctionals: Meta-GGA (e.g., SCAN), hybrids (e.g., B3LYP), nonlocal functionals\nfor van der Waals forces, Grimme's DFT+D (a semi-empirical correction to GGA).\nThey usually produces more accurate result, but computationally more expensive\nand sometimes numerically unstable."}),"\n",(0,l.jsx)(e.h2,{id:"algorithmic-implementation",children:"Algorithmic implementation"}),"\n",(0,l.jsx)(e.p,{children:"We can write our Schr\xf6dinger in Dirac Bra-Ket notation:"}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.mover,{accent:"true",children:[(0,l.jsx)(e.mi,{children:"H"}),(0,l.jsx)(e.mo,{children:"^"})]}),(0,l.jsxs)(e.mpadded,{children:[(0,l.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"}),(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"\u27e9"})]}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mi,{children:"E"}),(0,l.jsxs)(e.mpadded,{children:[(0,l.jsx)(e.mi,{mathvariant:"normal",children:"\u2223"}),(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"\u27e9"})]})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\hat{H} \\ket{\\psi} = E\\ket{\\psi}"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1.1968em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord accent",children:(0,l.jsx)(e.span,{className:"vlist-t",children:(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsxs)(e.span,{className:"vlist",style:{height:"0.9468em"},children:[(0,l.jsxs)(e.span,{style:{top:"-3em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.08125em"},children:"H"})]}),(0,l.jsxs)(e.span,{style:{top:"-3.2523em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"accent-body",style:{left:"-0.1944em"},children:(0,l.jsx)(e.span,{className:"mord",children:"^"})})]})]})})})}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"minner",children:[(0,l.jsx)(e.span,{className:"mord",children:"\u2223"}),(0,l.jsx)(e.span,{className:"mord",children:(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"})}),(0,l.jsx)(e.span,{className:"mclose",children:"\u27e9"})]}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"minner",children:[(0,l.jsx)(e.span,{className:"mord",children:"\u2223"}),(0,l.jsx)(e.span,{className:"mord",children:(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"})}),(0,l.jsx)(e.span,{className:"mclose",children:"\u27e9"})]})]})]})]})}),"\n",(0,l.jsxs)(e.p,{children:["we are going to solve non-interacting single particle Hamiltonian in terms of\nknown basis functions (plane waves) with unknown coefficients. We start with an\ninitial guess for the electron density ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", and construct a pseudo\npotential for the nuclear potential. In turn, we have the Hamiltonian. Solve for\n",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"\u03c8"}),(0,l.jsx)(e.mi,{children:"i"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\psi_i(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"\u03c8"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3117em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"i"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200b"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", subsequently ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"n"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"n(\\textbf{r})"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"n"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord text",children:(0,l.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]}),", and iterate until self\nconsistency is achieved."]}),"\n",(0,l.jsxs)("picture",{children:[(0,l.jsx)("source",{type:"image/webp",srcSet:a(7814).A}),(0,l.jsx)("img",{src:a(5525).A,alt:"self-consistent-solution"})]}),"\n",(0,l.jsxs)("p",{className:"fig-caption",children:["Self consistency loop in DFT calculation. The above screenshot was taken from lecture slide of Professor Ralph Gevauer from ",(0,l.jsx)("a",{href:"http://indico.ictp.it/event/9616/other-view?view=ictptimetable",children:" ICTP MAX School 2021"}),"."]}),"\n",(0,l.jsx)(e.p,{children:"The potential due to the ions is replaced by the pseudo potentials which removes\nthe oscillations near the atomic core (reducing number of required plane wave\nbasis vectors) and simulates the exact behavior elsewhere. The pseudo potential\nis also different for different exchange correlation functional, and it is\nspecified in the pseudo potential file. If a system had more than one type of\natom, always choose the pseudo potentials with same exchange correlation (e.g.,\nPBE)."}),"\n",(0,l.jsxs)(e.p,{children:["It is important to note that DFT is calculations are not exact solution to the\nreal systems because exact functional (",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"v"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mi,{children:"c"})]})]})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"v_{xc}"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03588em"},children:"v"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.1514em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"x"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"c"})]})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200b"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})})]}),") we need to solve the Kohn-Sham\nequation is not known. Therefore, we have to compare the results with\nexperimental observations. The Kohn-Sham wavefunction of orbitals is not an\napproximation to the exact wavefunction. Rather it is precisely defined property\nof any electronic system, which is uniquely determined by the density. The\nin-exactness of DFT results come from the fact that we do not know the exact\ncorrelation functional that truly describes real systems."]}),"\n",(0,l.jsx)(e.h2,{id:"plane-wave-expansion",children:"Plane-wave expansion"}),"\n",(0,l.jsx)(e.p,{children:"The wavefunctions are expanded in terms of a basis set. In quantum espresso, the\nthe basis function is plane waves. There exists other DFT codes that use\nlocalized basis function as well. Plane waves are simpler but generally requires\nmuch large number of them compared to other localized basis 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Here is a sample job\nscript for ",(0,s.jsx)(n.a,{href:"https://nusit.nus.edu.sg/hpc/",children:"NUS HPC"})," clusters:"]}),"\n","\n",(0,s.jsx)(a.A,{language:"bash",title:"scripts/pbs_job.sh",showLineNumbers:!0,children:t}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["Notice that the lines beginning with ",(0,s.jsx)(n.code,{children:"#PBS"})," are actually PBS commands, not\ncomments. 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Create an empty file named ",(0,s.jsx)(n.code,{children:"{prefix}.EXIT"})," in\nthe directory where you have the input file or in the ",(0,s.jsx)(n.code,{children:"outdir"})," as set in the\n",(0,s.jsx)(n.code,{children:"&CONTROL"})," card of input file."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"touch {prefix}.EXIT\n"})}),"\n",(0,s.jsxs)(n.p,{children:["That will stop the program on the next iteration, and save the state. In order\nto restart, set the ",(0,s.jsx)(n.code,{children:"restart_mode"})," in ",(0,s.jsx)(n.code,{children:"&CONTROL"})," card to ",(0,s.jsx)(n.code,{children:"'restart'"})," and re-run\nafter necessary changes. You must re-submit the job with the same number of\nprocessors."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"&CONTROL\n ...\n restart_mode = 'restart'\n ...\n/\n"})}),"\n",(0,s.jsx)(n.h2,{id:"compiling-quantum-espresso-using-intel-math-kernel-library-mkl",children:"Compiling Quantum Espresso using Intel\xae Math Kernel Library (MKL)"}),"\n",(0,s.jsx)(n.p,{children:"If you need a newer or specific version of Quantum Espresso that is not\ninstalled in the NUS clusters or you have modified the source codes yourself,\nhere are the steps that I followed to successfully compile."}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["Quantum Espresso project is primarily hosted on GitLab, and its mirror is\nmaintained at ",(0,s.jsx)(n.a,{href:"https://github.com/QEF/q-e",children:"GitHub"}),". You may check their\nrepository at ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e",children:"GitLab"})," for more up to date\ninformation. The releases via GitLab can be found under:\n",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"https://gitlab.com/QEF/q-e/-/releases"})]})}),"\n",(0,s.jsxs)(n.p,{children:[(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"Download"})," and decompress the source\nfiles."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\ntar -zxvf q-e-qe-7.2.tar.gz\n"})}),"\n",(0,s.jsx)(n.p,{children:"Load the necessary modules (applicable for NUS clusters, last checked in Jun\n2022):"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module load xe_2018\nmodule load fftw/3.3.7\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Go to QE directory and run ",(0,s.jsx)(n.code,{children:"configure"}),":"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\n./configure\n"})}),"\n",(0,s.jsx)(n.p,{children:"You will see output something like:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"...\nBLAS_LIBS= -lmkl_intel_lp64 -lmkl_sequential -lmkl_core\nLAPACK_LIBS=\nFFT_LIBS=\n...\n"})}),"\n",(0,s.jsxs)(n.p,{children:["For me, the ",(0,s.jsx)(n.code,{children:"LAPACK_LIBS"})," and ",(0,s.jsx)(n.code,{children:"FFT_LIBS"})," libs were not automatically detected. We\nneed to specify them manually. First, get the link libraries line specific to\nyour version of MKL and other configurations from the ",(0,s.jsx)(n.a,{href:"https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/onemkl/link-line-advisor.html",children:"Intel link advisor"}),".\nFor my case, the link line was:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:l(2236).A}),(0,s.jsx)("img",{src:l(2143).A,alt:"intel-link-line-adviser",width:"600px"})]}),"\n",(0,s.jsxs)(n.p,{children:["We need to insert the link for ",(0,s.jsx)(n.code,{children:"BLAS_LIBS"}),", ",(0,s.jsx)(n.code,{children:"LAPACK_LIBS"}),", and ",(0,s.jsx)(n.code,{children:"SCALAPACK_LIBS"}),".\nWe also need to find out where is the FFTW lib located. In NUS HPC, we can use\n",(0,s.jsx)(n.code,{children:"module avail"})," command to see where a particular module is located, usually\nunder ",(0,s.jsx)(n.code,{children:"/app1/modules/"}),". Open ",(0,s.jsx)(n.code,{children:"make.inc"})," and make the following changes:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-diff",metastring:'title="make.inc"',children:"# ...\nCFLAGS = -O2 $(DFLAGS) $(IFLAGS)\nCFLAGS = -O3 $(DFLAGS) $(IFLAGS)\nF90FLAGS = $(FFLAGS) -nomodule -fpp $(FDFLAGS) $(CUDA_F90FLAGS) $(IFLAGS) $(MODFLAGS)\n\n# compiler flags with and without optimization for fortran-77\n# the latter is NEEDED to properly compile dlamch.f, used by lapack\n- FFLAGS = -O2 -assume byterecl -g -traceback\n+ FFLAGS = -O3 -assume byterecl -g -traceback\nFFLAGS_NOOPT = -O0 -assume byterecl -g -traceback\n# ...\n# If you have nothing better, use the local copy\n# BLAS_LIBS = $(TOPDIR)/LAPACK/libblas.a\n- BLAS_LIBS = -lmkl_intel_lp64 -lmkl_sequential -lmkl_core\n+ BLAS_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n# If you have nothing better, use the local copy\n# LAPACK = liblapack\n# LAPACK_LIBS = $(TOPDIR)/external/lapack/liblapack.a\n- LAPACK =\n+ LAPACK = liblapack\n- LAPACK_LIBS =\n+ LAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n- SCALAPACK_LIBS =\n+ SCALAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n# nothing is needed here if the internal copy of FFTW is compiled\n# (needs -D__FFTW in DFLAGS)\n\n- FFT_LIBS =\n+ FFT_LIBS = -L/app1/centos6.3/gnu/fftw/3.3.7/lib/ -lmpi\n# ...\n"})}),"\n",(0,s.jsx)(n.p,{children:"Now we are ready to compile:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"make -j8 all\n"})}),"\n",(0,s.jsxs)(n.p,{children:["I am parallelizing with 8 processors to speed things up. You may add the\n",(0,s.jsx)(n.code,{children:"q-e-qe-7.2/bin"})," path to your ",(0,s.jsx)(n.code,{children:".bashrc"}),":"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"echo 'export PATH=\"/home/svu/{username}/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc\n"})}),"\n",(0,s.jsx)(n.p,{children:"And don't forget to load dependencies before calling QE executables."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module load xe_2018\nmodule load fftw/3.3.7\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["If you are submitting job via PBS queue, you need to provide full path of the QE\nexecutables, e.g., ",(0,s.jsx)(n.code,{children:"/home/svu/{username}/q-e-qe-7.2/bin/pw.x"}),". PBS system won't\nread your bash settings, neither the relative paths of your login node would\napply."]})}),"\n",(0,s.jsx)(n.h2,{id:"installing-intel-oneapi-libraries",children:"Installing Intel oneAPI libraries"}),"\n",(0,s.jsxs)(n.p,{children:["If you need to install Intel oneAPI libraries yourself, following instructions\nmight be useful. Please refer to Intel ",(0,s.jsx)(n.a,{href:"https://www.intel.com/content/www/us/en/developer/tools/oneapi/overview.html",children:"website"}),"\nfor up to date information."]}),"\n",(0,s.jsx)(n.h4,{id:"intel-oneapi-base-toolkit",children:"Intel oneAPI Base Toolkit:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/992857b9-624c-45de-9701-f6445d845359/l_BaseKit_p_2023.2.0.49397_offline.sh\n\n# requires gnu-awk\nsudo apt update && sudo apt install -y --no-install-recommends gawk gcc g++\n\n# interactive cli installation\nsudo apt install -y --no-install-recommends ncurses-term\nsudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --cli\n\n# list components included in oneAPI Base Toolkit\nsh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --list-components\n\n# install a subset of components with silent/unattended option\nsudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --silent --eula accept --components intel.oneapi.lin.dpcpp-cpp-compiler:intel.oneapi.lin.mkl.devel\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["If you install oneAPI without ",(0,s.jsx)(n.code,{children:"sudo"})," privilege, it will be installed under the\nuser directory: ",(0,s.jsx)(n.code,{children:"/home/{username}/intel/oneapi/"}),". After installation is\ncompleted, the setup script will print the installation location."]})}),"\n",(0,s.jsx)(n.h4,{id:"hpc-toolkit",children:"HPC Toolkit"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/0722521a-34b5-4c41-af3f-d5d14e88248d/l_HPCKit_p_2023.2.0.49440_offline.sh\nsudo sh ./l_HPCKit_p_2023.2.0.49440_offline.sh -a --silent --eula accept\n"})}),"\n",(0,s.jsx)(n.h4,{id:"intel-mkl-library",children:"Intel MKL library"}),"\n",(0,s.jsx)(n.p,{children:"Installing individual components:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/adb8a02c-4ee7-4882-97d6-a524150da358/l_onemkl_p_2023.2.0.49497_offline.sh\nsudo sh ./l_onemkl_p_2023.2.0.49497_offline.sh -a --silent --eula accept\n"})}),"\n",(0,s.jsxs)(n.p,{children:["After installation, do not forget to ",(0,s.jsx)(n.code,{children:"source"})," the environment variables before\nusing:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"source /opt/intel/oneapi/setvars.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"Compile quantum espresso:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:'wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\ntar -zxvf q-e-qe-7.2.tar.gz\nrm q-e-qe-7.2.tar.gz\ncd q-e-qe-7.2\n./configure \\\n F90=mpiifort \\\n MPIF90=mpiifort \\\n CC=mpicc CXX=icc \\\n F77=mpiifort \\\n FFLAGS="-O3 -assume byterecl -g -traceback" \\\n LAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \\\n BLAS_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \\\n SCALAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl"\nmake -j4 all\n'})}),"\n",(0,s.jsx)(n.h2,{id:"compiling-quantum-espresso-with-cmake",children:"Compiling Quantum Espresso with CMake"}),"\n",(0,s.jsxs)(n.p,{children:["Please check out the ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/wikis/Developers/CMake-build-system",children:"official documentation"})," for more\ndetails. It requires ",(0,s.jsx)(n.code,{children:"cmake"})," version ",(0,s.jsx)(n.code,{children:"3.14"})," or later."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"apt update && apt install autoconf cmake gawk gcc g++ make\n"})}),"\n",(0,s.jsx)(n.p,{children:"I used following steps to successfully compile Quantum Espresso using 2023\nversions of Intel libraries in Ubuntu 22.04 system:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\nmkdir build && cd build\ncmake -DCMAKE_C_COMPILER=mpiicc -DCMAKE_Fortran_COMPILER=mpiifort -DQE_ENABLE_SCALAPACK=ON ..\nmake -j4\nmv bin ..\ncd ..\nrm -rf build\n"})}),"\n",(0,s.jsx)(n.h2,{id:"resources",children:"Resources"}),"\n",(0,s.jsxs)(n.ul,{children:["\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/",children:"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/"})}),"\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://help.nscc.sg/pbspro-quickstartguide/",children:"https://help.nscc.sg/pbspro-quickstartguide/"})}),"\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://www.youtube.com/watch?v=doudMLEaq3w",children:"https://www.youtube.com/watch?v=doudMLEaq3w"})}),"\n"]})]})}function u(e={}){const{wrapper:n}={...(0,i.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(p,{...e})}):p(e)}},2143:(e,n,l)=>{l.d(n,{A:()=>s});const s=l.p+"assets/images/intel-link-line-adviser-30a0f6af6980b2624093d9941f4f2097.png"},2236:(e,n,l)=>{l.d(n,{A:()=>s});const s=l.p+"assets/images/intel-link-line-adviser-c3f2cc310ec8d4c9ea5d90e49a5e32b9.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[6201],{5428:(e,n,l)=>{l.r(n),l.d(n,{assets:()=>d,contentTitle:()=>o,default:()=>u,frontMatter:()=>r,metadata:()=>c,toc:()=>h});var s=l(4848),i=l(8453),a=l(1432);const t="#!/bin/bash\n#PBS -q parallel24\n#PBS -l select=2:ncpus=24:mpiprocs=24:mem=96GB\n#PBS -j eo\n#PBS -N qe-project-xx\nsource /etc/profile.d/rec_modules.sh\nmodule load espresso6.5-intel_18\n## module load espresso6.5-Centos6_Intel\ncd $PBS_O_WORKDIR;\nnp=$( cat ${PBS_NODEFILE} | wc -l );\nmpirun -np $np -f ${PBS_NODEFILE} pw.x -inp qe-scf.in > qe-scf.out\n",r={title:"High Performance Computing",keywords:["HPC","High Performance Computing","Compiling Quantum Espresso","Installing Quantum Espresso","Quantum Espresso Installation","Intel MKL","Parallel Computing","PBS job","HPC job"]},o=void 0,c={id:"setup/hpc",title:"High Performance Computing",description:"In order to perform computationally heavy calculations, we would require access",source:"@site/docs/setup/hpc.mdx",sourceDirName:"setup",slug:"/setup/hpc",permalink:"/espresso/setup/hpc",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/setup/hpc.mdx",tags:[],version:"current",frontMatter:{title:"High Performance Computing",keywords:["HPC","High Performance Computing","Compiling Quantum Espresso","Installing Quantum Espresso","Quantum Espresso Installation","Intel MKL","Parallel Computing","PBS job","HPC job"]},sidebar:"docs",previous:{title:"Installation",permalink:"/espresso/setup/install"},next:{title:"Jupyter notebooks",permalink:"/espresso/setup/jupyter"}},d={},h=[{value:"Useful UNIX commands",id:"useful-unix-commands",level:2},{value:"Running jobs at NUS HPC",id:"running-jobs-at-nus-hpc",level:2},{value:"Abort and restart a calculation",id:"abort-and-restart-a-calculation",level:2},{value:"Compiling Quantum Espresso using Intel\xae Math Kernel Library (MKL)",id:"compiling-quantum-espresso-using-intel-math-kernel-library-mkl",level:2},{value:"Installing Intel oneAPI libraries",id:"installing-intel-oneapi-libraries",level:2},{value:"Intel oneAPI Base Toolkit:",id:"intel-oneapi-base-toolkit",level:4},{value:"HPC Toolkit",id:"hpc-toolkit",level:4},{value:"Intel MKL library",id:"intel-mkl-library",level:4},{value:"Compiling Quantum Espresso with CMake",id:"compiling-quantum-espresso-with-cmake",level:2},{value:"Resources",id:"resources",level:2}];function p(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",h4:"h4",li:"li",p:"p",pre:"pre",ul:"ul",...(0,i.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsx)(n.p,{children:"In order to perform computationally heavy calculations, we would require access\nto high performance computing facilities."}),"\n",(0,s.jsx)(n.h2,{id:"useful-unix-commands",children:"Useful UNIX commands"}),"\n",(0,s.jsx)(n.p,{children:"Connect to a login node via ssh:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"ssh {username}@atlas9.nus.edu.sg\n"})}),"\n",(0,s.jsx)(n.p,{children:"Secure copy files between local and remote machines:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"scp {username}@10.10.0.2:/remote/file.txt /local/directory\nscp local/file.txt {username}@10.10.0.2:/remote/directory\n"})}),"\n",(0,s.jsx)(n.p,{children:"Check disk usage:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"du -hs .\ndu -hs /path/\n"})}),"\n",(0,s.jsx)(n.p,{children:"Rsync to synchronize two folders:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"rsync -azhv --delete /source/my_project/ /destination/my_project\n"})}),"\n",(0,s.jsx)(n.h2,{id:"running-jobs-at-nus-hpc",children:"Running jobs at NUS HPC"}),"\n",(0,s.jsx)(n.p,{children:"Check your storage quota:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"hpc s\n"})}),"\n",(0,s.jsx)(n.p,{children:"PBS commands:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"hpc pbs summary\n"})}),"\n",(0,s.jsx)(n.p,{children:"Example scrips for job submissions:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"hpc pbs script parallel20\nhpc pbs vasp\n"})}),"\n",(0,s.jsx)(n.p,{children:"List available modules:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module avail\n"})}),"\n",(0,s.jsx)(n.p,{children:"Load a module:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module load {module-name}\n"})}),"\n",(0,s.jsx)(n.p,{children:"Purge loaded modules:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module purge\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Quantum Espresso is already installed in NUS HPC clusters. Here is a sample job\nscript for ",(0,s.jsx)(n.a,{href:"https://nusit.nus.edu.sg/hpc/",children:"NUS HPC"})," clusters:"]}),"\n","\n",(0,s.jsx)(a.A,{language:"bash",title:"scripts/pbs_job.sh",showLineNumbers:!0,children:t}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["Notice that the lines beginning with ",(0,s.jsx)(n.code,{children:"#PBS"})," are actually PBS commands, not\ncomments. For comments, I am using ",(0,s.jsx)(n.code,{children:"##"}),"."]})}),"\n",(0,s.jsx)(n.p,{children:"Query about a queue system:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qstat -q\n"})}),"\n",(0,s.jsx)(n.p,{children:"Check status of a particular queue system:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qstat -Qx parallel24\n"})}),"\n",(0,s.jsx)(n.p,{children:"Submitting a job:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qsub pbs_job.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"Check running jobs:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qstat\n"})}),"\n",(0,s.jsx)(n.p,{children:"Details about a job:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qstat -f {job-id}\n"})}),"\n",(0,s.jsx)(n.p,{children:"Stopping a job:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"qdel {job-id}\n"})}),"\n",(0,s.jsx)(n.h2,{id:"abort-and-restart-a-calculation",children:"Abort and restart a calculation"}),"\n",(0,s.jsxs)(n.p,{children:["If you need to modify certain parameters while the program is running, e.g., you\nwant to change the ",(0,s.jsx)(n.code,{children:"mixing_beta"})," value because SCF accuracy is oscillation\nwithout any sign of convergence. Create an empty file named ",(0,s.jsx)(n.code,{children:"{prefix}.EXIT"})," in\nthe directory where you have the input file or in the ",(0,s.jsx)(n.code,{children:"outdir"})," as set in the\n",(0,s.jsx)(n.code,{children:"&CONTROL"})," card of input file."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"touch {prefix}.EXIT\n"})}),"\n",(0,s.jsxs)(n.p,{children:["That will stop the program on the next iteration, and save the state. In order\nto restart, set the ",(0,s.jsx)(n.code,{children:"restart_mode"})," in ",(0,s.jsx)(n.code,{children:"&CONTROL"})," card to ",(0,s.jsx)(n.code,{children:"'restart'"})," and re-run\nafter necessary changes. You must re-submit the job with the same number of\nprocessors."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"&CONTROL\n ...\n restart_mode = 'restart'\n ...\n/\n"})}),"\n",(0,s.jsx)(n.h2,{id:"compiling-quantum-espresso-using-intel-math-kernel-library-mkl",children:"Compiling Quantum Espresso using Intel\xae Math Kernel Library (MKL)"}),"\n",(0,s.jsx)(n.p,{children:"If you need a newer or specific version of Quantum Espresso that is not\ninstalled in the NUS clusters or you have modified the source codes yourself,\nhere are the steps that I followed to successfully compile."}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["Quantum Espresso project is primarily hosted on GitLab, and its mirror is\nmaintained at ",(0,s.jsx)(n.a,{href:"https://github.com/QEF/q-e",children:"GitHub"}),". You may check their\nrepository at ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e",children:"GitLab"})," for more up to date\ninformation. The releases via GitLab can be found under:\n",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"https://gitlab.com/QEF/q-e/-/releases"})]})}),"\n",(0,s.jsxs)(n.p,{children:[(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/releases",children:"Download"})," and decompress the source\nfiles."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\ntar -zxvf q-e-qe-7.2.tar.gz\n"})}),"\n",(0,s.jsx)(n.p,{children:"Load the necessary modules (applicable for NUS clusters, last checked in Jun\n2022):"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module load xe_2018\nmodule load fftw/3.3.7\n"})}),"\n",(0,s.jsxs)(n.p,{children:["Go to QE directory and run ",(0,s.jsx)(n.code,{children:"configure"}),":"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\n./configure\n"})}),"\n",(0,s.jsx)(n.p,{children:"You will see output something like:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"...\nBLAS_LIBS= -lmkl_intel_lp64 -lmkl_sequential -lmkl_core\nLAPACK_LIBS=\nFFT_LIBS=\n...\n"})}),"\n",(0,s.jsxs)(n.p,{children:["For me, the ",(0,s.jsx)(n.code,{children:"LAPACK_LIBS"})," and ",(0,s.jsx)(n.code,{children:"FFT_LIBS"})," libs were not automatically detected. We\nneed to specify them manually. First, get the link libraries line specific to\nyour version of MKL and other configurations from the ",(0,s.jsx)(n.a,{href:"https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/onemkl/link-line-advisor.html",children:"Intel link advisor"}),".\nFor my case, the link line was:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:l(2236).A}),(0,s.jsx)("img",{src:l(2143).A,alt:"intel-link-line-adviser",width:"600px"})]}),"\n",(0,s.jsxs)(n.p,{children:["We need to insert the link for ",(0,s.jsx)(n.code,{children:"BLAS_LIBS"}),", ",(0,s.jsx)(n.code,{children:"LAPACK_LIBS"}),", and ",(0,s.jsx)(n.code,{children:"SCALAPACK_LIBS"}),".\nWe also need to find out where is the FFTW lib located. In NUS HPC, we can use\n",(0,s.jsx)(n.code,{children:"module avail"})," command to see where a particular module is located, usually\nunder ",(0,s.jsx)(n.code,{children:"/app1/modules/"}),". Open ",(0,s.jsx)(n.code,{children:"make.inc"})," and make the following changes:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-diff",metastring:'title="make.inc"',children:"# ...\nCFLAGS = -O2 $(DFLAGS) $(IFLAGS)\nCFLAGS = -O3 $(DFLAGS) $(IFLAGS)\nF90FLAGS = $(FFLAGS) -nomodule -fpp $(FDFLAGS) $(CUDA_F90FLAGS) $(IFLAGS) $(MODFLAGS)\n\n# compiler flags with and without optimization for fortran-77\n# the latter is NEEDED to properly compile dlamch.f, used by lapack\n- FFLAGS = -O2 -assume byterecl -g -traceback\n+ FFLAGS = -O3 -assume byterecl -g -traceback\nFFLAGS_NOOPT = -O0 -assume byterecl -g -traceback\n# ...\n# If you have nothing better, use the local copy\n# BLAS_LIBS = $(TOPDIR)/LAPACK/libblas.a\n- BLAS_LIBS = -lmkl_intel_lp64 -lmkl_sequential -lmkl_core\n+ BLAS_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n# If you have nothing better, use the local copy\n# LAPACK = liblapack\n# LAPACK_LIBS = $(TOPDIR)/external/lapack/liblapack.a\n- LAPACK =\n+ LAPACK = liblapack\n- LAPACK_LIBS =\n+ LAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n- SCALAPACK_LIBS =\n+ SCALAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\n\n# nothing is needed here if the internal copy of FFTW is compiled\n# (needs -D__FFTW in DFLAGS)\n\n- FFT_LIBS =\n+ FFT_LIBS = -L/app1/centos6.3/gnu/fftw/3.3.7/lib/ -lmpi\n# ...\n"})}),"\n",(0,s.jsx)(n.p,{children:"Now we are ready to compile:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"make -j8 all\n"})}),"\n",(0,s.jsxs)(n.p,{children:["I am parallelizing with 8 processors to speed things up. You may add the\n",(0,s.jsx)(n.code,{children:"q-e-qe-7.2/bin"})," path to your ",(0,s.jsx)(n.code,{children:".bashrc"}),":"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"echo 'export PATH=\"/home/svu/{username}/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc\n"})}),"\n",(0,s.jsx)(n.p,{children:"And don't forget to load dependencies before calling QE executables."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"module load xe_2018\nmodule load fftw/3.3.7\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["If you are submitting job via PBS queue, you need to provide full path of the QE\nexecutables, e.g., ",(0,s.jsx)(n.code,{children:"/home/svu/{username}/q-e-qe-7.2/bin/pw.x"}),". PBS system won't\nread your bash settings, neither the relative paths of your login node would\napply."]})}),"\n",(0,s.jsx)(n.h2,{id:"installing-intel-oneapi-libraries",children:"Installing Intel oneAPI libraries"}),"\n",(0,s.jsxs)(n.p,{children:["If you need to install Intel oneAPI libraries yourself, following instructions\nmight be useful. Please refer to Intel ",(0,s.jsx)(n.a,{href:"https://www.intel.com/content/www/us/en/developer/tools/oneapi/overview.html",children:"website"}),"\nfor up to date information."]}),"\n",(0,s.jsx)(n.h4,{id:"intel-oneapi-base-toolkit",children:"Intel oneAPI Base Toolkit:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/992857b9-624c-45de-9701-f6445d845359/l_BaseKit_p_2023.2.0.49397_offline.sh\n\n# requires gnu-awk\nsudo apt update && sudo apt install -y --no-install-recommends gawk gcc g++\n\n# interactive cli installation\nsudo apt install -y --no-install-recommends ncurses-term\nsudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --cli\n\n# list components included in oneAPI Base Toolkit\nsh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --list-components\n\n# install a subset of components with silent/unattended option\nsudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --silent --eula accept --components intel.oneapi.lin.dpcpp-cpp-compiler:intel.oneapi.lin.mkl.devel\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["If you install oneAPI without ",(0,s.jsx)(n.code,{children:"sudo"})," privilege, it will be installed under the\nuser directory: ",(0,s.jsx)(n.code,{children:"/home/{username}/intel/oneapi/"}),". After installation is\ncompleted, the setup script will print the installation location."]})}),"\n",(0,s.jsx)(n.h4,{id:"hpc-toolkit",children:"HPC Toolkit"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/0722521a-34b5-4c41-af3f-d5d14e88248d/l_HPCKit_p_2023.2.0.49440_offline.sh\nsudo sh ./l_HPCKit_p_2023.2.0.49440_offline.sh -a --silent --eula accept\n"})}),"\n",(0,s.jsx)(n.h4,{id:"intel-mkl-library",children:"Intel MKL library"}),"\n",(0,s.jsx)(n.p,{children:"Installing individual components:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/adb8a02c-4ee7-4882-97d6-a524150da358/l_onemkl_p_2023.2.0.49497_offline.sh\nsudo sh ./l_onemkl_p_2023.2.0.49497_offline.sh -a --silent --eula accept\n"})}),"\n",(0,s.jsxs)(n.p,{children:["After installation, do not forget to ",(0,s.jsx)(n.code,{children:"source"})," the environment variables before\nusing:"]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"source /opt/intel/oneapi/setvars.sh\n"})}),"\n",(0,s.jsx)(n.p,{children:"Compile quantum espresso:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:'wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz\ntar -zxvf q-e-qe-7.2.tar.gz\nrm q-e-qe-7.2.tar.gz\ncd q-e-qe-7.2\n./configure \\\n F90=mpiifort \\\n MPIF90=mpiifort \\\n CC=mpicc CXX=icc \\\n F77=mpiifort \\\n FFLAGS="-O3 -assume byterecl -g -traceback" \\\n LAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \\\n BLAS_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \\\n SCALAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl"\nmake -j4 all\n'})}),"\n",(0,s.jsx)(n.h2,{id:"compiling-quantum-espresso-with-cmake",children:"Compiling Quantum Espresso with CMake"}),"\n",(0,s.jsxs)(n.p,{children:["Please check out the ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/q-e/-/wikis/Developers/CMake-build-system",children:"official documentation"})," for more\ndetails. It requires ",(0,s.jsx)(n.code,{children:"cmake"})," version ",(0,s.jsx)(n.code,{children:"3.14"})," or later."]}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"apt update && apt install autoconf cmake gawk gcc g++ make\n"})}),"\n",(0,s.jsx)(n.p,{children:"I used following steps to successfully compile Quantum Espresso using 2023\nversions of Intel libraries in Ubuntu 22.04 system:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"cd q-e-qe-7.2\nmkdir build && cd build\ncmake -DCMAKE_C_COMPILER=mpiicc -DCMAKE_Fortran_COMPILER=mpiifort -DQE_ENABLE_SCALAPACK=ON ..\nmake -j4\nmv bin ..\ncd ..\nrm -rf build\n"})}),"\n",(0,s.jsx)(n.h2,{id:"resources",children:"Resources"}),"\n",(0,s.jsxs)(n.ul,{children:["\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/",children:"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/"})}),"\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://help.nscc.sg/pbspro-quickstartguide/",children:"https://help.nscc.sg/pbspro-quickstartguide/"})}),"\n",(0,s.jsx)(n.li,{children:(0,s.jsx)(n.a,{href:"https://www.youtube.com/watch?v=doudMLEaq3w",children:"https://www.youtube.com/watch?v=doudMLEaq3w"})}),"\n"]})]})}function u(e={}){const{wrapper:n}={...(0,i.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(p,{...e})}):p(e)}},2143:(e,n,l)=>{l.d(n,{A:()=>s});const s=l.p+"assets/images/intel-link-line-adviser-30a0f6af6980b2624093d9941f4f2097.png"},2236:(e,n,l)=>{l.d(n,{A:()=>s});const s=l.p+"assets/images/intel-link-line-adviser-c3f2cc310ec8d4c9ea5d90e49a5e32b9.webp"}}]); \ No newline at end of file diff --git a/assets/js/f21bf01f.9642f582.js b/assets/js/f21bf01f.9642f582.js new file mode 100644 index 00000000..d57610ff --- /dev/null +++ b/assets/js/f21bf01f.9642f582.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[7277],{410:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>m,contentTitle:()=>d,default:()=>p,frontMatter:()=>l,metadata:()=>f,toc:()=>u});var s=t(4848),a=t(8453),i=t(1432);t(6025);const o='# load the pw.x input from file\nload_fromPWI fe_scf_fm.in\n\n# dual is the ratio ecutrho/ecutwfc\nforeach dual { 4 8 12 } {\n\n set fid [open etot-vs-ecutwfc.dual$dual.dat w]\n\n foreach ecutwfc [seq 25 5 50] {\n\n set name pw.Fe.scf.ecutwfc-$ecutwfc.dual-$dual\n\n SYSTEM "ecutwfc = $ecutwfc\n ecutrho = $ecutwfc*$dual "\n runPW $name.in\n\n set Etot [pwo_totene $name.out]\n puts $fid "$ecutwfc $Etot"\n }\n\n close $fid\n}\n',c="load_fromPWI fe_scf_fm.in\n\nSYSTEM \" ecutwfc = 40\n ecutrho = 320 \"\n\nset name Fe\n\nrunPW pw.$name.scf.in\n\nCONTROL { calculation = 'nscf' }\nSYSTEM { occupations = 'tetrahedra' ,\n degauss = , ! this is how variable is unset in PWTK\n}\nK_POINTS automatic {\n 12 12 12 1 1 1\n}\nrunPW pw.$name.nscf.in\n\nDOS \"\n fildos = '$name.dos.dat'\n Emin = 5.0\n Emax = 20.0,\n DeltaE = 0.1\n\"\nrunDOS dos.$name.in\n\nPROJWFC \"\n filpdos = '$name.pdos.dat'\n Emin = 5.0\n Emax = 20.0,\n DeltaE = 0.1\n\"\nrunPROJWFC projwfc.$name.in\n",r="# this is a specification for crystal structure\nCRYSTAL\n\n# primitive lattice vectors (in Angstroms)\nPRIMVEC\n 2.8681404710 0.0000000000 0.0000000000\n 0.0000000000 2.8681404710 0.0000000000\n 0.0000000000 0.0000000000 2.8681404710\n\n# conventional lattice vectors (in Angstroms)\nCONVVEC\n 2.8681404710 0.0000000000 0.0000000000\n 0.0000000000 2.8681404710 0.0000000000\n 0.0000000000 0.0000000000 2.8681404710\n\n# First number stands for number of atoms in primitive cell\n# the second number is always 1 for PRIMCOORD coordinates\n# followed by atomic coordinates (in Angstroms) and forces:\n# AtNum X Y Z Fx Fy Fz\nPRIMCOORD\n 2 1\n 26 0.0000000000 0.0000000000 0.0000000000 0.00 0.00 0.01\n 26 1.4340702350 1.4340702350 1.4340702350 0.00 0.00 -0.01\n",l={title:"Magnetic system: bulk iron",sidebar_label:"Fe (magnetic)"},d=void 0,f={id:"hands-on/fe",title:"Magnetic system: bulk iron",description:"I am following this example from the [ICTP online school 2021](",source:"@site/docs/hands-on/fe.mdx",sourceDirName:"hands-on",slug:"/hands-on/fe",permalink:"/espresso/hands-on/fe",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/fe.mdx",tags:[],version:"current",frontMatter:{title:"Magnetic system: bulk iron",sidebar_label:"Fe (magnetic)"},sidebar:"docs",previous:{title:"GaAs",permalink:"/espresso/hands-on/GaAs"},next:{title:"Ni (spin pol. bands)",permalink:"/espresso/hands-on/ni"}},m={},u=[{value:"Convergence test for USPP",id:"convergence-test-for-uspp",level:2},{value:"Density of states calculation",id:"density-of-states-calculation",level:2},{value:"Paramagnetism",id:"paramagnetism",level:2},{value:"Visualizing magnetic moments",id:"visualizing-magnetic-moments",level:2}];function h(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsxs)(n.p,{children:["I am following this example from the ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/materials-for-max-qe2021-online-school",children:"ICTP online school 2021"}),"."]}),"\n",(0,s.jsxs)(n.p,{children:["We will perform the SCF KS orbital calculations on magnetic (",(0,s.jsx)(n.code,{children:"nspin=2"}),") iron.\nSince the d-orbitals of Fe atom are localized/ hard, we will use ultra-soft\npseudo potential (USPP)."]}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsx)(n.p,{children:"If we have crystal structure with only one atom per unit cell, or only one type\nof atoms, the only possible ordering is ferromagnetic. In such cases, we need to\nform supercell with more number of atoms or label multiple atoms separately, so\nthat their magnetic orientation could be different thus having the possibility\nof ferro- or antiferromagnetic final states."})}),"\n",(0,s.jsx)(n.p,{children:"Run the SCF calculations for both ferro- and antiferromagnetic structures.\nNotice that for ferromagnetic, we have BCC structure with only one type of atom,\nwhile we use simple cubic structure for antiferromagnetic case with two\ndifferent atomic labels. For antiferromagnetic calculation, we need to start\nwith opposite initial spins."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pw.x -i pw.scf.fe_fm.in > pw.scf.fe_fm.out\npw.x -i pw.scf.fe_afm.in > pw.scf.fe_afm.out\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["In case of the AFM calculation, if we have started with FM (say, for both atom\ntypes ",(0,s.jsx)(n.code,{children:"starting_magnetization=0.6"})," ), the calculation would still converge to\nAFM state as it is the true ground state for this system, albeit it would take\nmore iteration to converge. If a system has complex potential surface with local\nminima, it it possible to get different final state magnetization depending on\nthe starting magnetization. In such cases, a stricter convergence criteria might\nhelp."]})}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["In case of ultrasoft pseudo potentials, the Quantum Espresso default of\n",(0,s.jsx)(n.code,{children:"ecutrho"})," 4 times of ",(0,s.jsx)(n.code,{children:"ecutoff"})," is not sufficient. We need to set ",(0,s.jsx)(n.code,{children:"ecutrho"})," 8 or\neven 12 times that of ",(0,s.jsx)(n.code,{children:"ecutoff"}),". We must test the convergence for our set\nvalues."]})}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-for-uspp",children:"Convergence test for USPP"}),"\n",(0,s.jsx)(n.p,{children:"Below is the PWTK script file:"}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe_ecut.pwtk",showLineNumbers:!0,children:o}),"\n",(0,s.jsx)(n.p,{children:"Run the script:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pwtk fe_ecut.pwtk\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5296).A}),(0,s.jsx)("img",{src:t(2571).A,alt:"fe-convergence"})]}),"\n",(0,s.jsx)(n.h2,{id:"density-of-states-calculation",children:"Density of states calculation"}),"\n",(0,s.jsx)(n.p,{children:"PWTK script to calculate DOS and p-DOS:"}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe_dos.pwtk",showLineNumbers:!0,children:c}),"\n",(0,s.jsx)(n.p,{children:"Below is the plots of total and projected density of states."}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(4343).A}),(0,s.jsx)("img",{src:t(718).A,alt:"fe-dos"})]}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5813).A}),(0,s.jsx)("img",{src:t(792).A,alt:"fe-pdos"})]}),"\n",(0,s.jsxs)(n.p,{children:["Also see bandstructure of Fe with and without ",(0,s.jsx)(n.a,{href:"soc#bandstructure-of-fe-with-soc",children:"SOC"}),"."]}),"\n",(0,s.jsx)(n.h2,{id:"paramagnetism",children:"Paramagnetism"}),"\n",(0,s.jsx)(n.p,{children:"Paramagnetic materials have fluctuating magnetic moments that may not be\nproperly described DFT. One approach is to model paramagnetic materials in DFT\ncalculation by building a large supercell and assign randomly oriented magnetic\nmoments."}),"\n",(0,s.jsx)(n.p,{children:"Also note that DFT assumes zero temperature, so it makes sense to perform FM or\nAFM calculation for magnetic systems."}),"\n",(0,s.jsx)(n.h2,{id:"visualizing-magnetic-moments",children:"Visualizing magnetic moments"}),"\n",(0,s.jsxs)(n.p,{children:["We can use ",(0,s.jsx)(n.a,{href:"http://www.xcrysden.org",children:"XCrySDen"})," to visualize the orientation of\nmagnetic moments. XCrySDen cannot directly read the Quantum Espresso output\nfiles for magnetic moment vectors, instead we need to create the input ",(0,s.jsx)(n.code,{children:".xsf"}),"\nfile with magnetic moments as force vector. You can also change the background\ncolor from black from the Palette Menu which is located in the left of File\nmenu."]}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe.xsf",showLineNumbers:!0,children:r}),"\n",(0,s.jsxs)(n.p,{children:["Open the file from XCrySDen Menu: ",(0,s.jsx)(n.strong,{children:"File \u2192 Open Structure \u2192 Open XSF"}),". Then go\nto ",(0,s.jsx)(n.strong,{children:"Display"})," menu and select ",(0,s.jsx)(n.strong,{children:"Forces"}),". If you want to adjust scaling for the\nforce vectors, go to ",(0,s.jsx)(n.strong,{children:"Modify \u2192 Force Settings"})," and set suitable Length factor."]}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(1921).A}),(0,s.jsx)("img",{src:t(636).A,alt:"fe-magnetic-structure",width:"450px"})]})]})}function p(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(h,{...e})}):h(e)}},2571:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-convergence-2aefca15b3e0939d06ca680afb8a71a1.png"},5296:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-convergence-1caa80f7711acec59f3b9525d07b8390.webp"},718:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-dos-27c1fcc8eaec7d396fa1bc74be579cc2.png"},4343:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-dos-45bd46db4a4f74412e22c64fb9c918d2.webp"},636:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-magnetic-structure-6333f03af80ee46bef29023302cf3bd7.png"},1921:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-magnetic-structure-1ce9f8ece4ab92800fa14b0eccf00352.webp"},792:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-pdos-776c198dd46078519795539284ddfcd0.png"},5813:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-pdos-a6849fd938c58dcc54c60d2f9dd711c5.webp"}}]); \ No newline at end of file diff --git a/assets/js/f21bf01f.9b0b6ca7.js b/assets/js/f21bf01f.9b0b6ca7.js deleted file mode 100644 index 796ab17a..00000000 --- a/assets/js/f21bf01f.9b0b6ca7.js +++ /dev/null @@ -1 +0,0 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[7277],{5064:(e,n,t)=>{t.r(n),t.d(n,{assets:()=>m,contentTitle:()=>d,default:()=>p,frontMatter:()=>l,metadata:()=>f,toc:()=>u});var s=t(4848),a=t(8453),i=t(1432);t(6025);const o='# load the pw.x input from file\nload_fromPWI fe_scf_fm.in\n\n# dual is the ratio ecutrho/ecutwfc\nforeach dual { 4 8 12 } {\n\n set fid [open etot-vs-ecutwfc.dual$dual.dat w]\n\n foreach ecutwfc [seq 25 5 50] {\n\n set name pw.Fe.scf.ecutwfc-$ecutwfc.dual-$dual\n\n SYSTEM "ecutwfc = $ecutwfc\n ecutrho = $ecutwfc*$dual "\n runPW $name.in\n\n set Etot [pwo_totene $name.out]\n puts $fid "$ecutwfc $Etot"\n }\n\n close $fid\n}\n',c="load_fromPWI fe_scf_fm.in\n\nSYSTEM \" ecutwfc = 40\n ecutrho = 320 \"\n\nset name Fe\n\nrunPW pw.$name.scf.in\n\nCONTROL { calculation = 'nscf' }\nSYSTEM { occupations = 'tetrahedra' ,\n degauss = , ! this is how variable is unset in PWTK\n}\nK_POINTS automatic {\n 12 12 12 1 1 1\n}\nrunPW pw.$name.nscf.in\n\nDOS \"\n fildos = '$name.dos.dat'\n Emin = 5.0\n Emax = 20.0,\n DeltaE = 0.1\n\"\nrunDOS dos.$name.in\n\nPROJWFC \"\n filpdos = '$name.pdos.dat'\n Emin = 5.0\n Emax = 20.0,\n DeltaE = 0.1\n\"\nrunPROJWFC projwfc.$name.in\n",r="# this is a specification for crystal structure\nCRYSTAL\n\n# primitive lattice vectors (in Angstroms)\nPRIMVEC\n 2.8681404710 0.0000000000 0.0000000000\n 0.0000000000 2.8681404710 0.0000000000\n 0.0000000000 0.0000000000 2.8681404710\n\n# conventional lattice vectors (in Angstroms)\nCONVVEC\n 2.8681404710 0.0000000000 0.0000000000\n 0.0000000000 2.8681404710 0.0000000000\n 0.0000000000 0.0000000000 2.8681404710\n\n# First number stands for number of atoms in primitive cell\n# the second number is always 1 for PRIMCOORD coordinates\n# followed by atomic coordinates (in Angstroms) and forces:\n# AtNum X Y Z Fx Fy Fz\nPRIMCOORD\n 2 1\n 26 0.0000000000 0.0000000000 0.0000000000 0.00 0.00 0.01\n 26 1.4340702350 1.4340702350 1.4340702350 0.00 0.00 -0.01\n",l={title:"Magnetic system: bulk iron",sidebar_label:"Fe (magnetic)"},d=void 0,f={id:"hands-on/fe",title:"Magnetic system: bulk iron",description:"I am following this example from the [ICTP online school 2021](",source:"@site/docs/hands-on/fe.mdx",sourceDirName:"hands-on",slug:"/hands-on/fe",permalink:"/espresso/hands-on/fe",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/fe.mdx",tags:[],version:"current",frontMatter:{title:"Magnetic system: bulk iron",sidebar_label:"Fe (magnetic)"},sidebar:"docs",previous:{title:"GaAs",permalink:"/espresso/hands-on/GaAs"},next:{title:"Ni (spin pol. bands)",permalink:"/espresso/hands-on/ni"}},m={},u=[{value:"Convergence test for USPP",id:"convergence-test-for-uspp",level:2},{value:"Density of states calculation",id:"density-of-states-calculation",level:2},{value:"Paramagnetism",id:"paramagnetism",level:2},{value:"Visualizing magnetic moments",id:"visualizing-magnetic-moments",level:2}];function h(e){const n={a:"a",admonition:"admonition",code:"code",h2:"h2",p:"p",pre:"pre",strong:"strong",...(0,a.R)(),...e.components};return(0,s.jsxs)(s.Fragment,{children:[(0,s.jsxs)(n.p,{children:["I am following this example from the ",(0,s.jsx)(n.a,{href:"https://gitlab.com/QEF/materials-for-max-qe2021-online-school",children:"ICTP online school 2021"}),"."]}),"\n",(0,s.jsxs)(n.p,{children:["We will perform the SCF KS orbital calculations on magnetic (",(0,s.jsx)(n.code,{children:"nspin=2"}),") iron.\nSince the d-orbitals of Fe atom are localized/ hard, we will use ultra-soft\npseudo potential (USPP)."]}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsx)(n.p,{children:"If we have crystal structure with only one atom per unit cell, or only one type\nof atoms, the only possible ordering is ferromagnetic. In such cases, we need to\nform supercell with more number of atoms or label multiple atoms separately, so\nthat their magnetic orientation could be different thus having the possibility\nof ferro- or antiferromagnetic final states."})}),"\n",(0,s.jsx)(n.p,{children:"Run the SCF calculations for both ferro- and antiferromagnetic structures.\nNotice that for ferromagnetic, we have BCC structure with only one type of atom,\nwhile we use simple cubic structure for antiferromagnetic case with two\ndifferent atomic labels. For antiferromagnetic calculation, we need to start\nwith opposite initial spins."}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pw.x -i pw.scf.fe_fm.in > pw.scf.fe_fm.out\npw.x -i pw.scf.fe_afm.in > pw.scf.fe_afm.out\n"})}),"\n",(0,s.jsx)(n.admonition,{type:"note",children:(0,s.jsxs)(n.p,{children:["In case of the AFM calculation, if we have started with FM (say, for both atom\ntypes ",(0,s.jsx)(n.code,{children:"starting_magnetization=0.6"})," ), the calculation would still converge to\nAFM state as it is the true ground state for this system, albeit it would take\nmore iteration to converge. If a system has complex potential surface with local\nminima, it it possible to get different final state magnetization depending on\nthe starting magnetization. In such cases, a stricter convergence criteria might\nhelp."]})}),"\n",(0,s.jsx)(n.admonition,{type:"info",children:(0,s.jsxs)(n.p,{children:["In case of ultrasoft pseudo potentials, the Quantum Espresso default of\n",(0,s.jsx)(n.code,{children:"ecutrho"})," 4 times of ",(0,s.jsx)(n.code,{children:"ecutoff"})," is not sufficient. We need to set ",(0,s.jsx)(n.code,{children:"ecutrho"})," 8 or\neven 12 times that of ",(0,s.jsx)(n.code,{children:"ecutoff"}),". We must test the convergence for our set\nvalues."]})}),"\n",(0,s.jsx)(n.h2,{id:"convergence-test-for-uspp",children:"Convergence test for USPP"}),"\n",(0,s.jsx)(n.p,{children:"Below is the PWTK script file:"}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe_ecut.pwtk",showLineNumbers:!0,children:o}),"\n",(0,s.jsx)(n.p,{children:"Run the script:"}),"\n",(0,s.jsx)(n.pre,{children:(0,s.jsx)(n.code,{className:"language-bash",children:"pwtk fe_ecut.pwtk\n"})}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5296).A}),(0,s.jsx)("img",{src:t(2571).A,alt:"fe-convergence"})]}),"\n",(0,s.jsx)(n.h2,{id:"density-of-states-calculation",children:"Density of states calculation"}),"\n",(0,s.jsx)(n.p,{children:"PWTK script to calculate DOS and p-DOS:"}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe_dos.pwtk",showLineNumbers:!0,children:c}),"\n",(0,s.jsx)(n.p,{children:"Below is the plots of total and projected density of states."}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(4343).A}),(0,s.jsx)("img",{src:t(718).A,alt:"fe-dos"})]}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(5813).A}),(0,s.jsx)("img",{src:t(792).A,alt:"fe-pdos"})]}),"\n",(0,s.jsxs)(n.p,{children:["Also see bandstructure of Fe with and without ",(0,s.jsx)(n.a,{href:"soc#bandstructure-of-fe-with-soc",children:"SOC"}),"."]}),"\n",(0,s.jsx)(n.h2,{id:"paramagnetism",children:"Paramagnetism"}),"\n",(0,s.jsx)(n.p,{children:"Paramagnetic materials have fluctuating magnetic moments that may not be\nproperly described DFT. One approach is to model paramagnetic materials in DFT\ncalculation by building a large supercell and assign randomly oriented magnetic\nmoments."}),"\n",(0,s.jsx)(n.p,{children:"Also note that DFT assumes zero temperature, so it makes sense to perform FM or\nAFM calculation for magnetic systems."}),"\n",(0,s.jsx)(n.h2,{id:"visualizing-magnetic-moments",children:"Visualizing magnetic moments"}),"\n",(0,s.jsxs)(n.p,{children:["We can use ",(0,s.jsx)(n.a,{href:"http://www.xcrysden.org",children:"XCrySDen"})," to visualize the orientation of\nmagnetic moments. XCrySDen cannot directly read the Quantum Espresso output\nfiles for magnetic moment vectors, instead we need to create the input ",(0,s.jsx)(n.code,{children:".xsf"}),"\nfile with magnetic moments as force vector. You can also change the background\ncolor from black from the Palette Menu which is located in the left of File\nmenu."]}),"\n","\n",(0,s.jsx)(i.A,{language:"bash",title:"src/fe/fe.xsf",showLineNumbers:!0,children:r}),"\n",(0,s.jsxs)(n.p,{children:["Open the file from XCrySDen Menu: ",(0,s.jsx)(n.strong,{children:"File \u2192 Open Structure \u2192 Open XSF"}),". Then go\nto ",(0,s.jsx)(n.strong,{children:"Display"})," menu and select ",(0,s.jsx)(n.strong,{children:"Forces"}),". If you want to adjust scaling for the\nforce vectors, go to ",(0,s.jsx)(n.strong,{children:"Modify \u2192 Force Settings"})," and set suitable Length factor."]}),"\n",(0,s.jsxs)("picture",{children:[(0,s.jsx)("source",{type:"image/webp",srcSet:t(1921).A}),(0,s.jsx)("img",{src:t(636).A,alt:"fe-magnetic-structure",width:"450px"})]})]})}function p(e={}){const{wrapper:n}={...(0,a.R)(),...e.components};return n?(0,s.jsx)(n,{...e,children:(0,s.jsx)(h,{...e})}):h(e)}},2571:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-convergence-2aefca15b3e0939d06ca680afb8a71a1.png"},5296:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-convergence-1caa80f7711acec59f3b9525d07b8390.webp"},718:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-dos-27c1fcc8eaec7d396fa1bc74be579cc2.png"},4343:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-dos-45bd46db4a4f74412e22c64fb9c918d2.webp"},636:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-magnetic-structure-6333f03af80ee46bef29023302cf3bd7.png"},1921:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-magnetic-structure-1ce9f8ece4ab92800fa14b0eccf00352.webp"},792:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-pdos-776c198dd46078519795539284ddfcd0.png"},5813:(e,n,t)=>{t.d(n,{A:()=>s});const s=t.p+"assets/images/fe-pdos-a6849fd938c58dcc54c60d2f9dd711c5.webp"}}]); \ No newline at end of file diff --git a/assets/js/fb82bcb7.84756885.js b/assets/js/fb82bcb7.56376cf7.js similarity index 98% rename from assets/js/fb82bcb7.84756885.js rename to assets/js/fb82bcb7.56376cf7.js index 7396e92e..8cdc4b42 100644 --- a/assets/js/fb82bcb7.84756885.js +++ b/assets/js/fb82bcb7.56376cf7.js @@ -1 +1 @@ -"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[5281],{5837:(e,s,n)=>{n.r(s),n.d(s,{assets:()=>c,contentTitle:()=>o,default:()=>d,frontMatter:()=>a,metadata:()=>r,toc:()=>l});var t=n(4848),i=n(8453);const a={title:"Bandstructure of topological insulating Bi2Se3",sidebar_label:"Bi2Se3 (TI)"},o=void 0,r={id:"hands-on/Bi2Se3",title:"Bandstructure of topological insulating Bi2Se3",description:"Topological insulators are a special class of material that is insulating in the",source:"@site/docs/hands-on/Bi2Se3.md",sourceDirName:"hands-on",slug:"/hands-on/Bi2Se3",permalink:"/espresso/hands-on/Bi2Se3",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/Bi2Se3.md",tags:[],version:"current",frontMatter:{title:"Bandstructure of topological insulating Bi2Se3",sidebar_label:"Bi2Se3 (TI)"},sidebar:"docs",previous:{title:"Spin-Orbit Coupling",permalink:"/espresso/hands-on/soc"},next:{title:"Dielectric constant",permalink:"/espresso/hands-on/epsilon"}},c={},l=[{value:"Resources",id:"resources",level:2}];function p(e){const s={a:"a",annotation:"annotation",code:"code",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,i.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsxs)(s.p,{children:["Topological insulators are a special class of material that is insulating in the\nbulk, however exhibit conducting states in the surface.\nBi",(0,t.jsx)("sub",{children:"2"}),"Se",(0,t.jsx)("sub",{children:"3"})," is such a material. Spin orbit coupling and\nbreaking of the inversion symmetry at the surface of the crystal is crucial to\nthe existence of the Dirac surface state. Here we will calculate the\nbandstructure step by step: first for the bulk, next including SOC, and finally\nfor the slab. Please check the respective ",(0,t.jsx)(s.a,{href:"https://github.com/pranabdas/espresso/tree/master/src/Bi2Se3",children:"input files"}),". I followed the\nfollowing steps:"]}),"\n",(0,t.jsx)(s.pre,{children:(0,t.jsx)(s.code,{className:"language-bash",children:"# SCF calculation for bulk\nmpirun -np 24 pw.x -i pw.scf.bi2se3_01.in > pw.scf.bi2se3_01.out\n# bands calculation for bulk\nmpirun -np 24 pw.x -i pw.bands.bi2se3_01.in > pw.bands.bi2se3_01.out\n# post processing for bulk bands\nmpirun -np 24 bands.x -i pp.bands.bi2se3_01.in > pp.bands.bi2se3_01.out\n\n# for bulk with SOC\nmpirun -np 24 pw.x -i pw.scf.bi2se3_02.in > pw.scf.bi2se3_02.out\nmpirun -np 24 pw.x -i pw.bands.bi2se3_02.in > pw.bands.bi2se3_02.out\nmpirun -np 24 bands.x -i pp.bands.bi2se3_02.in > pp.bands.bi2se3_02.out\n\n# slab calculation\nmpirun -np 24 pw.x -i pw.scf.bi2se3_03.in > pw.scf.bi2se3_03.out\nmpirun -np 24 pw.x -i pw.bands.bi2se3_03.in > pw.bands.bi2se3_03.out\nmpirun -np 24 bands.x -i pp.bands.bi2se3_03.in > pp.bands.bi2se3_03.out\n\n# DOS\nmpirun -np 24 pw.x -i pw.nscf.bi2se3_04.in > pw.nscf.bi2se3_04.out\nmpirun -np 24 dos.x -i pp.dos.bi2se3_04.in > pp.dos.bi2se3_04.out\n"})}),"\n",(0,t.jsxs)(s.p,{children:["For the slab calculation the periodicity of the lattice was broken along the\nc-axis to artificially add 10 \u212b vacuum. In above calculation electronic spin\nwas not considered (meaning the states are degenerate with spin up and down).\nIf ",(0,t.jsx)(s.code,{children:"starting_magnetization"})," is set to zero (or not given) the code makes a\nspin-orbit calculation without spin magnetization. It assumes that time reversal\nsymmetry holds and it does not calculate the magnetization. The states are\nstill two-component spinors but the total magnetization is zero."]}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:n(2970).A}),(0,t.jsx)("img",{src:n(2737).A,alt:"Bi2Se3-bands"})]}),"\n",(0,t.jsx)(s.p,{children:"Notice that for the Dirac surface states the gap did not completely close at the\nFermi energy. This is possibly due to finite size effect. We could repeat the\ncalculation with larger vacuum, and see what happens. Also the Fermi energy\nestimation seems incorrect."}),"\n",(0,t.jsxs)(s.p,{children:["In order to sample the ",(0,t.jsxs)(s.span,{className:"katex",children:[(0,t.jsx)(s.span,{className:"katex-mathml",children:(0,t.jsx)(s.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,t.jsxs)(s.semantics,{children:[(0,t.jsx)(s.mrow,{children:(0,t.jsx)(s.mi,{mathvariant:"normal",children:"\u0393"})}),(0,t.jsx)(s.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,t.jsx)(s.span,{className:"katex-html","aria-hidden":"true",children:(0,t.jsxs)(s.span,{className:"base",children:[(0,t.jsx)(s.span,{className:"strut",style:{height:"0.6833em"}}),(0,t.jsx)(s.span,{className:"mord",children:"\u0393"})]})})]})," point for our DOS calculation, an odd k-grid\nmesh (25\u271525\u27155) was used. The signature of Dirac cone is evident from the DOS\nfigure."]}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:n(6708).A}),(0,t.jsx)("img",{src:n(2871).A,alt:"Bi2Se3-dos"})]}),"\n",(0,t.jsx)(s.h2,{id:"resources",children:"Resources"}),"\n",(0,t.jsxs)(s.ul,{children:["\n",(0,t.jsx)(s.li,{children:(0,t.jsx)(s.a,{href:"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/topological_insulator_bi2se3.html",children:"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/"})}),"\n"]})]})}function d(e={}){const{wrapper:s}={...(0,i.R)(),...e.components};return s?(0,t.jsx)(s,{...e,children:(0,t.jsx)(p,{...e})}):p(e)}},2737:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-bands-4f1ec6a96553c148f399d1e7d559974b.png"},2970:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-bands-398bb56f7ede3a3314f95ee86bc5ada8.webp"},2871:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-dos-f7444238983f1683a714c9184984d972.png"},6708:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-dos-9b13e51a7bcda6fbee0ca43d715fac7b.webp"},8453:(e,s,n)=>{n.d(s,{R:()=>o,x:()=>r});var t=n(6540);const i={},a=t.createContext(i);function o(e){const s=t.useContext(a);return t.useMemo((function(){return"function"==typeof e?e(s):{...s,...e}}),[s,e])}function r(e){let s;return s=e.disableParentContext?"function"==typeof e.components?e.components(i):e.components||i:o(e.components),t.createElement(a.Provider,{value:s},e.children)}}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[5281],{8850:(e,s,n)=>{n.r(s),n.d(s,{assets:()=>c,contentTitle:()=>o,default:()=>d,frontMatter:()=>a,metadata:()=>r,toc:()=>l});var t=n(4848),i=n(8453);const a={title:"Bandstructure of topological insulating Bi2Se3",sidebar_label:"Bi2Se3 (TI)"},o=void 0,r={id:"hands-on/Bi2Se3",title:"Bandstructure of topological insulating Bi2Se3",description:"Topological insulators are a special class of material that is insulating in the",source:"@site/docs/hands-on/Bi2Se3.md",sourceDirName:"hands-on",slug:"/hands-on/Bi2Se3",permalink:"/espresso/hands-on/Bi2Se3",draft:!1,unlisted:!1,editUrl:"https://github.com/pranabdas/espresso/blob/main/docs/hands-on/Bi2Se3.md",tags:[],version:"current",frontMatter:{title:"Bandstructure of topological insulating Bi2Se3",sidebar_label:"Bi2Se3 (TI)"},sidebar:"docs",previous:{title:"Spin-Orbit Coupling",permalink:"/espresso/hands-on/soc"},next:{title:"Dielectric constant",permalink:"/espresso/hands-on/epsilon"}},c={},l=[{value:"Resources",id:"resources",level:2}];function p(e){const s={a:"a",annotation:"annotation",code:"code",h2:"h2",li:"li",math:"math",mi:"mi",mrow:"mrow",p:"p",pre:"pre",semantics:"semantics",span:"span",ul:"ul",...(0,i.R)(),...e.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsxs)(s.p,{children:["Topological insulators are a special class of material that is insulating in the\nbulk, however exhibit conducting states in the surface.\nBi",(0,t.jsx)("sub",{children:"2"}),"Se",(0,t.jsx)("sub",{children:"3"})," is such a material. Spin orbit coupling and\nbreaking of the inversion symmetry at the surface of the crystal is crucial to\nthe existence of the Dirac surface state. Here we will calculate the\nbandstructure step by step: first for the bulk, next including SOC, and finally\nfor the slab. Please check the respective ",(0,t.jsx)(s.a,{href:"https://github.com/pranabdas/espresso/tree/master/src/Bi2Se3",children:"input files"}),". I followed the\nfollowing steps:"]}),"\n",(0,t.jsx)(s.pre,{children:(0,t.jsx)(s.code,{className:"language-bash",children:"# SCF calculation for bulk\nmpirun -np 24 pw.x -i pw.scf.bi2se3_01.in > pw.scf.bi2se3_01.out\n# bands calculation for bulk\nmpirun -np 24 pw.x -i pw.bands.bi2se3_01.in > pw.bands.bi2se3_01.out\n# post processing for bulk bands\nmpirun -np 24 bands.x -i pp.bands.bi2se3_01.in > pp.bands.bi2se3_01.out\n\n# for bulk with SOC\nmpirun -np 24 pw.x -i pw.scf.bi2se3_02.in > pw.scf.bi2se3_02.out\nmpirun -np 24 pw.x -i pw.bands.bi2se3_02.in > pw.bands.bi2se3_02.out\nmpirun -np 24 bands.x -i pp.bands.bi2se3_02.in > pp.bands.bi2se3_02.out\n\n# slab calculation\nmpirun -np 24 pw.x -i pw.scf.bi2se3_03.in > pw.scf.bi2se3_03.out\nmpirun -np 24 pw.x -i pw.bands.bi2se3_03.in > pw.bands.bi2se3_03.out\nmpirun -np 24 bands.x -i pp.bands.bi2se3_03.in > pp.bands.bi2se3_03.out\n\n# DOS\nmpirun -np 24 pw.x -i pw.nscf.bi2se3_04.in > pw.nscf.bi2se3_04.out\nmpirun -np 24 dos.x -i pp.dos.bi2se3_04.in > pp.dos.bi2se3_04.out\n"})}),"\n",(0,t.jsxs)(s.p,{children:["For the slab calculation the periodicity of the lattice was broken along the\nc-axis to artificially add 10 \u212b vacuum. In above calculation electronic spin\nwas not considered (meaning the states are degenerate with spin up and down).\nIf ",(0,t.jsx)(s.code,{children:"starting_magnetization"})," is set to zero (or not given) the code makes a\nspin-orbit calculation without spin magnetization. It assumes that time reversal\nsymmetry holds and it does not calculate the magnetization. The states are\nstill two-component spinors but the total magnetization is zero."]}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:n(2970).A}),(0,t.jsx)("img",{src:n(2737).A,alt:"Bi2Se3-bands"})]}),"\n",(0,t.jsx)(s.p,{children:"Notice that for the Dirac surface states the gap did not completely close at the\nFermi energy. This is possibly due to finite size effect. We could repeat the\ncalculation with larger vacuum, and see what happens. Also the Fermi energy\nestimation seems incorrect."}),"\n",(0,t.jsxs)(s.p,{children:["In order to sample the ",(0,t.jsxs)(s.span,{className:"katex",children:[(0,t.jsx)(s.span,{className:"katex-mathml",children:(0,t.jsx)(s.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,t.jsxs)(s.semantics,{children:[(0,t.jsx)(s.mrow,{children:(0,t.jsx)(s.mi,{mathvariant:"normal",children:"\u0393"})}),(0,t.jsx)(s.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,t.jsx)(s.span,{className:"katex-html","aria-hidden":"true",children:(0,t.jsxs)(s.span,{className:"base",children:[(0,t.jsx)(s.span,{className:"strut",style:{height:"0.6833em"}}),(0,t.jsx)(s.span,{className:"mord",children:"\u0393"})]})})]})," point for our DOS calculation, an odd k-grid\nmesh (25\u271525\u27155) was used. The signature of Dirac cone is evident from the DOS\nfigure."]}),"\n",(0,t.jsxs)("picture",{children:[(0,t.jsx)("source",{type:"image/webp",srcSet:n(6708).A}),(0,t.jsx)("img",{src:n(2871).A,alt:"Bi2Se3-dos"})]}),"\n",(0,t.jsx)(s.h2,{id:"resources",children:"Resources"}),"\n",(0,t.jsxs)(s.ul,{children:["\n",(0,t.jsx)(s.li,{children:(0,t.jsx)(s.a,{href:"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/topological_insulator_bi2se3.html",children:"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/"})}),"\n"]})]})}function d(e={}){const{wrapper:s}={...(0,i.R)(),...e.components};return s?(0,t.jsx)(s,{...e,children:(0,t.jsx)(p,{...e})}):p(e)}},2737:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-bands-4f1ec6a96553c148f399d1e7d559974b.png"},2970:(e,s,n)=>{n.d(s,{A:()=>t});const t=n.p+"assets/images/Bi2Se3-bands-398bb56f7ede3a3314f95ee86bc5ada8.webp"},2871:(e,s,n)=>{n.d(s,{A:()=>t});const 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mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mclose",children:")"})]})]})]})]}),"\n",(0,n.jsx)(e.p,{children:"Before we can run the Density of States (DOS) calculation, we need"}),"\n",(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Perform fixed-ion self consistent filed (scf) calculation. In plane-wave\nbased DFT calculations the electronic density is expressed by functions of the\nform ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"exp"}),(0,n.jsx)(e.mo,{children:"\u2061"}),(0,n.jsx)(e.mo,{stretchy:"false",children:"("}),(0,n.jsx)(e.mi,{children:"i"}),(0,n.jsx)(e.mtext,{mathvariant:"bold",children:"k"}),(0,n.jsx)(e.mo,{children:"\u22c5"}),(0,n.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,n.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\exp (i \\textbf{k} \\cdot \\textbf{r})"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mop",children:"exp"}),(0,n.jsx)(e.span,{className:"mopen",children:"("}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"i"}),(0,n.jsx)(e.span,{className:"mord text",children:(0,n.jsx)(e.span,{className:"mord textbf",children:"k"})}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\u22c5"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mord text",children:(0,n.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,n.jsx)(e.span,{className:"mclose",children:")"})]})]})]})," with energy given by\n",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"E"}),(0,n.jsx)(e.mo,{children:"="}),(0,n.jsxs)(e.msup,{children:[(0,n.jsx)(e.mi,{mathvariant:"normal",children:"\u210f"}),(0,n.jsx)(e.mn,{children:"2"})]}),(0,n.jsxs)(e.msup,{children:[(0,n.jsx)(e.mi,{children:"k"}),(0,n.jsx)(e.mn,{children:"2"})]}),(0,n.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,n.jsx)(e.mn,{children:"2"}),(0,n.jsx)(e.mi,{children:"m"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"E = \\hbar^2k^2/2m"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.jsx)(e.span,{className:"mrel",children:"="}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),(0,n.jsxs)(e.span,{className:"mord",children:[(0,n.jsx)(e.span,{className:"mord",children:"\u210f"}),(0,n.jsx)(e.span,{className:"msupsub",children:(0,n.jsx)(e.span,{className:"vlist-t",children:(0,n.jsx)(e.span,{className:"vlist-r",children:(0,n.jsx)(e.span,{className:"vlist",style:{height:"0.8141em"},children:(0,n.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,n.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,n.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,n.jsx)(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),(0,n.jsxs)(e.span,{className:"mord",children:[(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"}),(0,n.jsx)(e.span,{className:"msupsub",children:(0,n.jsx)(e.span,{className:"vlist-t",children:(0,n.jsx)(e.span,{className:"vlist-r",children:(0,n.jsx)(e.span,{className:"vlist",style:{height:"0.8141em"},children:(0,n.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,n.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,n.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,n.jsx)(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),(0,n.jsx)(e.span,{className:"mord",children:"/2"}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"m"})]})]})]}),"."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Perform non-self consistent field (nscf) calculation with denser k-point\ngrid. A large number of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]})," points are required DOS calculation, as the accuracy\nof DOS depends on the integration in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]})," space."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Finally, the DOS can be determined by integrating the electron density in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]}),"\nspace."]}),"\n"]}),"\n"]}),"\n",(0,n.jsxs)(e.p,{children:["I have created a new input file (",(0,n.jsx)(e.code,{children:"pw.scf.silicon_dos.in"}),") which is very much the same as\nour previous scf input file except some parameters are modified. You can find\nall the input files in my ",(0,n.jsx)(e.a,{href:"https://github.com/pranabdas/espresso/",children:"GitHub repository"}),". We used the lattice constant value that\nwe obtained from the relaxation calculation. We should not directly use the\nexperimental/real lattice constant values. Depending on the method and\npseudo-potential, it might result stress in the system. We have increased the\n",(0,n.jsx)(e.code,{children:"ecutwfc"})," to have better precision. We run the scf calculation:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.scf.silicon_dos.in > pw.scf.silicon_dos.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Next, we have prepared the input file for the ",(0,n.jsx)(e.code,{children:"nscf"})," calculation. Where is have\nadded ",(0,n.jsx)(e.code,{children:"occupations"})," in the ",(0,n.jsx)(e.code,{children:"&system"})," card as ",(0,n.jsx)(e.code,{children:"tetrahedra"})," (appropriate for DOS\ncalculation). We have increased the number of k-points to 12 \xd7 12 \xd7 12 with\nautomatic option. Also specify ",(0,n.jsx)(e.code,{children:"nosym = .TRUE."})," to avoid generation of\nadditional k-points in low symmetry cases. ",(0,n.jsx)(e.code,{children:"outdir"})," and ",(0,n.jsx)(e.code,{children:"prefix"})," must be the\nsame as in the ",(0,n.jsx)(e.code,{children:"scf"})," step, some of the inputs and output are read from previous\nstep. Here we can specify a larger number of ",(0,n.jsx)(e.code,{children:"nbnd"})," to calculate unoccupied\nbands. Number of occupied bands can be found in the ",(0,n.jsx)(e.code,{children:"scf"})," output as number of\nKohn-Sham states."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.nscf.silicon_dos.in > pw.nscf.silicon_dos.out\n"})}),"\n",(0,n.jsx)(e.p,{children:"Now our final step is to calculate the density of states. The DOS input file as\nfollows:"}),"\n","\n",(0,n.jsx)(i.A,{language:"bash",title:"src/silicon/pp.dos.silicon.in",showLineNumbers:!0,children:l}),"\n",(0,n.jsx)(e.p,{children:"We run:"}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"dos.x < pp.dos.silicon.in > pp.dos.silicon.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["The DOS data in the ",(0,n.jsx)(e.code,{children:"si_dos.dat"})," file that we specified in our input file. We\ncan plot the DOS:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-python",metastring:'title="notebooks/silicon-dos.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\n\n# load data\nenergy, dos, idos = np.loadtxt('../src/silicon/si_dos.dat', unpack=True)\n\n# make plot\nplt.figure(figsize = (12, 6))\nplt.plot(energy, dos, linewidth=0.75, color='red')\nplt.yticks([])\nplt.xlabel('Energy (eV)')\nplt.ylabel('DOS')\nplt.axvline(x=6.642, linewidth=0.5, color='k', linestyle=(0, (8, 10)))\nplt.xlim(-6, 16)\nplt.ylim(0, )\nplt.fill_between(energy, 0, dos, where=(energy < 6.642), facecolor='red', alpha=0.25)\nplt.text(6, 1.7, 'Fermi energy', fontsize= med, rotation=90)\nplt.show()\n"})}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(1725).A}),(0,n.jsx)("img",{src:a(4336).A,alt:"silicon-dos"})]}),"\n",(0,n.jsx)(e.admonition,{title:"Important",type:"info",children:(0,n.jsxs)(e.p,{children:["For a set of calculation, we must keep the ",(0,n.jsx)(e.code,{children:"prefix"})," same. For example, the\n",(0,n.jsx)(e.strong,{children:"nscf"})," or ",(0,n.jsx)(e.strong,{children:"bands"})," calculation uses the wavefunction calculated by the\n",(0,n.jsx)(e.strong,{children:"scf"})," calculation. When performing different calculations, for example you\nchange a parameter and want to see the changes, you must use different output\nfolder or unique ",(0,n.jsx)(e.code,{children:"prefix"})," for different calculations so that the outputs do not\nget mixed."]})}),"\n",(0,n.jsx)(e.admonition,{type:"tip",children:(0,n.jsxs)(e.p,{children:["Sometimes it is important to sample the ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]})," point for DOS calculation\n(e.g., the conducting bands cross the Fermi surface only at ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{mathvariant:"normal",children:"\u0393"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\Gamma"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord",children:"\u0393"})]})})]})," point). In\nsuch cases, we need to use odd k-grid (e.g., 9\u27159\u27155)."]})})]})}function p(s={}){const{wrapper:e}={...(0,t.R)(),...s.components};return e?(0,n.jsx)(e,{...s,children:(0,n.jsx)(o,{...s})}):o(s)}},4336:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/silicon-dos-9d095ddb8c71cd03ee572f2fe9f8356c.png"},1725:(s,e,a)=>{a.d(e,{A:()=>n});const n=a.p+"assets/images/silicon-dos-edf95503cd6527685b73ada318c5cf68.webp"}}]); \ No newline at end of file +"use strict";(self.webpackChunkespresso=self.webpackChunkespresso||[]).push([[6424],{4707:(s,e,a)=>{a.r(e),a.d(e,{assets:()=>h,contentTitle:()=>r,default:()=>p,frontMatter:()=>c,metadata:()=>m,toc:()=>d});var n=a(4848),t=a(8453),i=a(1432);const l="&DOS\n prefix='silicon',\n outdir='./tmp/',\n fildos='si_dos.dat',\n emin=-9.0,\n emax=16.0\n/\n",c={title:"Density of States calculation",sidebar_label:"DOS calculation"},r=void 0,m={id:"hands-on/dos",title:"Density of States calculation",description:"Electronic density of states is an 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dE)"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mopen",children:"("}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mpunct",children:","}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"+"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"d"}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mclose",children:")"})]})]})]})]}),"\n",(0,n.jsx)(e.p,{children:"Before we can run the Density of States (DOS) calculation, we need"}),"\n",(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Perform fixed-ion self consistent filed (scf) calculation. In plane-wave\nbased DFT calculations the electronic density is expressed by functions of the\nform ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"exp"}),(0,n.jsx)(e.mo,{children:"\u2061"}),(0,n.jsx)(e.mo,{stretchy:"false",children:"("}),(0,n.jsx)(e.mi,{children:"i"}),(0,n.jsx)(e.mtext,{mathvariant:"bold",children:"k"}),(0,n.jsx)(e.mo,{children:"\u22c5"}),(0,n.jsx)(e.mtext,{mathvariant:"bold",children:"r"}),(0,n.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\exp (i \\textbf{k} \\cdot \\textbf{r})"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mop",children:"exp"}),(0,n.jsx)(e.span,{className:"mopen",children:"("}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"i"}),(0,n.jsx)(e.span,{className:"mord text",children:(0,n.jsx)(e.span,{className:"mord textbf",children:"k"})}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.jsx)(e.span,{className:"mbin",children:"\u22c5"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.jsx)(e.span,{className:"mord text",children:(0,n.jsx)(e.span,{className:"mord textbf",children:"r"})}),(0,n.jsx)(e.span,{className:"mclose",children:")"})]})]})]})," with energy given by\n",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsxs)(e.mrow,{children:[(0,n.jsx)(e.mi,{children:"E"}),(0,n.jsx)(e.mo,{children:"="}),(0,n.jsxs)(e.msup,{children:[(0,n.jsx)(e.mi,{mathvariant:"normal",children:"\u210f"}),(0,n.jsx)(e.mn,{children:"2"})]}),(0,n.jsxs)(e.msup,{children:[(0,n.jsx)(e.mi,{children:"k"}),(0,n.jsx)(e.mn,{children:"2"})]}),(0,n.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,n.jsx)(e.mn,{children:"2"}),(0,n.jsx)(e.mi,{children:"m"})]}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"E = \\hbar^2k^2/2m"})]})})}),(0,n.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"E"}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.jsx)(e.span,{className:"mrel",children:"="}),(0,n.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),(0,n.jsxs)(e.span,{className:"mord",children:[(0,n.jsx)(e.span,{className:"mord",children:"\u210f"}),(0,n.jsx)(e.span,{className:"msupsub",children:(0,n.jsx)(e.span,{className:"vlist-t",children:(0,n.jsx)(e.span,{className:"vlist-r",children:(0,n.jsx)(e.span,{className:"vlist",style:{height:"0.8141em"},children:(0,n.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,n.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,n.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,n.jsx)(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),(0,n.jsxs)(e.span,{className:"mord",children:[(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"}),(0,n.jsx)(e.span,{className:"msupsub",children:(0,n.jsx)(e.span,{className:"vlist-t",children:(0,n.jsx)(e.span,{className:"vlist-r",children:(0,n.jsx)(e.span,{className:"vlist",style:{height:"0.8141em"},children:(0,n.jsxs)(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[(0,n.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,n.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,n.jsx)(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),(0,n.jsx)(e.span,{className:"mord",children:"/2"}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"m"})]})]})]}),"."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Perform non-self consistent field (nscf) calculation with denser k-point\ngrid. A large number of ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]})," points are required DOS calculation, as the accuracy\nof DOS depends on the integration in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]})," space."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:["Finally, the DOS can be determined by integrating the electron density in ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"k"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"k"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.03148em"},children:"k"})]})})]}),"\nspace."]}),"\n"]}),"\n"]}),"\n",(0,n.jsxs)(e.p,{children:["I have created a new input file (",(0,n.jsx)(e.code,{children:"pw.scf.silicon_dos.in"}),") which is very much the same as\nour previous scf input file except some parameters are modified. You can find\nall the input files in my ",(0,n.jsx)(e.a,{href:"https://github.com/pranabdas/espresso/",children:"GitHub repository"}),". We used the lattice constant value that\nwe obtained from the relaxation calculation. We should not directly use the\nexperimental/real lattice constant values. Depending on the method and\npseudo-potential, it might result stress in the system. We have increased the\n",(0,n.jsx)(e.code,{children:"ecutwfc"})," to have better precision. We run the scf calculation:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.scf.silicon_dos.in > pw.scf.silicon_dos.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["Next, we have prepared the input file for the ",(0,n.jsx)(e.code,{children:"nscf"})," calculation. Where is have\nadded ",(0,n.jsx)(e.code,{children:"occupations"})," in the ",(0,n.jsx)(e.code,{children:"&system"})," card as ",(0,n.jsx)(e.code,{children:"tetrahedra"})," (appropriate for DOS\ncalculation). We have increased the number of k-points to 12 \xd7 12 \xd7 12 with\nautomatic option. Also specify ",(0,n.jsx)(e.code,{children:"nosym = .TRUE."})," to avoid generation of\nadditional k-points in low symmetry cases. ",(0,n.jsx)(e.code,{children:"outdir"})," and ",(0,n.jsx)(e.code,{children:"prefix"})," must be the\nsame as in the ",(0,n.jsx)(e.code,{children:"scf"})," step, some of the inputs and output are read from previous\nstep. Here we can specify a larger number of ",(0,n.jsx)(e.code,{children:"nbnd"})," to calculate unoccupied\nbands. Number of occupied bands can be found in the ",(0,n.jsx)(e.code,{children:"scf"})," output as number of\nKohn-Sham states."]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"pw.x < pw.nscf.silicon_dos.in > pw.nscf.silicon_dos.out\n"})}),"\n",(0,n.jsx)(e.p,{children:"Now our final step is to calculate the density of states. The DOS input file as\nfollows:"}),"\n","\n",(0,n.jsx)(i.A,{language:"bash",title:"src/silicon/pp.dos.silicon.in",showLineNumbers:!0,children:l}),"\n",(0,n.jsx)(e.p,{children:"We run:"}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-bash",children:"dos.x < pp.dos.silicon.in > pp.dos.silicon.out\n"})}),"\n",(0,n.jsxs)(e.p,{children:["The DOS data in the ",(0,n.jsx)(e.code,{children:"si_dos.dat"})," file that we specified in our input file. We\ncan plot the DOS:"]}),"\n",(0,n.jsx)(e.pre,{children:(0,n.jsx)(e.code,{className:"language-python",metastring:'title="notebooks/silicon-dos.ipynb" showLineNumbers',children:"import matplotlib.pyplot as plt\nfrom matplotlib import rcParamsDefault\nimport numpy as np\n%matplotlib inline\n\n# load data\nenergy, dos, idos = np.loadtxt('../src/silicon/si_dos.dat', unpack=True)\n\n# make plot\nplt.figure(figsize = (12, 6))\nplt.plot(energy, dos, linewidth=0.75, color='red')\nplt.yticks([])\nplt.xlabel('Energy (eV)')\nplt.ylabel('DOS')\nplt.axvline(x=6.642, linewidth=0.5, color='k', linestyle=(0, (8, 10)))\nplt.xlim(-6, 16)\nplt.ylim(0, )\nplt.fill_between(energy, 0, dos, where=(energy < 6.642), facecolor='red', alpha=0.25)\nplt.text(6, 1.7, 'Fermi energy', fontsize= med, rotation=90)\nplt.show()\n"})}),"\n",(0,n.jsxs)("picture",{children:[(0,n.jsx)("source",{type:"image/webp",srcSet:a(1725).A}),(0,n.jsx)("img",{src:a(4336).A,alt:"silicon-dos"})]}),"\n",(0,n.jsx)(e.admonition,{title:"Important",type:"info",children:(0,n.jsxs)(e.p,{children:["For a set of calculation, we must keep the ",(0,n.jsx)(e.code,{children:"prefix"})," same. For example, the\n",(0,n.jsx)(e.strong,{children:"nscf"})," or ",(0,n.jsx)(e.strong,{children:"bands"})," calculation uses the wavefunction calculated by the\n",(0,n.jsx)(e.strong,{children:"scf"})," calculation. 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e=[],t=[{prefix:"",node:this}];t.length;){var n=t.pop(),r=Object.keys(n.node.edges),a=r.length;n.node.final&&(n.prefix.charAt(0),e.push(n.prefix));for(var o=0;o<a;o++){var i=r[o];t.push({prefix:n.prefix.concat(i),node:n.node.edges[i]})}}return e},j.TokenSet.prototype.toString=function(){if(this._str)return this._str;for(var e=this.final?"1":"0",t=Object.keys(this.edges).sort(),n=t.length,r=0;r<n;r++){var a=t[r];e=e+a+this.edges[a].id}return e},j.TokenSet.prototype.intersect=function(e){for(var t=new j.TokenSet,n=void 0,r=[{qNode:e,output:t,node:this}];r.length;){n=r.pop();for(var a=Object.keys(n.qNode.edges),o=a.length,i=Object.keys(n.node.edges),s=i.length,l=0;l<o;l++)for(var u=a[l],c=0;c<s;c++){var d=i[c];if(d==u||"*"==u){var p=n.node.edges[d],f=n.qNode.edges[u],h=p.final&&f.final,g=void 0;d in n.output.edges?(g=n.output.edges[d]).final=g.final||h:((g=new j.TokenSet).final=h,n.output.edges[d]=g),r.push({qNode:f,output:g,node:p})}}}return t},j.TokenSet.Builder=function(){this.previousWord="",this.root=new j.TokenSet,this.uncheckedNodes=[],this.minimizedNodes={}},j.TokenSet.Builder.prototype.insert=function(e){var t,n=0;if(e<this.previousWord)throw new Error("Out of order word insertion");for(var r=0;r<e.length&&r<this.previousWord.length&&e[r]==this.previousWord[r];r++)n++;this.minimize(n),t=0==this.uncheckedNodes.length?this.root:this.uncheckedNodes[this.uncheckedNodes.length-1].child;for(r=n;r<e.length;r++){var a=new j.TokenSet,o=e[r];t.edges[o]=a,this.uncheckedNodes.push({parent:t,char:o,child:a}),t=a}t.final=!0,this.previousWord=e},j.TokenSet.Builder.prototype.finish=function(){this.minimize(0)},j.TokenSet.Builder.prototype.minimize=function(e){for(var t=this.uncheckedNodes.length-1;t>=e;t--){var n=this.uncheckedNodes[t],r=n.child.toString();r in 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g=0;g<l.fields.length;g++){o[O=l.fields[g]]=j.Set.empty}break}for(var m=0;m<h.length;m++){var y=h[m],b=this.invertedIndex[y],v=b._index;for(g=0;g<l.fields.length;g++){var w=b[O=l.fields[g]],x=Object.keys(w),k=y+"/"+O,S=new j.Set(x);if(l.presence==j.Query.presence.REQUIRED&&(c=c.union(S),void 0===o[O]&&(o[O]=j.Set.complete)),l.presence!=j.Query.presence.PROHIBITED){if(r[O].upsert(v,l.boost,(function(e,t){return e+t})),!a[k]){for(var E=0;E<x.length;E++){var _,C=x[E],T=new j.FieldRef(C,O),A=w[C];void 0===(_=n[T])?n[T]=new j.MatchData(y,O,A):_.add(y,O,A)}a[k]=!0}}else void 0===i[O]&&(i[O]=j.Set.empty),i[O]=i[O].union(S)}}}if(l.presence===j.Query.presence.REQUIRED)for(g=0;g<l.fields.length;g++){o[O=l.fields[g]]=o[O].intersect(c)}}var N=j.Set.complete,L=j.Set.empty;for(s=0;s<this.fields.length;s++){var O;o[O=this.fields[s]]&&(N=N.intersect(o[O])),i[O]&&(L=L.union(i[O]))}var P=Object.keys(n),R=[],I=Object.create(null);if(t.isNegated()){P=Object.keys(this.fieldVectors);for(s=0;s<P.length;s++){T=P[s];var F=j.FieldRef.fromString(T);n[T]=new j.MatchData}}for(s=0;s<P.length;s++){var D=(F=j.FieldRef.fromString(P[s])).docRef;if(N.contains(D)&&!L.contains(D)){var M,B=this.fieldVectors[F],z=r[F.fieldName].similarity(B);if(void 0!==(M=I[D]))M.score+=z,M.matchData.combine(n[F]);else{var U={ref:D,score:z,matchData:n[F]};I[D]=U,R.push(U)}}}return R.sort((function(e,t){return t.score-e.score}))},j.Index.prototype.toJSON=function(){var e=Object.keys(this.invertedIndex).sort().map((function(e){return[e,this.invertedIndex[e]]}),this),t=Object.keys(this.fieldVectors).map((function(e){return[e,this.fieldVectors[e].toJSON()]}),this);return{version:j.version,fields:this.fields,fieldVectors:t,invertedIndex:e,pipeline:this.pipeline.toJSON()}},j.Index.load=function(e){var t={},n={},r=e.fieldVectors,a=Object.create(null),o=e.invertedIndex,i=new j.TokenSet.Builder,s=j.Pipeline.load(e.pipeline);e.version!=j.version&&j.utils.warn("Version mismatch when loading serialised index. Current version of lunr '"+j.version+"' does not match serialized index '"+e.version+"'");for(var l=0;l<r.length;l++){var u=(d=r[l])[0],c=d[1];n[u]=new j.Vector(c)}for(l=0;l<o.length;l++){var d,p=(d=o[l])[0],f=d[1];i.insert(p),a[p]=f}return i.finish(),t.fields=e.fields,t.fieldVectors=n,t.invertedIndex=a,t.tokenSet=i.root,t.pipeline=s,new j.Index(t)},j.Builder=function(){this._ref="id",this._fields=Object.create(null),this._documents=Object.create(null),this.invertedIndex=Object.create(null),this.fieldTermFrequencies={},this.fieldLengths={},this.tokenizer=j.tokenizer,this.pipeline=new j.Pipeline,this.searchPipeline=new j.Pipeline,this.documentCount=0,this._b=.75,this._k1=1.2,this.termIndex=0,this.metadataWhitelist=[]},j.Builder.prototype.ref=function(e){this._ref=e},j.Builder.prototype.field=function(e,t){if(/\//.test(e))throw new RangeError("Field '"+e+"' contains illegal character '/'");this._fields[e]=t||{}},j.Builder.prototype.b=function(e){this._b=e<0?0:e>1?1:e},j.Builder.prototype.k1=function(e){this._k1=e},j.Builder.prototype.add=function(e,t){var n=e[this._ref],r=Object.keys(this._fields);this._documents[n]=t||{},this.documentCount+=1;for(var a=0;a<r.length;a++){var o=r[a],i=this._fields[o].extractor,s=i?i(e):e[o],l=this.tokenizer(s,{fields:[o]}),u=this.pipeline.run(l),c=new j.FieldRef(n,o),d=Object.create(null);this.fieldTermFrequencies[c]=d,this.fieldLengths[c]=0,this.fieldLengths[c]+=u.length;for(var p=0;p<u.length;p++){var f=u[p];if(null==d[f]&&(d[f]=0),d[f]+=1,null==this.invertedIndex[f]){var h=Object.create(null);h._index=this.termIndex,this.termIndex+=1;for(var g=0;g<r.length;g++)h[r[g]]=Object.create(null);this.invertedIndex[f]=h}null==this.invertedIndex[f][o][n]&&(this.invertedIndex[f][o][n]=Object.create(null));for(var m=0;m<this.metadataWhitelist.length;m++){var y=this.metadataWhitelist[m],b=f.metadata[y];null==this.invertedIndex[f][o][n][y]&&(this.invertedIndex[f][o][n][y]=[]),this.invertedIndex[f][o][n][y].push(b)}}}},j.Builder.prototype.calculateAverageFieldLengths=function(){for(var e=Object.keys(this.fieldLengths),t=e.length,n={},r={},a=0;a<t;a++){var o=j.FieldRef.fromString(e[a]),i=o.fieldName;r[i]||(r[i]=0),r[i]+=1,n[i]||(n[i]=0),n[i]+=this.fieldLengths[o]}var s=Object.keys(this._fields);for(a=0;a<s.length;a++){var l=s[a];n[l]=n[l]/r[l]}this.averageFieldLength=n},j.Builder.prototype.createFieldVectors=function(){for(var e={},t=Object.keys(this.fieldTermFrequencies),n=t.length,r=Object.create(null),a=0;a<n;a++){for(var o=j.FieldRef.fromString(t[a]),i=o.fieldName,s=this.fieldLengths[o],l=new j.Vector,u=this.fieldTermFrequencies[o],c=Object.keys(u),d=c.length,p=this._fields[i].boost||1,f=this._documents[o.docRef].boost||1,h=0;h<d;h++){var g,m,y,b=c[h],v=u[b],w=this.invertedIndex[b]._index;void 0===r[b]?(g=j.idf(this.invertedIndex[b],this.documentCount),r[b]=g):g=r[b],m=g*((this._k1+1)*v)/(this._k1*(1-this._b+this._b*(s/this.averageFieldLength[i]))+v),m*=p,m*=f,y=Math.round(1e3*m)/1e3,l.insert(w,y)}e[o]=l}this.fieldVectors=e},j.Builder.prototype.createTokenSet=function(){this.tokenSet=j.TokenSet.fromArray(Object.keys(this.invertedIndex).sort())},j.Builder.prototype.build=function(){return this.calculateAverageFieldLengths(),this.createFieldVectors(),this.createTokenSet(),new j.Index({invertedIndex:this.invertedIndex,fieldVectors:this.fieldVectors,tokenSet:this.tokenSet,fields:Object.keys(this._fields),pipeline:this.searchPipeline})},j.Builder.prototype.use=function(e){var t=Array.prototype.slice.call(arguments,1);t.unshift(this),e.apply(this,t)},j.MatchData=function(e,t,n){for(var r=Object.create(null),a=Object.keys(n||{}),o=0;o<a.length;o++){var i=a[o];r[i]=n[i].slice()}this.metadata=Object.create(null),void 0!==e&&(this.metadata[e]=Object.create(null),this.metadata[e][t]=r)},j.MatchData.prototype.combine=function(e){for(var t=Object.keys(e.metadata),n=0;n<t.length;n++){var r=t[n],a=Object.keys(e.metadata[r]);null==this.metadata[r]&&(this.metadata[r]=Object.create(null));for(var o=0;o<a.length;o++){var i=a[o],s=Object.keys(e.metadata[r][i]);null==this.metadata[r][i]&&(this.metadata[r][i]=Object.create(null));for(var l=0;l<s.length;l++){var u=s[l];null==this.metadata[r][i][u]?this.metadata[r][i][u]=e.metadata[r][i][u]:this.metadata[r][i][u]=this.metadata[r][i][u].concat(e.metadata[r][i][u])}}}},j.MatchData.prototype.add=function(e,t,n){if(!(e in this.metadata))return this.metadata[e]=Object.create(null),void(this.metadata[e][t]=n);if(t in this.metadata[e])for(var r=Object.keys(n),a=0;a<r.length;a++){var o=r[a];o in this.metadata[e][t]?this.metadata[e][t][o]=this.metadata[e][t][o].concat(n[o]):this.metadata[e][t][o]=n[o]}else this.metadata[e][t]=n},j.Query=function(e){this.clauses=[],this.allFields=e},j.Query.wildcard=new String("*"),j.Query.wildcard.NONE=0,j.Query.wildcard.LEADING=1,j.Query.wildcard.TRAILING=2,j.Query.presence={OPTIONAL:1,REQUIRED:2,PROHIBITED:3},j.Query.prototype.clause=function(e){return"fields"in e||(e.fields=this.allFields),"boost"in e||(e.boost=1),"usePipeline"in e||(e.usePipeline=!0),"wildcard"in e||(e.wildcard=j.Query.wildcard.NONE),e.wildcard&j.Query.wildcard.LEADING&&e.term.charAt(0)!=j.Query.wildcard&&(e.term="*"+e.term),e.wildcard&j.Query.wildcard.TRAILING&&e.term.slice(-1)!=j.Query.wildcard&&(e.term=e.term+"*"),"presence"in e||(e.presence=j.Query.presence.OPTIONAL),this.clauses.push(e),this},j.Query.prototype.isNegated=function(){for(var e=0;e<this.clauses.length;e++)if(this.clauses[e].presence!=j.Query.presence.PROHIBITED)return!1;return!0},j.Query.prototype.term=function(e,t){if(Array.isArray(e))return e.forEach((function(e){this.term(e,j.utils.clone(t))}),this),this;var n=t||{};return n.term=e.toString(),this.clause(n),this},j.QueryParseError=function(e,t,n){this.name="QueryParseError",this.message=e,this.start=t,this.end=n},j.QueryParseError.prototype=new Error,j.QueryLexer=function(e){this.lexemes=[],this.str=e,this.length=e.length,this.pos=0,this.start=0,this.escapeCharPositions=[]},j.QueryLexer.prototype.run=function(){for(var e=j.QueryLexer.lexText;e;)e=e(this)},j.QueryLexer.prototype.sliceString=function(){for(var e=[],t=this.start,n=this.pos,r=0;r<this.escapeCharPositions.length;r++)n=this.escapeCharPositions[r],e.push(this.str.slice(t,n)),t=n+1;return e.push(this.str.slice(t,this.pos)),this.escapeCharPositions.length=0,e.join("")},j.QueryLexer.prototype.emit=function(e){this.lexemes.push({type:e,str:this.sliceString(),start:this.start,end:this.pos}),this.start=this.pos},j.QueryLexer.prototype.escapeCharacter=function(){this.escapeCharPositions.push(this.pos-1),this.pos+=1},j.QueryLexer.prototype.next=function(){if(this.pos>=this.length)return j.QueryLexer.EOS;var e=this.str.charAt(this.pos);return this.pos+=1,e},j.QueryLexer.prototype.width=function(){return this.pos-this.start},j.QueryLexer.prototype.ignore=function(){this.start==this.pos&&(this.pos+=1),this.start=this.pos},j.QueryLexer.prototype.backup=function(){this.pos-=1},j.QueryLexer.prototype.acceptDigitRun=function(){var e,t;do{t=(e=this.next()).charCodeAt(0)}while(t>47&&t<58);e!=j.QueryLexer.EOS&&this.backup()},j.QueryLexer.prototype.more=function(){return this.pos<this.length},j.QueryLexer.EOS="EOS",j.QueryLexer.FIELD="FIELD",j.QueryLexer.TERM="TERM",j.QueryLexer.EDIT_DISTANCE="EDIT_DISTANCE",j.QueryLexer.BOOST="BOOST",j.QueryLexer.PRESENCE="PRESENCE",j.QueryLexer.lexField=function(e){return e.backup(),e.emit(j.QueryLexer.FIELD),e.ignore(),j.QueryLexer.lexText},j.QueryLexer.lexTerm=function(e){if(e.width()>1&&(e.backup(),e.emit(j.QueryLexer.TERM)),e.ignore(),e.more())return j.QueryLexer.lexText},j.QueryLexer.lexEditDistance=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(j.QueryLexer.EDIT_DISTANCE),j.QueryLexer.lexText},j.QueryLexer.lexBoost=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(j.QueryLexer.BOOST),j.QueryLexer.lexText},j.QueryLexer.lexEOS=function(e){e.width()>0&&e.emit(j.QueryLexer.TERM)},j.QueryLexer.termSeparator=j.tokenizer.separator,j.QueryLexer.lexText=function(e){for(;;){var t=e.next();if(t==j.QueryLexer.EOS)return j.QueryLexer.lexEOS;if(92!=t.charCodeAt(0)){if(":"==t)return j.QueryLexer.lexField;if("~"==t)return e.backup(),e.width()>0&&e.emit(j.QueryLexer.TERM),j.QueryLexer.lexEditDistance;if("^"==t)return e.backup(),e.width()>0&&e.emit(j.QueryLexer.TERM),j.QueryLexer.lexBoost;if("+"==t&&1===e.width())return e.emit(j.QueryLexer.PRESENCE),j.QueryLexer.lexText;if("-"==t&&1===e.width())return e.emit(j.QueryLexer.PRESENCE),j.QueryLexer.lexText;if(t.match(j.QueryLexer.termSeparator))return j.QueryLexer.lexTerm}else e.escapeCharacter()}},j.QueryParser=function(e,t){this.lexer=new j.QueryLexer(e),this.query=t,this.currentClause={},this.lexemeIdx=0},j.QueryParser.prototype.parse=function(){this.lexer.run(),this.lexemes=this.lexer.lexemes;for(var e=j.QueryParser.parseClause;e;)e=e(this);return this.query},j.QueryParser.prototype.peekLexeme=function(){return this.lexemes[this.lexemeIdx]},j.QueryParser.prototype.consumeLexeme=function(){var e=this.peekLexeme();return this.lexemeIdx+=1,e},j.QueryParser.prototype.nextClause=function(){var e=this.currentClause;this.query.clause(e),this.currentClause={}},j.QueryParser.parseClause=function(e){var t=e.peekLexeme();if(null!=t)switch(t.type){case j.QueryLexer.PRESENCE:return j.QueryParser.parsePresence;case j.QueryLexer.FIELD:return j.QueryParser.parseField;case j.QueryLexer.TERM:return j.QueryParser.parseTerm;default:var n="expected either a field or a term, found "+t.type;throw t.str.length>=1&&(n+=" with value '"+t.str+"'"),new j.QueryParseError(n,t.start,t.end)}},j.QueryParser.parsePresence=function(e){var t=e.consumeLexeme();if(null!=t){switch(t.str){case"-":e.currentClause.presence=j.Query.presence.PROHIBITED;break;case"+":e.currentClause.presence=j.Query.presence.REQUIRED;break;default:var n="unrecognised presence operator'"+t.str+"'";throw new j.QueryParseError(n,t.start,t.end)}var r=e.peekLexeme();if(null==r){n="expecting term or field, found nothing";throw new j.QueryParseError(n,t.start,t.end)}switch(r.type){case j.QueryLexer.FIELD:return j.QueryParser.parseField;case j.QueryLexer.TERM:return j.QueryParser.parseTerm;default:n="expecting term or field, found '"+r.type+"'";throw new j.QueryParseError(n,r.start,r.end)}}},j.QueryParser.parseField=function(e){var t=e.consumeLexeme();if(null!=t){if(-1==e.query.allFields.indexOf(t.str)){var n=e.query.allFields.map((function(e){return"'"+e+"'"})).join(", "),r="unrecognised field '"+t.str+"', possible fields: "+n;throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.fields=[t.str];var a=e.peekLexeme();if(null==a){r="expecting term, found nothing";throw new j.QueryParseError(r,t.start,t.end)}if(a.type===j.QueryLexer.TERM)return j.QueryParser.parseTerm;r="expecting term, found '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}},j.QueryParser.parseTerm=function(e){var t=e.consumeLexeme();if(null!=t){e.currentClause.term=t.str.toLowerCase(),-1!=t.str.indexOf("*")&&(e.currentClause.usePipeline=!1);var n=e.peekLexeme();if(null!=n)switch(n.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:var r="Unexpected lexeme type '"+n.type+"'";throw new j.QueryParseError(r,n.start,n.end)}else e.nextClause()}},j.QueryParser.parseEditDistance=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="edit distance must be numeric";throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.editDistance=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}else e.nextClause()}},j.QueryParser.parseBoost=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="boost must be numeric";throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.boost=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}else e.nextClause()}},void 0===(a="function"==typeof(r=function(){return j})?r.call(t,n,t,e):r)||(e.exports=a)}()},689:function(e){e.exports=function(){"use strict";var e="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(e){return typeof e}:function(e){return e&&"function"==typeof Symbol&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e},t=function(e,t){if(!(e instanceof t))throw new TypeError("Cannot call a class as a function")},n=function(){function e(e,t){for(var n=0;n<t.length;n++){var r=t[n];r.enumerable=r.enumerable||!1,r.configurable=!0,"value"in r&&(r.writable=!0),Object.defineProperty(e,r.key,r)}}return function(t,n,r){return n&&e(t.prototype,n),r&&e(t,r),t}}(),r=Object.assign||function(e){for(var t=1;t<arguments.length;t++){var n=arguments[t];for(var r in n)Object.prototype.hasOwnProperty.call(n,r)&&(e[r]=n[r])}return e},a=function(){function e(n){var r=!(arguments.length>1&&void 0!==arguments[1])||arguments[1],a=arguments.length>2&&void 0!==arguments[2]?arguments[2]:[],o=arguments.length>3&&void 0!==arguments[3]?arguments[3]:5e3;t(this,e),this.ctx=n,this.iframes=r,this.exclude=a,this.iframesTimeout=o}return n(e,[{key:"getContexts",value:function(){var e=[];return(void 0!==this.ctx&&this.ctx?NodeList.prototype.isPrototypeOf(this.ctx)?Array.prototype.slice.call(this.ctx):Array.isArray(this.ctx)?this.ctx:"string"==typeof this.ctx?Array.prototype.slice.call(document.querySelectorAll(this.ctx)):[this.ctx]:[]).forEach((function(t){var n=e.filter((function(e){return e.contains(t)})).length>0;-1!==e.indexOf(t)||n||e.push(t)})),e}},{key:"getIframeContents",value:function(e,t){var n=arguments.length>2&&void 0!==arguments[2]?arguments[2]:function(){},r=void 0;try{var a=e.contentWindow;if(r=a.document,!a||!r)throw new Error("iframe inaccessible")}catch(o){n()}r&&t(r)}},{key:"isIframeBlank",value:function(e){var t="about:blank",n=e.getAttribute("src").trim();return e.contentWindow.location.href===t&&n!==t&&n}},{key:"observeIframeLoad",value:function(e,t,n){var r=this,a=!1,o=null,i=function i(){if(!a){a=!0,clearTimeout(o);try{r.isIframeBlank(e)||(e.removeEventListener("load",i),r.getIframeContents(e,t,n))}catch(s){n()}}};e.addEventListener("load",i),o=setTimeout(i,this.iframesTimeout)}},{key:"onIframeReady",value:function(e,t,n){try{"complete"===e.contentWindow.document.readyState?this.isIframeBlank(e)?this.observeIframeLoad(e,t,n):this.getIframeContents(e,t,n):this.observeIframeLoad(e,t,n)}catch(r){n()}}},{key:"waitForIframes",value:function(e,t){var n=this,r=0;this.forEachIframe(e,(function(){return!0}),(function(e){r++,n.waitForIframes(e.querySelector("html"),(function(){--r||t()}))}),(function(e){e||t()}))}},{key:"forEachIframe",value:function(t,n,r){var a=this,o=arguments.length>3&&void 0!==arguments[3]?arguments[3]:function(){},i=t.querySelectorAll("iframe"),s=i.length,l=0;i=Array.prototype.slice.call(i);var u=function(){--s<=0&&o(l)};s||u(),i.forEach((function(t){e.matches(t,a.exclude)?u():a.onIframeReady(t,(function(e){n(t)&&(l++,r(e)),u()}),u)}))}},{key:"createIterator",value:function(e,t,n){return document.createNodeIterator(e,t,n,!1)}},{key:"createInstanceOnIframe",value:function(t){return new e(t.querySelector("html"),this.iframes)}},{key:"compareNodeIframe",value:function(e,t,n){if(e.compareDocumentPosition(n)&Node.DOCUMENT_POSITION_PRECEDING){if(null===t)return!0;if(t.compareDocumentPosition(n)&Node.DOCUMENT_POSITION_FOLLOWING)return!0}return!1}},{key:"getIteratorNode",value:function(e){var t=e.previousNode();return{prevNode:t,node:(null===t||e.nextNode())&&e.nextNode()}}},{key:"checkIframeFilter",value:function(e,t,n,r){var a=!1,o=!1;return r.forEach((function(e,t){e.val===n&&(a=t,o=e.handled)})),this.compareNodeIframe(e,t,n)?(!1!==a||o?!1===a||o||(r[a].handled=!0):r.push({val:n,handled:!0}),!0):(!1===a&&r.push({val:n,handled:!1}),!1)}},{key:"handleOpenIframes",value:function(e,t,n,r){var a=this;e.forEach((function(e){e.handled||a.getIframeContents(e.val,(function(e){a.createInstanceOnIframe(e).forEachNode(t,n,r)}))}))}},{key:"iterateThroughNodes",value:function(e,t,n,r,a){for(var o=this,i=this.createIterator(t,e,r),s=[],l=[],u=void 0,c=void 0,d=function(){var e=o.getIteratorNode(i);return c=e.prevNode,u=e.node};d();)this.iframes&&this.forEachIframe(t,(function(e){return o.checkIframeFilter(u,c,e,s)}),(function(t){o.createInstanceOnIframe(t).forEachNode(e,(function(e){return 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0!==arguments[1]?arguments[1]:"debug",r=this.opt.log;this.opt.debug&&"object"===(void 0===r?"undefined":e(r))&&"function"==typeof r[n]&&r[n]("mark.js: "+t)}},{key:"escapeStr",value:function(e){return e.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}},{key:"createRegExp",value:function(e){return"disabled"!==this.opt.wildcards&&(e=this.setupWildcardsRegExp(e)),e=this.escapeStr(e),Object.keys(this.opt.synonyms).length&&(e=this.createSynonymsRegExp(e)),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),this.opt.diacritics&&(e=this.createDiacriticsRegExp(e)),e=this.createMergedBlanksRegExp(e),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.createJoinersRegExp(e)),"disabled"!==this.opt.wildcards&&(e=this.createWildcardsRegExp(e)),e=this.createAccuracyRegExp(e)}},{key:"createSynonymsRegExp",value:function(e){var 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e.languages.flow.parameter,e.languages.insertBefore("flow","operator",{"flow-punctuation":{pattern:/\{\||\|\}/,alias:"punctuation"}}),Array.isArray(e.languages.flow.keyword)||(e.languages.flow.keyword=[e.languages.flow.keyword]),e.languages.flow.keyword.unshift({pattern:/(^|[^$]\b)(?:Class|declare|opaque|type)\b(?!\$)/,lookbehind:!0},{pattern:/(^|[^$]\B)\$(?:Diff|Enum|Exact|Keys|ObjMap|PropertyType|Record|Shape|Subtype|Supertype|await)\b(?!\$)/,lookbehind:!0})}(C),C.languages.n4js=C.languages.extend("javascript",{keyword:/\b(?:Array|any|boolean|break|case|catch|class|const|constructor|continue|debugger|declare|default|delete|do|else|enum|export|extends|false|finally|for|from|function|get|if|implements|import|in|instanceof|interface|let|module|new|null|number|package|private|protected|public|return|set|static|string|super|switch|this|throw|true|try|typeof|var|void|while|with|yield)\b/}),C.languages.insertBefore("n4js","constant",{annotation:{pattern:/@+\w+/,alias:"operator"}}),C.languages.n4jsd=C.languages.n4js,function(e){function t(e,t){return RegExp(e.replace(/<ID>/g,(function(){return/(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*/.source})),t)}e.languages.insertBefore("javascript","function-variable",{"method-variable":{pattern:RegExp("(\\.\\s*)"+e.languages.javascript["function-variable"].pattern.source),lookbehind:!0,alias:["function-variable","method","function","property-access"]}}),e.languages.insertBefore("javascript","function",{method:{pattern:RegExp("(\\.\\s*)"+e.languages.javascript.function.source),lookbehind:!0,alias:["function","property-access"]}}),e.languages.insertBefore("javascript","constant",{"known-class-name":[{pattern:/\b(?:(?:Float(?:32|64)|(?:Int|Uint)(?:8|16|32)|Uint8Clamped)?Array|ArrayBuffer|BigInt|Boolean|DataView|Date|Error|Function|Intl|JSON|(?:Weak)?(?:Map|Set)|Math|Number|Object|Promise|Proxy|Reflect|RegExp|String|Symbol|WebAssembly)\b/,alias:"class-name"},{pattern:/\b(?:[A-Z]\w*)Error\b/,alias:"class-name"}]}),e.languages.insertBefore("javascript","keyword",{imports:{pattern:t(/(\bimport\b\s*)(?:<ID>(?:\s*,\s*(?:\*\s*as\s+<ID>|\{[^{}]*\}))?|\*\s*as\s+<ID>|\{[^{}]*\})(?=\s*\bfrom\b)/.source),lookbehind:!0,inside:e.languages.javascript},exports:{pattern:t(/(\bexport\b\s*)(?:\*(?:\s*as\s+<ID>)?(?=\s*\bfrom\b)|\{[^{}]*\})/.source),lookbehind:!0,inside:e.languages.javascript}}),e.languages.javascript.keyword.unshift({pattern:/\b(?:as|default|export|from|import)\b/,alias:"module"},{pattern:/\b(?:await|break|catch|continue|do|else|finally|for|if|return|switch|throw|try|while|yield)\b/,alias:"control-flow"},{pattern:/\bnull\b/,alias:["null","nil"]},{pattern:/\bundefined\b/,alias:"nil"}),e.languages.insertBefore("javascript","operator",{spread:{pattern:/\.{3}/,alias:"operator"},arrow:{pattern:/=>/,alias:"operator"}}),e.languages.insertBefore("javascript","punctuation",{"property-access":{pattern:t(/(\.\s*)#?<ID>/.source),lookbehind:!0},"maybe-class-name":{pattern:/(^|[^$\w\xA0-\uFFFF])[A-Z][$\w\xA0-\uFFFF]+/,lookbehind:!0},dom:{pattern:/\b(?:document|(?:local|session)Storage|location|navigator|performance|window)\b/,alias:"variable"},console:{pattern:/\bconsole(?=\s*\.)/,alias:"class-name"}});for(var n=["function","function-variable","method","method-variable","property-access"],r=0;r<n.length;r++){var a=n[r],o=e.languages.javascript[a];a=(o="RegExp"===e.util.type(o)?e.languages.javascript[a]={pattern:o}:o).inside||{};(o.inside=a)["maybe-class-name"]=/^[A-Z][\s\S]*/}}(C),function(e){var t=e.util.clone(e.languages.javascript),n=/(?:\s|\/\/.*(?!.)|\/\*(?:[^*]|\*(?!\/))\*\/)/.source,r=/(?:\{(?:\{(?:\{[^{}]*\}|[^{}])*\}|[^{}])*\})/.source,a=/(?:\{<S>*\.{3}(?:[^{}]|<BRACES>)*\})/.source;function o(e,t){return e=e.replace(/<S>/g,(function(){return n})).replace(/<BRACES>/g,(function(){return r})).replace(/<SPREAD>/g,(function(){return a})),RegExp(e,t)}function i(t){for(var n=[],r=0;r<t.length;r++){var a=t[r],o=!1;"string"!=typeof a&&("tag"===a.type&&a.content[0]&&"tag"===a.content[0].type?"</"===a.content[0].content[0].content?0<n.length&&n[n.length-1].tagName===s(a.content[0].content[1])&&n.pop():"/>"!==a.content[a.content.length-1].content&&n.push({tagName:s(a.content[0].content[1]),openedBraces:0}):0<n.length&&"punctuation"===a.type&&"{"===a.content?n[n.length-1].openedBraces++:0<n.length&&0<n[n.length-1].openedBraces&&"punctuation"===a.type&&"}"===a.content?n[n.length-1].openedBraces--:o=!0),(o||"string"==typeof a)&&0<n.length&&0===n[n.length-1].openedBraces&&(o=s(a),r<t.length-1&&("string"==typeof t[r+1]||"plain-text"===t[r+1].type)&&(o+=s(t[r+1]),t.splice(r+1,1)),0<r&&("string"==typeof t[r-1]||"plain-text"===t[r-1].type)&&(o=s(t[r-1])+o,t.splice(r-1,1),r--),t[r]=new e.Token("plain-text",o,null,o)),a.content&&"string"!=typeof a.content&&i(a.content)}}a=o(a).source,e.languages.jsx=e.languages.extend("markup",t),e.languages.jsx.tag.pattern=o(/<\/?(?:[\w.:-]+(?:<S>+(?:[\w.:$-]+(?:=(?:"(?:\\[\s\S]|[^\\"])*"|'(?:\\[\s\S]|[^\\'])*'|[^\s{'"/>=]+|<BRACES>))?|<SPREAD>))*<S>*\/?)?>/.source),e.languages.jsx.tag.inside.tag.pattern=/^<\/?[^\s>\/]*/,e.languages.jsx.tag.inside["attr-value"].pattern=/=(?!\{)(?:"(?:\\[\s\S]|[^\\"])*"|'(?:\\[\s\S]|[^\\'])*'|[^\s'">]+)/,e.languages.jsx.tag.inside.tag.inside["class-name"]=/^[A-Z]\w*(?:\.[A-Z]\w*)*$/,e.languages.jsx.tag.inside.comment=t.comment,e.languages.insertBefore("inside","attr-name",{spread:{pattern:o(/<SPREAD>/.source),inside:e.languages.jsx}},e.languages.jsx.tag),e.languages.insertBefore("inside","special-attr",{script:{pattern:o(/=<BRACES>/.source),alias:"language-javascript",inside:{"script-punctuation":{pattern:/^=(?=\{)/,alias:"punctuation"},rest:e.languages.jsx}}},e.languages.jsx.tag);var s=function(e){return e?"string"==typeof e?e:"string"==typeof e.content?e.content:e.content.map(s).join(""):""};e.hooks.add("after-tokenize",(function(e){"jsx"!==e.language&&"tsx"!==e.language||i(e.tokens)}))}(C),function(e){var t=e.util.clone(e.languages.typescript);(t=(e.languages.tsx=e.languages.extend("jsx",t),delete e.languages.tsx.parameter,delete e.languages.tsx["literal-property"],e.languages.tsx.tag)).pattern=RegExp(/(^|[^\w$]|(?=<\/))/.source+"(?:"+t.pattern.source+")",t.pattern.flags),t.lookbehind=!0}(C),C.languages.swift={comment:{pattern:/(^|[^\\:])(?:\/\/.*|\/\*(?:[^/*]|\/(?!\*)|\*(?!\/)|\/\*(?:[^*]|\*(?!\/))*\*\/)*\*\/)/,lookbehind:!0,greedy:!0},"string-literal":[{pattern:RegExp(/(^|[^"#])/.source+"(?:"+/"(?:\\(?:\((?:[^()]|\([^()]*\))*\)|\r\n|[^(])|[^\\\r\n"])*"/.source+"|"+/"""(?:\\(?:\((?:[^()]|\([^()]*\))*\)|[^(])|[^\\"]|"(?!""))*"""/.source+")"+/(?!["#])/.source),lookbehind:!0,greedy:!0,inside:{interpolation:{pattern:/(\\\()(?:[^()]|\([^()]*\))*(?=\))/,lookbehind:!0,inside:null},"interpolation-punctuation":{pattern:/^\)|\\\($/,alias:"punctuation"},punctuation:/\\(?=[\r\n])/,string:/[\s\S]+/}},{pattern:RegExp(/(^|[^"#])(#+)/.source+"(?:"+/"(?:\\(?:#+\((?:[^()]|\([^()]*\))*\)|\r\n|[^#])|[^\\\r\n])*?"/.source+"|"+/"""(?:\\(?:#+\((?:[^()]|\([^()]*\))*\)|[^#])|[^\\])*?"""/.source+")\\2"),lookbehind:!0,greedy:!0,inside:{interpolation:{pattern:/(\\#+\()(?:[^()]|\([^()]*\))*(?=\))/,lookbehind:!0,inside:null},"interpolation-punctuation":{pattern:/^\)|\\#+\($/,alias:"punctuation"},string:/[\s\S]+/}}],directive:{pattern:RegExp(/#/.source+"(?:"+/(?:elseif|if)\b/.source+"(?:[ \t]*"+/(?:![ \t]*)?(?:\b\w+\b(?:[ \t]*\((?:[^()]|\([^()]*\))*\))?|\((?:[^()]|\([^()]*\))*\))(?:[ \t]*(?:&&|\|\|))?/.source+")+|"+/(?:else|endif)\b/.source+")"),alias:"property",inside:{"directive-name":/^#\w+/,boolean:/\b(?:false|true)\b/,number:/\b\d+(?:\.\d+)*\b/,operator:/!|&&|\|\||[<>]=?/,punctuation:/[(),]/}},literal:{pattern:/#(?:colorLiteral|column|dsohandle|file(?:ID|Literal|Path)?|function|imageLiteral|line)\b/,alias:"constant"},"other-directive":{pattern:/#\w+\b/,alias:"property"},attribute:{pattern:/@\w+/,alias:"atrule"},"function-definition":{pattern:/(\bfunc\s+)\w+/,lookbehind:!0,alias:"function"},label:{pattern:/\b(break|continue)\s+\w+|\b[a-zA-Z_]\w*(?=\s*:\s*(?:for|repeat|while)\b)/,lookbehind:!0,alias:"important"},keyword:/\b(?:Any|Protocol|Self|Type|actor|as|assignment|associatedtype|associativity|async|await|break|case|catch|class|continue|convenience|default|defer|deinit|didSet|do|dynamic|else|enum|extension|fallthrough|fileprivate|final|for|func|get|guard|higherThan|if|import|in|indirect|infix|init|inout|internal|is|isolated|lazy|left|let|lowerThan|mutating|none|nonisolated|nonmutating|open|operator|optional|override|postfix|precedencegroup|prefix|private|protocol|public|repeat|required|rethrows|return|right|safe|self|set|some|static|struct|subscript|super|switch|throw|throws|try|typealias|unowned|unsafe|var|weak|where|while|willSet)\b/,boolean:/\b(?:false|true)\b/,nil:{pattern:/\bnil\b/,alias:"constant"},"short-argument":/\$\d+\b/,omit:{pattern:/\b_\b/,alias:"keyword"},number:/\b(?:[\d_]+(?:\.[\de_]+)?|0x[a-f0-9_]+(?:\.[a-f0-9p_]+)?|0b[01_]+|0o[0-7_]+)\b/i,"class-name":/\b[A-Z](?:[A-Z_\d]*[a-z]\w*)?\b/,function:/\b[a-z_]\w*(?=\s*\()/i,constant:/\b(?:[A-Z_]{2,}|k[A-Z][A-Za-z_]+)\b/,operator:/[-+*/%=!<>&|^~?]+|\.[.\-+*/%=!<>&|^~?]+/,punctuation:/[{}[\]();,.:\\]/},C.languages.swift["string-literal"].forEach((function(e){e.inside.interpolation.inside=C.languages.swift})),function(e){e.languages.kotlin=e.languages.extend("clike",{keyword:{pattern:/(^|[^.])\b(?:abstract|actual|annotation|as|break|by|catch|class|companion|const|constructor|continue|crossinline|data|do|dynamic|else|enum|expect|external|final|finally|for|fun|get|if|import|in|infix|init|inline|inner|interface|internal|is|lateinit|noinline|null|object|open|operator|out|override|package|private|protected|public|reified|return|sealed|set|super|suspend|tailrec|this|throw|to|try|typealias|val|var|vararg|when|where|while)\b/,lookbehind:!0},function:[{pattern:/(?:`[^\r\n`]+`|\b\w+)(?=\s*\()/,greedy:!0},{pattern:/(\.)(?:`[^\r\n`]+`|\w+)(?=\s*\{)/,lookbehind:!0,greedy:!0}],number:/\b(?:0[xX][\da-fA-F]+(?:_[\da-fA-F]+)*|0[bB][01]+(?:_[01]+)*|\d+(?:_\d+)*(?:\.\d+(?:_\d+)*)?(?:[eE][+-]?\d+(?:_\d+)*)?[fFL]?)\b/,operator:/\+[+=]?|-[-=>]?|==?=?|!(?:!|==?)?|[\/*%<>]=?|[?:]:?|\.\.|&&|\|\||\b(?:and|inv|or|shl|shr|ushr|xor)\b/}),delete e.languages.kotlin["class-name"];var t={"interpolation-punctuation":{pattern:/^\$\{?|\}$/,alias:"punctuation"},expression:{pattern:/[\s\S]+/,inside:e.languages.kotlin}};e.languages.insertBefore("kotlin","string",{"string-literal":[{pattern:/"""(?:[^$]|\$(?:(?!\{)|\{[^{}]*\}))*?"""/,alias:"multiline",inside:{interpolation:{pattern:/\$(?:[a-z_]\w*|\{[^{}]*\})/i,inside:t},string:/[\s\S]+/}},{pattern:/"(?:[^"\\\r\n$]|\\.|\$(?:(?!\{)|\{[^{}]*\}))*"/,alias:"singleline",inside:{interpolation:{pattern:/((?:^|[^\\])(?:\\{2})*)\$(?:[a-z_]\w*|\{[^{}]*\})/i,lookbehind:!0,inside:t},string:/[\s\S]+/}}],char:{pattern:/'(?:[^'\\\r\n]|\\(?:.|u[a-fA-F0-9]{0,4}))'/,greedy:!0}}),delete e.languages.kotlin.string,e.languages.insertBefore("kotlin","keyword",{annotation:{pattern:/\B@(?:\w+:)?(?:[A-Z]\w*|\[[^\]]+\])/,alias:"builtin"}}),e.languages.insertBefore("kotlin","function",{label:{pattern:/\b\w+@|@\w+\b/,alias:"symbol"}}),e.languages.kt=e.languages.kotlin,e.languages.kts=e.languages.kotlin}(C),C.languages.c=C.languages.extend("clike",{comment:{pattern:/\/\/(?:[^\r\n\\]|\\(?:\r\n?|\n|(?![\r\n])))*|\/\*[\s\S]*?(?:\*\/|$)/,greedy:!0},string:{pattern:/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},"class-name":{pattern:/(\b(?:enum|struct)\s+(?:__attribute__\s*\(\([\s\S]*?\)\)\s*)?)\w+|\b[a-z]\w*_t\b/,lookbehind:!0},keyword:/\b(?:_Alignas|_Alignof|_Atomic|_Bool|_Complex|_Generic|_Imaginary|_Noreturn|_Static_assert|_Thread_local|__attribute__|asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|inline|int|long|register|return|short|signed|sizeof|static|struct|switch|typedef|typeof|union|unsigned|void|volatile|while)\b/,function:/\b[a-z_]\w*(?=\s*\()/i,number:/(?:\b0x(?:[\da-f]+(?:\.[\da-f]*)?|\.[\da-f]+)(?:p[+-]?\d+)?|(?:\b\d+(?:\.\d*)?|\B\.\d+)(?:e[+-]?\d+)?)[ful]{0,4}/i,operator:/>>=?|<<=?|->|([-+&|:])\1|[?:~]|[-+*/%&|^!=<>]=?/}),C.languages.insertBefore("c","string",{char:{pattern:/'(?:\\(?:\r\n|[\s\S])|[^'\\\r\n]){0,32}'/,greedy:!0}}),C.languages.insertBefore("c","string",{macro:{pattern:/(^[\t ]*)#\s*[a-z](?:[^\r\n\\/]|\/(?!\*)|\/\*(?:[^*]|\*(?!\/))*\*\/|\\(?:\r\n|[\s\S]))*/im,lookbehind:!0,greedy:!0,alias:"property",inside:{string:[{pattern:/^(#\s*include\s*)<[^>]+>/,lookbehind:!0},C.languages.c.string],char:C.languages.c.char,comment:C.languages.c.comment,"macro-name":[{pattern:/(^#\s*define\s+)\w+\b(?!\()/i,lookbehind:!0},{pattern:/(^#\s*define\s+)\w+\b(?=\()/i,lookbehind:!0,alias:"function"}],directive:{pattern:/^(#\s*)[a-z]+/,lookbehind:!0,alias:"keyword"},"directive-hash":/^#/,punctuation:/##|\\(?=[\r\n])/,expression:{pattern:/\S[\s\S]*/,inside:C.languages.c}}}}),C.languages.insertBefore("c","function",{constant:/\b(?:EOF|NULL|SEEK_CUR|SEEK_END|SEEK_SET|__DATE__|__FILE__|__LINE__|__TIMESTAMP__|__TIME__|__func__|stderr|stdin|stdout)\b/}),delete C.languages.c.boolean,C.languages.objectivec=C.languages.extend("c",{string:{pattern:/@?"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},keyword:/\b(?:asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|in|inline|int|long|register|return|self|short|signed|sizeof|static|struct|super|switch|typedef|typeof|union|unsigned|void|volatile|while)\b|(?:@interface|@end|@implementation|@protocol|@class|@public|@protected|@private|@property|@try|@catch|@finally|@throw|@synthesize|@dynamic|@selector)\b/,operator:/-[->]?|\+\+?|!=?|<<?=?|>>?=?|==?|&&?|\|\|?|[~^%?*\/@]/}),delete 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e===j.Set.complete?j.Set.complete:e===j.Set.empty?this:new j.Set(Object.keys(this.elements).concat(Object.keys(e.elements)))},j.idf=function(e,t){var n=0;for(var r in e)"_index"!=r&&(n+=Object.keys(e[r]).length);var a=(t-n+.5)/(n+.5);return Math.log(1+Math.abs(a))},j.Token=function(e,t){this.str=e||"",this.metadata=t||{}},j.Token.prototype.toString=function(){return this.str},j.Token.prototype.update=function(e){return this.str=e(this.str,this.metadata),this},j.Token.prototype.clone=function(e){return e=e||function(e){return e},new j.Token(e(this.str,this.metadata),this.metadata)},j.tokenizer=function(e,t){if(null==e||null==e)return[];if(Array.isArray(e))return e.map((function(e){return new j.Token(j.utils.asString(e).toLowerCase(),j.utils.clone(t))}));for(var n=e.toString().toLowerCase(),r=n.length,a=[],o=0,i=0;o<=r;o++){var s=o-i;if(n.charAt(o).match(j.tokenizer.separator)||o==r){if(s>0){var l=j.utils.clone(t)||{};l.position=[i,s],l.index=a.length,a.push(new 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r=this._stack[n],a=[],o=0;o<e.length;o++){var i=r(e[o],o,e);if(null!=i&&""!==i)if(Array.isArray(i))for(var s=0;s<i.length;s++)a.push(i[s]);else a.push(i)}e=a}return e},j.Pipeline.prototype.runString=function(e,t){var n=new j.Token(e,t);return this.run([n]).map((function(e){return e.toString()}))},j.Pipeline.prototype.reset=function(){this._stack=[]},j.Pipeline.prototype.toJSON=function(){return this._stack.map((function(e){return j.Pipeline.warnIfFunctionNotRegistered(e),e.label}))},j.Vector=function(e){this._magnitude=0,this.elements=e||[]},j.Vector.prototype.positionForIndex=function(e){if(0==this.elements.length)return 0;for(var t=0,n=this.elements.length/2,r=n-t,a=Math.floor(r/2),o=this.elements[2*a];r>1&&(o<e&&(t=a),o>e&&(n=a),o!=e);)r=n-t,a=t+Math.floor(r/2),o=this.elements[2*a];return o==e||o>e?2*a:o<e?2*(a+1):void 0},j.Vector.prototype.insert=function(e,t){this.upsert(e,t,(function(){throw"duplicate index"}))},j.Vector.prototype.upsert=function(e,t,n){this._magnitude=0;var r=this.positionForIndex(e);this.elements[r]==e?this.elements[r+1]=n(this.elements[r+1],t):this.elements.splice(r,0,e,t)},j.Vector.prototype.magnitude=function(){if(this._magnitude)return this._magnitude;for(var e=0,t=this.elements.length,n=1;n<t;n+=2){var r=this.elements[n];e+=r*r}return this._magnitude=Math.sqrt(e)},j.Vector.prototype.dot=function(e){for(var t=0,n=this.elements,r=e.elements,a=n.length,o=r.length,i=0,s=0,l=0,u=0;l<a&&u<o;)(i=n[l])<(s=r[u])?l+=2:i>s?u+=2:i==s&&(t+=n[l+1]*r[u+1],l+=2,u+=2);return t},j.Vector.prototype.similarity=function(e){return this.dot(e)/this.magnitude()||0},j.Vector.prototype.toArray=function(){for(var e=new Array(this.elements.length/2),t=1,n=0;t<this.elements.length;t+=2,n++)e[n]=this.elements[t];return e},j.Vector.prototype.toJSON=function(){return this.elements},j.stemmer=(i={ational:"ate",tional:"tion",enci:"ence",anci:"ance",izer:"ize",bli:"ble",alli:"al",entli:"ent",eli:"e",ousli:"ous",ization:"ize",ation:"ate",ator:"ate",alism:"al",iveness:"ive",fulness:"ful",ousness:"ous",aliti:"al",iviti:"ive",biliti:"ble",logi:"log"},s={icate:"ic",ative:"",alize:"al",iciti:"ic",ical:"ic",ful:"",ness:""},d="^("+(u="[^aeiou][^aeiouy]*")+")?"+(c=(l="[aeiouy]")+"[aeiou]*")+u+"("+c+")?$",p="^("+u+")?"+c+u+c+u,f="^("+u+")?"+l,h=new RegExp("^("+u+")?"+c+u),g=new RegExp(p),m=new RegExp(d),y=new RegExp(f),b=/^(.+?)(ss|i)es$/,v=/^(.+?)([^s])s$/,w=/^(.+?)eed$/,x=/^(.+?)(ed|ing)$/,k=/.$/,S=/(at|bl|iz)$/,E=new RegExp("([^aeiouylsz])\\1$"),_=new RegExp("^"+u+l+"[^aeiouwxy]$"),C=/^(.+?[^aeiou])y$/,T=/^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/,A=/^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/,N=/^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/,L=/^(.+?)(s|t)(ion)$/,O=/^(.+?)e$/,P=/ll$/,R=new RegExp("^"+u+l+"[^aeiouwxy]$"),I=function(e){var t,n,r,a,o,l,u;if(e.length<3)return e;if("y"==(r=e.substr(0,1))&&(e=r.toUpperCase()+e.substr(1)),o=v,(a=b).test(e)?e=e.replace(a,"$1$2"):o.test(e)&&(e=e.replace(o,"$1$2")),o=x,(a=w).test(e)){var c=a.exec(e);(a=h).test(c[1])&&(a=k,e=e.replace(a,""))}else o.test(e)&&(t=(c=o.exec(e))[1],(o=y).test(t)&&(l=E,u=_,(o=S).test(e=t)?e+="e":l.test(e)?(a=k,e=e.replace(a,"")):u.test(e)&&(e+="e")));return(a=C).test(e)&&(e=(t=(c=a.exec(e))[1])+"i"),(a=T).test(e)&&(t=(c=a.exec(e))[1],n=c[2],(a=h).test(t)&&(e=t+i[n])),(a=A).test(e)&&(t=(c=a.exec(e))[1],n=c[2],(a=h).test(t)&&(e=t+s[n])),o=L,(a=N).test(e)?(t=(c=a.exec(e))[1],(a=g).test(t)&&(e=t)):o.test(e)&&(t=(c=o.exec(e))[1]+c[2],(o=g).test(t)&&(e=t)),(a=O).test(e)&&(t=(c=a.exec(e))[1],o=m,l=R,((a=g).test(t)||o.test(t)&&!l.test(t))&&(e=t)),o=g,(a=P).test(e)&&o.test(e)&&(a=k,e=e.replace(a,"")),"y"==r&&(e=r.toLowerCase()+e.substr(1)),e},function(e){return e.update(I)}),j.Pipeline.registerFunction(j.stemmer,"stemmer"),j.generateStopWordFilter=function(e){var t=e.reduce((function(e,t){return e[t]=t,e}),{});return function(e){if(e&&t[e.toString()]!==e.toString())return e}},j.stopWordFilter=j.generateStopWordFilter(["a","able","about","across","after","all","almost","also","am","among","an","and","any","are","as","at","be","because","been","but","by","can","cannot","could","dear","did","do","does","either","else","ever","every","for","from","get","got","had","has","have","he","her","hers","him","his","how","however","i","if","in","into","is","it","its","just","least","let","like","likely","may","me","might","most","must","my","neither","no","nor","not","of","off","often","on","only","or","other","our","own","rather","said","say","says","she","should","since","so","some","than","that","the","their","them","then","there","these","they","this","tis","to","too","twas","us","wants","was","we","were","what","when","where","which","while","who","whom","why","will","with","would","yet","you","your"]),j.Pipeline.registerFunction(j.stopWordFilter,"stopWordFilter"),j.trimmer=function(e){return e.update((function(e){return e.replace(/^\W+/,"").replace(/\W+$/,"")}))},j.Pipeline.registerFunction(j.trimmer,"trimmer"),j.TokenSet=function(){this.final=!1,this.edges={},this.id=j.TokenSet._nextId,j.TokenSet._nextId+=1},j.TokenSet._nextId=1,j.TokenSet.fromArray=function(e){for(var t=new j.TokenSet.Builder,n=0,r=e.length;n<r;n++)t.insert(e[n]);return t.finish(),t.root},j.TokenSet.fromClause=function(e){return"editDistance"in e?j.TokenSet.fromFuzzyString(e.term,e.editDistance):j.TokenSet.fromString(e.term)},j.TokenSet.fromFuzzyString=function(e,t){for(var n=new j.TokenSet,r=[{node:n,editsRemaining:t,str:e}];r.length;){var a=r.pop();if(a.str.length>0){var o,i=a.str.charAt(0);i in a.node.edges?o=a.node.edges[i]:(o=new j.TokenSet,a.node.edges[i]=o),1==a.str.length&&(o.final=!0),r.push({node:o,editsRemaining:a.editsRemaining,str:a.str.slice(1)})}if(0!=a.editsRemaining){if("*"in a.node.edges)var s=a.node.edges["*"];else{s=new j.TokenSet;a.node.edges["*"]=s}if(0==a.str.length&&(s.final=!0),r.push({node:s,editsRemaining:a.editsRemaining-1,str:a.str}),a.str.length>1&&r.push({node:a.node,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)}),1==a.str.length&&(a.node.final=!0),a.str.length>=1){if("*"in a.node.edges)var l=a.node.edges["*"];else{l=new j.TokenSet;a.node.edges["*"]=l}1==a.str.length&&(l.final=!0),r.push({node:l,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)})}if(a.str.length>1){var u,c=a.str.charAt(0),d=a.str.charAt(1);d in a.node.edges?u=a.node.edges[d]:(u=new j.TokenSet,a.node.edges[d]=u),1==a.str.length&&(u.final=!0),r.push({node:u,editsRemaining:a.editsRemaining-1,str:c+a.str.slice(2)})}}}return n},j.TokenSet.fromString=function(e){for(var t=new j.TokenSet,n=t,r=0,a=e.length;r<a;r++){var o=e[r],i=r==a-1;if("*"==o)t.edges[o]=t,t.final=i;else{var s=new j.TokenSet;s.final=i,t.edges[o]=s,t=s}}return n},j.TokenSet.prototype.toArray=function(){for(var e=[],t=[{prefix:"",node:this}];t.length;){var n=t.pop(),r=Object.keys(n.node.edges),a=r.length;n.node.final&&(n.prefix.charAt(0),e.push(n.prefix));for(var o=0;o<a;o++){var i=r[o];t.push({prefix:n.prefix.concat(i),node:n.node.edges[i]})}}return e},j.TokenSet.prototype.toString=function(){if(this._str)return this._str;for(var e=this.final?"1":"0",t=Object.keys(this.edges).sort(),n=t.length,r=0;r<n;r++){var a=t[r];e=e+a+this.edges[a].id}return e},j.TokenSet.prototype.intersect=function(e){for(var t=new j.TokenSet,n=void 0,r=[{qNode:e,output:t,node:this}];r.length;){n=r.pop();for(var a=Object.keys(n.qNode.edges),o=a.length,i=Object.keys(n.node.edges),s=i.length,l=0;l<o;l++)for(var u=a[l],c=0;c<s;c++){var d=i[c];if(d==u||"*"==u){var p=n.node.edges[d],f=n.qNode.edges[u],h=p.final&&f.final,g=void 0;d in n.output.edges?(g=n.output.edges[d]).final=g.final||h:((g=new j.TokenSet).final=h,n.output.edges[d]=g),r.push({qNode:f,output:g,node:p})}}}return t},j.TokenSet.Builder=function(){this.previousWord="",this.root=new j.TokenSet,this.uncheckedNodes=[],this.minimizedNodes={}},j.TokenSet.Builder.prototype.insert=function(e){var t,n=0;if(e<this.previousWord)throw new Error("Out of order word insertion");for(var r=0;r<e.length&&r<this.previousWord.length&&e[r]==this.previousWord[r];r++)n++;this.minimize(n),t=0==this.uncheckedNodes.length?this.root:this.uncheckedNodes[this.uncheckedNodes.length-1].child;for(r=n;r<e.length;r++){var a=new j.TokenSet,o=e[r];t.edges[o]=a,this.uncheckedNodes.push({parent:t,char:o,child:a}),t=a}t.final=!0,this.previousWord=e},j.TokenSet.Builder.prototype.finish=function(){this.minimize(0)},j.TokenSet.Builder.prototype.minimize=function(e){for(var t=this.uncheckedNodes.length-1;t>=e;t--){var n=this.uncheckedNodes[t],r=n.child.toString();r in this.minimizedNodes?n.parent.edges[n.char]=this.minimizedNodes[r]:(n.child._str=r,this.minimizedNodes[r]=n.child),this.uncheckedNodes.pop()}},j.Index=function(e){this.invertedIndex=e.invertedIndex,this.fieldVectors=e.fieldVectors,this.tokenSet=e.tokenSet,this.fields=e.fields,this.pipeline=e.pipeline},j.Index.prototype.search=function(e){return this.query((function(t){new j.QueryParser(e,t).parse()}))},j.Index.prototype.query=function(e){for(var t=new j.Query(this.fields),n=Object.create(null),r=Object.create(null),a=Object.create(null),o=Object.create(null),i=Object.create(null),s=0;s<this.fields.length;s++)r[this.fields[s]]=new j.Vector;e.call(t,t);for(s=0;s<t.clauses.length;s++){var l=t.clauses[s],u=null,c=j.Set.empty;u=l.usePipeline?this.pipeline.runString(l.term,{fields:l.fields}):[l.term];for(var d=0;d<u.length;d++){var p=u[d];l.term=p;var f=j.TokenSet.fromClause(l),h=this.tokenSet.intersect(f).toArray();if(0===h.length&&l.presence===j.Query.presence.REQUIRED){for(var g=0;g<l.fields.length;g++){o[O=l.fields[g]]=j.Set.empty}break}for(var m=0;m<h.length;m++){var y=h[m],b=this.invertedIndex[y],v=b._index;for(g=0;g<l.fields.length;g++){var w=b[O=l.fields[g]],x=Object.keys(w),k=y+"/"+O,S=new j.Set(x);if(l.presence==j.Query.presence.REQUIRED&&(c=c.union(S),void 0===o[O]&&(o[O]=j.Set.complete)),l.presence!=j.Query.presence.PROHIBITED){if(r[O].upsert(v,l.boost,(function(e,t){return e+t})),!a[k]){for(var E=0;E<x.length;E++){var _,C=x[E],T=new j.FieldRef(C,O),A=w[C];void 0===(_=n[T])?n[T]=new j.MatchData(y,O,A):_.add(y,O,A)}a[k]=!0}}else void 0===i[O]&&(i[O]=j.Set.empty),i[O]=i[O].union(S)}}}if(l.presence===j.Query.presence.REQUIRED)for(g=0;g<l.fields.length;g++){o[O=l.fields[g]]=o[O].intersect(c)}}var N=j.Set.complete,L=j.Set.empty;for(s=0;s<this.fields.length;s++){var O;o[O=this.fields[s]]&&(N=N.intersect(o[O])),i[O]&&(L=L.union(i[O]))}var P=Object.keys(n),R=[],I=Object.create(null);if(t.isNegated()){P=Object.keys(this.fieldVectors);for(s=0;s<P.length;s++){T=P[s];var F=j.FieldRef.fromString(T);n[T]=new j.MatchData}}for(s=0;s<P.length;s++){var D=(F=j.FieldRef.fromString(P[s])).docRef;if(N.contains(D)&&!L.contains(D)){var M,B=this.fieldVectors[F],z=r[F.fieldName].similarity(B);if(void 0!==(M=I[D]))M.score+=z,M.matchData.combine(n[F]);else{var U={ref:D,score:z,matchData:n[F]};I[D]=U,R.push(U)}}}return R.sort((function(e,t){return t.score-e.score}))},j.Index.prototype.toJSON=function(){var e=Object.keys(this.invertedIndex).sort().map((function(e){return[e,this.invertedIndex[e]]}),this),t=Object.keys(this.fieldVectors).map((function(e){return[e,this.fieldVectors[e].toJSON()]}),this);return{version:j.version,fields:this.fields,fieldVectors:t,invertedIndex:e,pipeline:this.pipeline.toJSON()}},j.Index.load=function(e){var t={},n={},r=e.fieldVectors,a=Object.create(null),o=e.invertedIndex,i=new j.TokenSet.Builder,s=j.Pipeline.load(e.pipeline);e.version!=j.version&&j.utils.warn("Version mismatch when loading serialised index. Current version of lunr '"+j.version+"' does not match serialized index '"+e.version+"'");for(var l=0;l<r.length;l++){var u=(d=r[l])[0],c=d[1];n[u]=new j.Vector(c)}for(l=0;l<o.length;l++){var d,p=(d=o[l])[0],f=d[1];i.insert(p),a[p]=f}return i.finish(),t.fields=e.fields,t.fieldVectors=n,t.invertedIndex=a,t.tokenSet=i.root,t.pipeline=s,new j.Index(t)},j.Builder=function(){this._ref="id",this._fields=Object.create(null),this._documents=Object.create(null),this.invertedIndex=Object.create(null),this.fieldTermFrequencies={},this.fieldLengths={},this.tokenizer=j.tokenizer,this.pipeline=new j.Pipeline,this.searchPipeline=new j.Pipeline,this.documentCount=0,this._b=.75,this._k1=1.2,this.termIndex=0,this.metadataWhitelist=[]},j.Builder.prototype.ref=function(e){this._ref=e},j.Builder.prototype.field=function(e,t){if(/\//.test(e))throw new RangeError("Field '"+e+"' contains illegal character '/'");this._fields[e]=t||{}},j.Builder.prototype.b=function(e){this._b=e<0?0:e>1?1:e},j.Builder.prototype.k1=function(e){this._k1=e},j.Builder.prototype.add=function(e,t){var n=e[this._ref],r=Object.keys(this._fields);this._documents[n]=t||{},this.documentCount+=1;for(var a=0;a<r.length;a++){var o=r[a],i=this._fields[o].extractor,s=i?i(e):e[o],l=this.tokenizer(s,{fields:[o]}),u=this.pipeline.run(l),c=new j.FieldRef(n,o),d=Object.create(null);this.fieldTermFrequencies[c]=d,this.fieldLengths[c]=0,this.fieldLengths[c]+=u.length;for(var p=0;p<u.length;p++){var f=u[p];if(null==d[f]&&(d[f]=0),d[f]+=1,null==this.invertedIndex[f]){var h=Object.create(null);h._index=this.termIndex,this.termIndex+=1;for(var g=0;g<r.length;g++)h[r[g]]=Object.create(null);this.invertedIndex[f]=h}null==this.invertedIndex[f][o][n]&&(this.invertedIndex[f][o][n]=Object.create(null));for(var m=0;m<this.metadataWhitelist.length;m++){var y=this.metadataWhitelist[m],b=f.metadata[y];null==this.invertedIndex[f][o][n][y]&&(this.invertedIndex[f][o][n][y]=[]),this.invertedIndex[f][o][n][y].push(b)}}}},j.Builder.prototype.calculateAverageFieldLengths=function(){for(var e=Object.keys(this.fieldLengths),t=e.length,n={},r={},a=0;a<t;a++){var o=j.FieldRef.fromString(e[a]),i=o.fieldName;r[i]||(r[i]=0),r[i]+=1,n[i]||(n[i]=0),n[i]+=this.fieldLengths[o]}var s=Object.keys(this._fields);for(a=0;a<s.length;a++){var l=s[a];n[l]=n[l]/r[l]}this.averageFieldLength=n},j.Builder.prototype.createFieldVectors=function(){for(var e={},t=Object.keys(this.fieldTermFrequencies),n=t.length,r=Object.create(null),a=0;a<n;a++){for(var o=j.FieldRef.fromString(t[a]),i=o.fieldName,s=this.fieldLengths[o],l=new j.Vector,u=this.fieldTermFrequencies[o],c=Object.keys(u),d=c.length,p=this._fields[i].boost||1,f=this._documents[o.docRef].boost||1,h=0;h<d;h++){var g,m,y,b=c[h],v=u[b],w=this.invertedIndex[b]._index;void 0===r[b]?(g=j.idf(this.invertedIndex[b],this.documentCount),r[b]=g):g=r[b],m=g*((this._k1+1)*v)/(this._k1*(1-this._b+this._b*(s/this.averageFieldLength[i]))+v),m*=p,m*=f,y=Math.round(1e3*m)/1e3,l.insert(w,y)}e[o]=l}this.fieldVectors=e},j.Builder.prototype.createTokenSet=function(){this.tokenSet=j.TokenSet.fromArray(Object.keys(this.invertedIndex).sort())},j.Builder.prototype.build=function(){return this.calculateAverageFieldLengths(),this.createFieldVectors(),this.createTokenSet(),new j.Index({invertedIndex:this.invertedIndex,fieldVectors:this.fieldVectors,tokenSet:this.tokenSet,fields:Object.keys(this._fields),pipeline:this.searchPipeline})},j.Builder.prototype.use=function(e){var t=Array.prototype.slice.call(arguments,1);t.unshift(this),e.apply(this,t)},j.MatchData=function(e,t,n){for(var r=Object.create(null),a=Object.keys(n||{}),o=0;o<a.length;o++){var i=a[o];r[i]=n[i].slice()}this.metadata=Object.create(null),void 0!==e&&(this.metadata[e]=Object.create(null),this.metadata[e][t]=r)},j.MatchData.prototype.combine=function(e){for(var t=Object.keys(e.metadata),n=0;n<t.length;n++){var r=t[n],a=Object.keys(e.metadata[r]);null==this.metadata[r]&&(this.metadata[r]=Object.create(null));for(var o=0;o<a.length;o++){var i=a[o],s=Object.keys(e.metadata[r][i]);null==this.metadata[r][i]&&(this.metadata[r][i]=Object.create(null));for(var l=0;l<s.length;l++){var u=s[l];null==this.metadata[r][i][u]?this.metadata[r][i][u]=e.metadata[r][i][u]:this.metadata[r][i][u]=this.metadata[r][i][u].concat(e.metadata[r][i][u])}}}},j.MatchData.prototype.add=function(e,t,n){if(!(e in this.metadata))return this.metadata[e]=Object.create(null),void(this.metadata[e][t]=n);if(t in this.metadata[e])for(var r=Object.keys(n),a=0;a<r.length;a++){var o=r[a];o in this.metadata[e][t]?this.metadata[e][t][o]=this.metadata[e][t][o].concat(n[o]):this.metadata[e][t][o]=n[o]}else this.metadata[e][t]=n},j.Query=function(e){this.clauses=[],this.allFields=e},j.Query.wildcard=new String("*"),j.Query.wildcard.NONE=0,j.Query.wildcard.LEADING=1,j.Query.wildcard.TRAILING=2,j.Query.presence={OPTIONAL:1,REQUIRED:2,PROHIBITED:3},j.Query.prototype.clause=function(e){return"fields"in e||(e.fields=this.allFields),"boost"in e||(e.boost=1),"usePipeline"in e||(e.usePipeline=!0),"wildcard"in e||(e.wildcard=j.Query.wildcard.NONE),e.wildcard&j.Query.wildcard.LEADING&&e.term.charAt(0)!=j.Query.wildcard&&(e.term="*"+e.term),e.wildcard&j.Query.wildcard.TRAILING&&e.term.slice(-1)!=j.Query.wildcard&&(e.term=e.term+"*"),"presence"in e||(e.presence=j.Query.presence.OPTIONAL),this.clauses.push(e),this},j.Query.prototype.isNegated=function(){for(var e=0;e<this.clauses.length;e++)if(this.clauses[e].presence!=j.Query.presence.PROHIBITED)return!1;return!0},j.Query.prototype.term=function(e,t){if(Array.isArray(e))return e.forEach((function(e){this.term(e,j.utils.clone(t))}),this),this;var n=t||{};return n.term=e.toString(),this.clause(n),this},j.QueryParseError=function(e,t,n){this.name="QueryParseError",this.message=e,this.start=t,this.end=n},j.QueryParseError.prototype=new Error,j.QueryLexer=function(e){this.lexemes=[],this.str=e,this.length=e.length,this.pos=0,this.start=0,this.escapeCharPositions=[]},j.QueryLexer.prototype.run=function(){for(var e=j.QueryLexer.lexText;e;)e=e(this)},j.QueryLexer.prototype.sliceString=function(){for(var e=[],t=this.start,n=this.pos,r=0;r<this.escapeCharPositions.length;r++)n=this.escapeCharPositions[r],e.push(this.str.slice(t,n)),t=n+1;return e.push(this.str.slice(t,this.pos)),this.escapeCharPositions.length=0,e.join("")},j.QueryLexer.prototype.emit=function(e){this.lexemes.push({type:e,str:this.sliceString(),start:this.start,end:this.pos}),this.start=this.pos},j.QueryLexer.prototype.escapeCharacter=function(){this.escapeCharPositions.push(this.pos-1),this.pos+=1},j.QueryLexer.prototype.next=function(){if(this.pos>=this.length)return j.QueryLexer.EOS;var e=this.str.charAt(this.pos);return this.pos+=1,e},j.QueryLexer.prototype.width=function(){return this.pos-this.start},j.QueryLexer.prototype.ignore=function(){this.start==this.pos&&(this.pos+=1),this.start=this.pos},j.QueryLexer.prototype.backup=function(){this.pos-=1},j.QueryLexer.prototype.acceptDigitRun=function(){var e,t;do{t=(e=this.next()).charCodeAt(0)}while(t>47&&t<58);e!=j.QueryLexer.EOS&&this.backup()},j.QueryLexer.prototype.more=function(){return this.pos<this.length},j.QueryLexer.EOS="EOS",j.QueryLexer.FIELD="FIELD",j.QueryLexer.TERM="TERM",j.QueryLexer.EDIT_DISTANCE="EDIT_DISTANCE",j.QueryLexer.BOOST="BOOST",j.QueryLexer.PRESENCE="PRESENCE",j.QueryLexer.lexField=function(e){return e.backup(),e.emit(j.QueryLexer.FIELD),e.ignore(),j.QueryLexer.lexText},j.QueryLexer.lexTerm=function(e){if(e.width()>1&&(e.backup(),e.emit(j.QueryLexer.TERM)),e.ignore(),e.more())return j.QueryLexer.lexText},j.QueryLexer.lexEditDistance=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(j.QueryLexer.EDIT_DISTANCE),j.QueryLexer.lexText},j.QueryLexer.lexBoost=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(j.QueryLexer.BOOST),j.QueryLexer.lexText},j.QueryLexer.lexEOS=function(e){e.width()>0&&e.emit(j.QueryLexer.TERM)},j.QueryLexer.termSeparator=j.tokenizer.separator,j.QueryLexer.lexText=function(e){for(;;){var t=e.next();if(t==j.QueryLexer.EOS)return j.QueryLexer.lexEOS;if(92!=t.charCodeAt(0)){if(":"==t)return j.QueryLexer.lexField;if("~"==t)return e.backup(),e.width()>0&&e.emit(j.QueryLexer.TERM),j.QueryLexer.lexEditDistance;if("^"==t)return e.backup(),e.width()>0&&e.emit(j.QueryLexer.TERM),j.QueryLexer.lexBoost;if("+"==t&&1===e.width())return e.emit(j.QueryLexer.PRESENCE),j.QueryLexer.lexText;if("-"==t&&1===e.width())return e.emit(j.QueryLexer.PRESENCE),j.QueryLexer.lexText;if(t.match(j.QueryLexer.termSeparator))return j.QueryLexer.lexTerm}else e.escapeCharacter()}},j.QueryParser=function(e,t){this.lexer=new j.QueryLexer(e),this.query=t,this.currentClause={},this.lexemeIdx=0},j.QueryParser.prototype.parse=function(){this.lexer.run(),this.lexemes=this.lexer.lexemes;for(var e=j.QueryParser.parseClause;e;)e=e(this);return this.query},j.QueryParser.prototype.peekLexeme=function(){return this.lexemes[this.lexemeIdx]},j.QueryParser.prototype.consumeLexeme=function(){var e=this.peekLexeme();return this.lexemeIdx+=1,e},j.QueryParser.prototype.nextClause=function(){var e=this.currentClause;this.query.clause(e),this.currentClause={}},j.QueryParser.parseClause=function(e){var t=e.peekLexeme();if(null!=t)switch(t.type){case j.QueryLexer.PRESENCE:return j.QueryParser.parsePresence;case j.QueryLexer.FIELD:return j.QueryParser.parseField;case j.QueryLexer.TERM:return j.QueryParser.parseTerm;default:var n="expected either a field or a term, found "+t.type;throw t.str.length>=1&&(n+=" with value '"+t.str+"'"),new j.QueryParseError(n,t.start,t.end)}},j.QueryParser.parsePresence=function(e){var t=e.consumeLexeme();if(null!=t){switch(t.str){case"-":e.currentClause.presence=j.Query.presence.PROHIBITED;break;case"+":e.currentClause.presence=j.Query.presence.REQUIRED;break;default:var n="unrecognised presence operator'"+t.str+"'";throw new j.QueryParseError(n,t.start,t.end)}var r=e.peekLexeme();if(null==r){n="expecting term or field, found nothing";throw new j.QueryParseError(n,t.start,t.end)}switch(r.type){case j.QueryLexer.FIELD:return j.QueryParser.parseField;case j.QueryLexer.TERM:return j.QueryParser.parseTerm;default:n="expecting term or field, found '"+r.type+"'";throw new j.QueryParseError(n,r.start,r.end)}}},j.QueryParser.parseField=function(e){var t=e.consumeLexeme();if(null!=t){if(-1==e.query.allFields.indexOf(t.str)){var n=e.query.allFields.map((function(e){return"'"+e+"'"})).join(", "),r="unrecognised field '"+t.str+"', possible fields: "+n;throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.fields=[t.str];var a=e.peekLexeme();if(null==a){r="expecting term, found nothing";throw new j.QueryParseError(r,t.start,t.end)}if(a.type===j.QueryLexer.TERM)return j.QueryParser.parseTerm;r="expecting term, found '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}},j.QueryParser.parseTerm=function(e){var t=e.consumeLexeme();if(null!=t){e.currentClause.term=t.str.toLowerCase(),-1!=t.str.indexOf("*")&&(e.currentClause.usePipeline=!1);var n=e.peekLexeme();if(null!=n)switch(n.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:var r="Unexpected lexeme type '"+n.type+"'";throw new j.QueryParseError(r,n.start,n.end)}else e.nextClause()}},j.QueryParser.parseEditDistance=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="edit distance must be numeric";throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.editDistance=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}else e.nextClause()}},j.QueryParser.parseBoost=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="boost must be numeric";throw new j.QueryParseError(r,t.start,t.end)}e.currentClause.boost=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case j.QueryLexer.TERM:return e.nextClause(),j.QueryParser.parseTerm;case j.QueryLexer.FIELD:return e.nextClause(),j.QueryParser.parseField;case j.QueryLexer.EDIT_DISTANCE:return j.QueryParser.parseEditDistance;case j.QueryLexer.BOOST:return j.QueryParser.parseBoost;case j.QueryLexer.PRESENCE:return e.nextClause(),j.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new j.QueryParseError(r,a.start,a.end)}else e.nextClause()}},void 0===(a="function"==typeof(r=function(){return j})?r.call(t,n,t,e):r)||(e.exports=a)}()},689:function(e){e.exports=function(){"use strict";var e="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(e){return typeof e}:function(e){return e&&"function"==typeof Symbol&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e},t=function(e,t){if(!(e instanceof t))throw new TypeError("Cannot call a class as a function")},n=function(){function e(e,t){for(var n=0;n<t.length;n++){var r=t[n];r.enumerable=r.enumerable||!1,r.configurable=!0,"value"in r&&(r.writable=!0),Object.defineProperty(e,r.key,r)}}return function(t,n,r){return n&&e(t.prototype,n),r&&e(t,r),t}}(),r=Object.assign||function(e){for(var t=1;t<arguments.length;t++){var n=arguments[t];for(var r in n)Object.prototype.hasOwnProperty.call(n,r)&&(e[r]=n[r])}return e},a=function(){function e(n){var r=!(arguments.length>1&&void 0!==arguments[1])||arguments[1],a=arguments.length>2&&void 0!==arguments[2]?arguments[2]:[],o=arguments.length>3&&void 0!==arguments[3]?arguments[3]:5e3;t(this,e),this.ctx=n,this.iframes=r,this.exclude=a,this.iframesTimeout=o}return n(e,[{key:"getContexts",value:function(){var e=[];return(void 0!==this.ctx&&this.ctx?NodeList.prototype.isPrototypeOf(this.ctx)?Array.prototype.slice.call(this.ctx):Array.isArray(this.ctx)?this.ctx:"string"==typeof this.ctx?Array.prototype.slice.call(document.querySelectorAll(this.ctx)):[this.ctx]:[]).forEach((function(t){var n=e.filter((function(e){return e.contains(t)})).length>0;-1!==e.indexOf(t)||n||e.push(t)})),e}},{key:"getIframeContents",value:function(e,t){var n=arguments.length>2&&void 0!==arguments[2]?arguments[2]:function(){},r=void 0;try{var a=e.contentWindow;if(r=a.document,!a||!r)throw new Error("iframe inaccessible")}catch(o){n()}r&&t(r)}},{key:"isIframeBlank",value:function(e){var t="about:blank",n=e.getAttribute("src").trim();return e.contentWindow.location.href===t&&n!==t&&n}},{key:"observeIframeLoad",value:function(e,t,n){var r=this,a=!1,o=null,i=function i(){if(!a){a=!0,clearTimeout(o);try{r.isIframeBlank(e)||(e.removeEventListener("load",i),r.getIframeContents(e,t,n))}catch(s){n()}}};e.addEventListener("load",i),o=setTimeout(i,this.iframesTimeout)}},{key:"onIframeReady",value:function(e,t,n){try{"complete"===e.contentWindow.document.readyState?this.isIframeBlank(e)?this.observeIframeLoad(e,t,n):this.getIframeContents(e,t,n):this.observeIframeLoad(e,t,n)}catch(r){n()}}},{key:"waitForIframes",value:function(e,t){var n=this,r=0;this.forEachIframe(e,(function(){return!0}),(function(e){r++,n.waitForIframes(e.querySelector("html"),(function(){--r||t()}))}),(function(e){e||t()}))}},{key:"forEachIframe",value:function(t,n,r){var a=this,o=arguments.length>3&&void 0!==arguments[3]?arguments[3]:function(){},i=t.querySelectorAll("iframe"),s=i.length,l=0;i=Array.prototype.slice.call(i);var u=function(){--s<=0&&o(l)};s||u(),i.forEach((function(t){e.matches(t,a.exclude)?u():a.onIframeReady(t,(function(e){n(t)&&(l++,r(e)),u()}),u)}))}},{key:"createIterator",value:function(e,t,n){return document.createNodeIterator(e,t,n,!1)}},{key:"createInstanceOnIframe",value:function(t){return new e(t.querySelector("html"),this.iframes)}},{key:"compareNodeIframe",value:function(e,t,n){if(e.compareDocumentPosition(n)&Node.DOCUMENT_POSITION_PRECEDING){if(null===t)return!0;if(t.compareDocumentPosition(n)&Node.DOCUMENT_POSITION_FOLLOWING)return!0}return!1}},{key:"getIteratorNode",value:function(e){var t=e.previousNode();return{prevNode:t,node:(null===t||e.nextNode())&&e.nextNode()}}},{key:"checkIframeFilter",value:function(e,t,n,r){var a=!1,o=!1;return r.forEach((function(e,t){e.val===n&&(a=t,o=e.handled)})),this.compareNodeIframe(e,t,n)?(!1!==a||o?!1===a||o||(r[a].handled=!0):r.push({val:n,handled:!0}),!0):(!1===a&&r.push({val:n,handled:!1}),!1)}},{key:"handleOpenIframes",value:function(e,t,n,r){var a=this;e.forEach((function(e){e.handled||a.getIframeContents(e.val,(function(e){a.createInstanceOnIframe(e).forEachNode(t,n,r)}))}))}},{key:"iterateThroughNodes",value:function(e,t,n,r,a){for(var o=this,i=this.createIterator(t,e,r),s=[],l=[],u=void 0,c=void 0,d=function(){var e=o.getIteratorNode(i);return c=e.prevNode,u=e.node};d();)this.iframes&&this.forEachIframe(t,(function(e){return o.checkIframeFilter(u,c,e,s)}),(function(t){o.createInstanceOnIframe(t).forEachNode(e,(function(e){return l.push(e)}),r)})),l.push(u);l.forEach((function(e){n(e)})),this.iframes&&this.handleOpenIframes(s,e,n,r),a()}},{key:"forEachNode",value:function(e,t,n){var r=this,a=arguments.length>3&&void 0!==arguments[3]?arguments[3]:function(){},o=this.getContexts(),i=o.length;i||a(),o.forEach((function(o){var s=function(){r.iterateThroughNodes(e,o,t,n,(function(){--i<=0&&a()}))};r.iframes?r.waitForIframes(o,s):s()}))}}],[{key:"matches",value:function(e,t){var n="string"==typeof t?[t]:t,r=e.matches||e.matchesSelector||e.msMatchesSelector||e.mozMatchesSelector||e.oMatchesSelector||e.webkitMatchesSelector;if(r){var a=!1;return n.every((function(t){return!r.call(e,t)||(a=!0,!1)})),a}return!1}}]),e}(),o=function(){function o(e){t(this,o),this.ctx=e,this.ie=!1;var n=window.navigator.userAgent;(n.indexOf("MSIE")>-1||n.indexOf("Trident")>-1)&&(this.ie=!0)}return n(o,[{key:"log",value:function(t){var n=arguments.length>1&&void 0!==arguments[1]?arguments[1]:"debug",r=this.opt.log;this.opt.debug&&"object"===(void 0===r?"undefined":e(r))&&"function"==typeof r[n]&&r[n]("mark.js: "+t)}},{key:"escapeStr",value:function(e){return e.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}},{key:"createRegExp",value:function(e){return"disabled"!==this.opt.wildcards&&(e=this.setupWildcardsRegExp(e)),e=this.escapeStr(e),Object.keys(this.opt.synonyms).length&&(e=this.createSynonymsRegExp(e)),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),this.opt.diacritics&&(e=this.createDiacriticsRegExp(e)),e=this.createMergedBlanksRegExp(e),(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.createJoinersRegExp(e)),"disabled"!==this.opt.wildcards&&(e=this.createWildcardsRegExp(e)),e=this.createAccuracyRegExp(e)}},{key:"createSynonymsRegExp",value:function(e){var t=this.opt.synonyms,n=this.opt.caseSensitive?"":"i",r=this.opt.ignoreJoiners||this.opt.ignorePunctuation.length?"\0":"";for(var a in t)if(t.hasOwnProperty(a)){var o=t[a],i="disabled"!==this.opt.wildcards?this.setupWildcardsRegExp(a):this.escapeStr(a),s="disabled"!==this.opt.wildcards?this.setupWildcardsRegExp(o):this.escapeStr(o);""!==i&&""!==s&&(e=e.replace(new RegExp("("+this.escapeStr(i)+"|"+this.escapeStr(s)+")","gm"+n),r+"("+this.processSynomyms(i)+"|"+this.processSynomyms(s)+")"+r))}return e}},{key:"processSynomyms",value:function(e){return(this.opt.ignoreJoiners||this.opt.ignorePunctuation.length)&&(e=this.setupIgnoreJoinersRegExp(e)),e}},{key:"setupWildcardsRegExp",value:function(e){return(e=e.replace(/(?:\\)*\?/g,(function(e){return"\\"===e.charAt(0)?"?":"\x01"}))).replace(/(?:\\)*\*/g,(function(e){return"\\"===e.charAt(0)?"*":"\x02"}))}},{key:"createWildcardsRegExp",value:function(e){var t="withSpaces"===this.opt.wildcards;return 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e.languages.flow.parameter,e.languages.insertBefore("flow","operator",{"flow-punctuation":{pattern:/\{\||\|\}/,alias:"punctuation"}}),Array.isArray(e.languages.flow.keyword)||(e.languages.flow.keyword=[e.languages.flow.keyword]),e.languages.flow.keyword.unshift({pattern:/(^|[^$]\b)(?:Class|declare|opaque|type)\b(?!\$)/,lookbehind:!0},{pattern:/(^|[^$]\B)\$(?:Diff|Enum|Exact|Keys|ObjMap|PropertyType|Record|Shape|Subtype|Supertype|await)\b(?!\$)/,lookbehind:!0})}(C),C.languages.n4js=C.languages.extend("javascript",{keyword:/\b(?:Array|any|boolean|break|case|catch|class|const|constructor|continue|debugger|declare|default|delete|do|else|enum|export|extends|false|finally|for|from|function|get|if|implements|import|in|instanceof|interface|let|module|new|null|number|package|private|protected|public|return|set|static|string|super|switch|this|throw|true|try|typeof|var|void|while|with|yield)\b/}),C.languages.insertBefore("n4js","constant",{annotation:{pattern:/@+\w+/,alias:"operator"}}),C.languages.n4jsd=C.languages.n4js,function(e){function t(e,t){return RegExp(e.replace(/<ID>/g,(function(){return/(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*/.source})),t)}e.languages.insertBefore("javascript","function-variable",{"method-variable":{pattern:RegExp("(\\.\\s*)"+e.languages.javascript["function-variable"].pattern.source),lookbehind:!0,alias:["function-variable","method","function","property-access"]}}),e.languages.insertBefore("javascript","function",{method:{pattern:RegExp("(\\.\\s*)"+e.languages.javascript.function.source),lookbehind:!0,alias:["function","property-access"]}}),e.languages.insertBefore("javascript","constant",{"known-class-name":[{pattern:/\b(?:(?:Float(?:32|64)|(?:Int|Uint)(?:8|16|32)|Uint8Clamped)?Array|ArrayBuffer|BigInt|Boolean|DataView|Date|Error|Function|Intl|JSON|(?:Weak)?(?:Map|Set)|Math|Number|Object|Promise|Proxy|Reflect|RegExp|String|Symbol|WebAssembly)\b/,alias:"class-name"},{pattern:/\b(?:[A-Z]\w*)Error\b/,alias:"class-name"}]}),e.languages.insertBefore("javascript","keyword",{imports:{pattern:t(/(\bimport\b\s*)(?:<ID>(?:\s*,\s*(?:\*\s*as\s+<ID>|\{[^{}]*\}))?|\*\s*as\s+<ID>|\{[^{}]*\})(?=\s*\bfrom\b)/.source),lookbehind:!0,inside:e.languages.javascript},exports:{pattern:t(/(\bexport\b\s*)(?:\*(?:\s*as\s+<ID>)?(?=\s*\bfrom\b)|\{[^{}]*\})/.source),lookbehind:!0,inside:e.languages.javascript}}),e.languages.javascript.keyword.unshift({pattern:/\b(?:as|default|export|from|import)\b/,alias:"module"},{pattern:/\b(?:await|break|catch|continue|do|else|finally|for|if|return|switch|throw|try|while|yield)\b/,alias:"control-flow"},{pattern:/\bnull\b/,alias:["null","nil"]},{pattern:/\bundefined\b/,alias:"nil"}),e.languages.insertBefore("javascript","operator",{spread:{pattern:/\.{3}/,alias:"operator"},arrow:{pattern:/=>/,alias:"operator"}}),e.languages.insertBefore("javascript","punctuation",{"property-access":{pattern:t(/(\.\s*)#?<ID>/.source),lookbehind:!0},"maybe-class-name":{pattern:/(^|[^$\w\xA0-\uFFFF])[A-Z][$\w\xA0-\uFFFF]+/,lookbehind:!0},dom:{pattern:/\b(?:document|(?:local|session)Storage|location|navigator|performance|window)\b/,alias:"variable"},console:{pattern:/\bconsole(?=\s*\.)/,alias:"class-name"}});for(var n=["function","function-variable","method","method-variable","property-access"],r=0;r<n.length;r++){var a=n[r],o=e.languages.javascript[a];a=(o="RegExp"===e.util.type(o)?e.languages.javascript[a]={pattern:o}:o).inside||{};(o.inside=a)["maybe-class-name"]=/^[A-Z][\s\S]*/}}(C),function(e){var t=e.util.clone(e.languages.javascript),n=/(?:\s|\/\/.*(?!.)|\/\*(?:[^*]|\*(?!\/))\*\/)/.source,r=/(?:\{(?:\{(?:\{[^{}]*\}|[^{}])*\}|[^{}])*\})/.source,a=/(?:\{<S>*\.{3}(?:[^{}]|<BRACES>)*\})/.source;function o(e,t){return e=e.replace(/<S>/g,(function(){return n})).replace(/<BRACES>/g,(function(){return r})).replace(/<SPREAD>/g,(function(){return a})),RegExp(e,t)}function i(t){for(var n=[],r=0;r<t.length;r++){var a=t[r],o=!1;"string"!=typeof a&&("tag"===a.type&&a.content[0]&&"tag"===a.content[0].type?"</"===a.content[0].content[0].content?0<n.length&&n[n.length-1].tagName===s(a.content[0].content[1])&&n.pop():"/>"!==a.content[a.content.length-1].content&&n.push({tagName:s(a.content[0].content[1]),openedBraces:0}):0<n.length&&"punctuation"===a.type&&"{"===a.content?n[n.length-1].openedBraces++:0<n.length&&0<n[n.length-1].openedBraces&&"punctuation"===a.type&&"}"===a.content?n[n.length-1].openedBraces--:o=!0),(o||"string"==typeof a)&&0<n.length&&0===n[n.length-1].openedBraces&&(o=s(a),r<t.length-1&&("string"==typeof t[r+1]||"plain-text"===t[r+1].type)&&(o+=s(t[r+1]),t.splice(r+1,1)),0<r&&("string"==typeof t[r-1]||"plain-text"===t[r-1].type)&&(o=s(t[r-1])+o,t.splice(r-1,1),r--),t[r]=new e.Token("plain-text",o,null,o)),a.content&&"string"!=typeof a.content&&i(a.content)}}a=o(a).source,e.languages.jsx=e.languages.extend("markup",t),e.languages.jsx.tag.pattern=o(/<\/?(?:[\w.:-]+(?:<S>+(?:[\w.:$-]+(?:=(?:"(?:\\[\s\S]|[^\\"])*"|'(?:\\[\s\S]|[^\\'])*'|[^\s{'"/>=]+|<BRACES>))?|<SPREAD>))*<S>*\/?)?>/.source),e.languages.jsx.tag.inside.tag.pattern=/^<\/?[^\s>\/]*/,e.languages.jsx.tag.inside["attr-value"].pattern=/=(?!\{)(?:"(?:\\[\s\S]|[^\\"])*"|'(?:\\[\s\S]|[^\\'])*'|[^\s'">]+)/,e.languages.jsx.tag.inside.tag.inside["class-name"]=/^[A-Z]\w*(?:\.[A-Z]\w*)*$/,e.languages.jsx.tag.inside.comment=t.comment,e.languages.insertBefore("inside","attr-name",{spread:{pattern:o(/<SPREAD>/.source),inside:e.languages.jsx}},e.languages.jsx.tag),e.languages.insertBefore("inside","special-attr",{script:{pattern:o(/=<BRACES>/.source),alias:"language-javascript",inside:{"script-punctuation":{pattern:/^=(?=\{)/,alias:"punctuation"},rest:e.languages.jsx}}},e.languages.jsx.tag);var s=function(e){return e?"string"==typeof e?e:"string"==typeof e.content?e.content:e.content.map(s).join(""):""};e.hooks.add("after-tokenize",(function(e){"jsx"!==e.language&&"tsx"!==e.language||i(e.tokens)}))}(C),function(e){var t=e.util.clone(e.languages.typescript);(t=(e.languages.tsx=e.languages.extend("jsx",t),delete e.languages.tsx.parameter,delete e.languages.tsx["literal-property"],e.languages.tsx.tag)).pattern=RegExp(/(^|[^\w$]|(?=<\/))/.source+"(?:"+t.pattern.source+")",t.pattern.flags),t.lookbehind=!0}(C),C.languages.swift={comment:{pattern:/(^|[^\\:])(?:\/\/.*|\/\*(?:[^/*]|\/(?!\*)|\*(?!\/)|\/\*(?:[^*]|\*(?!\/))*\*\/)*\*\/)/,lookbehind:!0,greedy:!0},"string-literal":[{pattern:RegExp(/(^|[^"#])/.source+"(?:"+/"(?:\\(?:\((?:[^()]|\([^()]*\))*\)|\r\n|[^(])|[^\\\r\n"])*"/.source+"|"+/"""(?:\\(?:\((?:[^()]|\([^()]*\))*\)|[^(])|[^\\"]|"(?!""))*"""/.source+")"+/(?!["#])/.source),lookbehind:!0,greedy:!0,inside:{interpolation:{pattern:/(\\\()(?:[^()]|\([^()]*\))*(?=\))/,lookbehind:!0,inside:null},"interpolation-punctuation":{pattern:/^\)|\\\($/,alias:"punctuation"},punctuation:/\\(?=[\r\n])/,string:/[\s\S]+/}},{pattern:RegExp(/(^|[^"#])(#+)/.source+"(?:"+/"(?:\\(?:#+\((?:[^()]|\([^()]*\))*\)|\r\n|[^#])|[^\\\r\n])*?"/.source+"|"+/"""(?:\\(?:#+\((?:[^()]|\([^()]*\))*\)|[^#])|[^\\])*?"""/.source+")\\2"),lookbehind:!0,greedy:!0,inside:{interpolation:{pattern:/(\\#+\()(?:[^()]|\([^()]*\))*(?=\))/,lookbehind:!0,inside:null},"interpolation-punctuation":{pattern:/^\)|\\#+\($/,alias:"punctuation"},string:/[\s\S]+/}}],directive:{pattern:RegExp(/#/.source+"(?:"+/(?:elseif|if)\b/.source+"(?:[ \t]*"+/(?:![ \t]*)?(?:\b\w+\b(?:[ \t]*\((?:[^()]|\([^()]*\))*\))?|\((?:[^()]|\([^()]*\))*\))(?:[ \t]*(?:&&|\|\|))?/.source+")+|"+/(?:else|endif)\b/.source+")"),alias:"property",inside:{"directive-name":/^#\w+/,boolean:/\b(?:false|true)\b/,number:/\b\d+(?:\.\d+)*\b/,operator:/!|&&|\|\||[<>]=?/,punctuation:/[(),]/}},literal:{pattern:/#(?:colorLiteral|column|dsohandle|file(?:ID|Literal|Path)?|function|imageLiteral|line)\b/,alias:"constant"},"other-directive":{pattern:/#\w+\b/,alias:"property"},attribute:{pattern:/@\w+/,alias:"atrule"},"function-definition":{pattern:/(\bfunc\s+)\w+/,lookbehind:!0,alias:"function"},label:{pattern:/\b(break|continue)\s+\w+|\b[a-zA-Z_]\w*(?=\s*:\s*(?:for|repeat|while)\b)/,lookbehind:!0,alias:"important"},keyword:/\b(?:Any|Protocol|Self|Type|actor|as|assignment|associatedtype|associativity|async|await|break|case|catch|class|continue|convenience|default|defer|deinit|didSet|do|dynamic|else|enum|extension|fallthrough|fileprivate|final|for|func|get|guard|higherThan|if|import|in|indirect|infix|init|inout|internal|is|isolated|lazy|left|let|lowerThan|mutating|none|nonisolated|nonmutating|open|operator|optional|override|postfix|precedencegroup|prefix|private|protocol|public|repeat|required|rethrows|return|right|safe|self|set|some|static|struct|subscript|super|switch|throw|throws|try|typealias|unowned|unsafe|var|weak|where|while|willSet)\b/,boolean:/\b(?:false|true)\b/,nil:{pattern:/\bnil\b/,alias:"constant"},"short-argument":/\$\d+\b/,omit:{pattern:/\b_\b/,alias:"keyword"},number:/\b(?:[\d_]+(?:\.[\de_]+)?|0x[a-f0-9_]+(?:\.[a-f0-9p_]+)?|0b[01_]+|0o[0-7_]+)\b/i,"class-name":/\b[A-Z](?:[A-Z_\d]*[a-z]\w*)?\b/,function:/\b[a-z_]\w*(?=\s*\()/i,constant:/\b(?:[A-Z_]{2,}|k[A-Z][A-Za-z_]+)\b/,operator:/[-+*/%=!<>&|^~?]+|\.[.\-+*/%=!<>&|^~?]+/,punctuation:/[{}[\]();,.:\\]/},C.languages.swift["string-literal"].forEach((function(e){e.inside.interpolation.inside=C.languages.swift})),function(e){e.languages.kotlin=e.languages.extend("clike",{keyword:{pattern:/(^|[^.])\b(?:abstract|actual|annotation|as|break|by|catch|class|companion|const|constructor|continue|crossinline|data|do|dynamic|else|enum|expect|external|final|finally|for|fun|get|if|import|in|infix|init|inline|inner|interface|internal|is|lateinit|noinline|null|object|open|operator|out|override|package|private|protected|public|reified|return|sealed|set|super|suspend|tailrec|this|throw|to|try|typealias|val|var|vararg|when|where|while)\b/,lookbehind:!0},function:[{pattern:/(?:`[^\r\n`]+`|\b\w+)(?=\s*\()/,greedy:!0},{pattern:/(\.)(?:`[^\r\n`]+`|\w+)(?=\s*\{)/,lookbehind:!0,greedy:!0}],number:/\b(?:0[xX][\da-fA-F]+(?:_[\da-fA-F]+)*|0[bB][01]+(?:_[01]+)*|\d+(?:_\d+)*(?:\.\d+(?:_\d+)*)?(?:[eE][+-]?\d+(?:_\d+)*)?[fFL]?)\b/,operator:/\+[+=]?|-[-=>]?|==?=?|!(?:!|==?)?|[\/*%<>]=?|[?:]:?|\.\.|&&|\|\||\b(?:and|inv|or|shl|shr|ushr|xor)\b/}),delete e.languages.kotlin["class-name"];var t={"interpolation-punctuation":{pattern:/^\$\{?|\}$/,alias:"punctuation"},expression:{pattern:/[\s\S]+/,inside:e.languages.kotlin}};e.languages.insertBefore("kotlin","string",{"string-literal":[{pattern:/"""(?:[^$]|\$(?:(?!\{)|\{[^{}]*\}))*?"""/,alias:"multiline",inside:{interpolation:{pattern:/\$(?:[a-z_]\w*|\{[^{}]*\})/i,inside:t},string:/[\s\S]+/}},{pattern:/"(?:[^"\\\r\n$]|\\.|\$(?:(?!\{)|\{[^{}]*\}))*"/,alias:"singleline",inside:{interpolation:{pattern:/((?:^|[^\\])(?:\\{2})*)\$(?:[a-z_]\w*|\{[^{}]*\})/i,lookbehind:!0,inside:t},string:/[\s\S]+/}}],char:{pattern:/'(?:[^'\\\r\n]|\\(?:.|u[a-fA-F0-9]{0,4}))'/,greedy:!0}}),delete e.languages.kotlin.string,e.languages.insertBefore("kotlin","keyword",{annotation:{pattern:/\B@(?:\w+:)?(?:[A-Z]\w*|\[[^\]]+\])/,alias:"builtin"}}),e.languages.insertBefore("kotlin","function",{label:{pattern:/\b\w+@|@\w+\b/,alias:"symbol"}}),e.languages.kt=e.languages.kotlin,e.languages.kts=e.languages.kotlin}(C),C.languages.c=C.languages.extend("clike",{comment:{pattern:/\/\/(?:[^\r\n\\]|\\(?:\r\n?|\n|(?![\r\n])))*|\/\*[\s\S]*?(?:\*\/|$)/,greedy:!0},string:{pattern:/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},"class-name":{pattern:/(\b(?:enum|struct)\s+(?:__attribute__\s*\(\([\s\S]*?\)\)\s*)?)\w+|\b[a-z]\w*_t\b/,lookbehind:!0},keyword:/\b(?:_Alignas|_Alignof|_Atomic|_Bool|_Complex|_Generic|_Imaginary|_Noreturn|_Static_assert|_Thread_local|__attribute__|asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|inline|int|long|register|return|short|signed|sizeof|static|struct|switch|typedef|typeof|union|unsigned|void|volatile|while)\b/,function:/\b[a-z_]\w*(?=\s*\()/i,number:/(?:\b0x(?:[\da-f]+(?:\.[\da-f]*)?|\.[\da-f]+)(?:p[+-]?\d+)?|(?:\b\d+(?:\.\d*)?|\B\.\d+)(?:e[+-]?\d+)?)[ful]{0,4}/i,operator:/>>=?|<<=?|->|([-+&|:])\1|[?:~]|[-+*/%&|^!=<>]=?/}),C.languages.insertBefore("c","string",{char:{pattern:/'(?:\\(?:\r\n|[\s\S])|[^'\\\r\n]){0,32}'/,greedy:!0}}),C.languages.insertBefore("c","string",{macro:{pattern:/(^[\t ]*)#\s*[a-z](?:[^\r\n\\/]|\/(?!\*)|\/\*(?:[^*]|\*(?!\/))*\*\/|\\(?:\r\n|[\s\S]))*/im,lookbehind:!0,greedy:!0,alias:"property",inside:{string:[{pattern:/^(#\s*include\s*)<[^>]+>/,lookbehind:!0},C.languages.c.string],char:C.languages.c.char,comment:C.languages.c.comment,"macro-name":[{pattern:/(^#\s*define\s+)\w+\b(?!\()/i,lookbehind:!0},{pattern:/(^#\s*define\s+)\w+\b(?=\()/i,lookbehind:!0,alias:"function"}],directive:{pattern:/^(#\s*)[a-z]+/,lookbehind:!0,alias:"keyword"},"directive-hash":/^#/,punctuation:/##|\\(?=[\r\n])/,expression:{pattern:/\S[\s\S]*/,inside:C.languages.c}}}}),C.languages.insertBefore("c","function",{constant:/\b(?:EOF|NULL|SEEK_CUR|SEEK_END|SEEK_SET|__DATE__|__FILE__|__LINE__|__TIMESTAMP__|__TIME__|__func__|stderr|stdin|stdout)\b/}),delete C.languages.c.boolean,C.languages.objectivec=C.languages.extend("c",{string:{pattern:/@?"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},keyword:/\b(?:asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|in|inline|int|long|register|return|self|short|signed|sizeof|static|struct|super|switch|typedef|typeof|union|unsigned|void|volatile|while)\b|(?:@interface|@end|@implementation|@protocol|@class|@public|@protected|@private|@property|@try|@catch|@finally|@throw|@synthesize|@dynamic|@selector)\b/,operator:/-[->]?|\+\+?|!=?|<<?=?|>>?=?|==?|&&?|\|\|?|[~^%?*\/@]/}),delete 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+2,12 @@ <html lang="en" dir="ltr" class="docs-wrapper plugin-docs plugin-id-default docs-version-current docs-doc-page" data-has-hydrated="false"> <head> <meta charset="UTF-8"> -<meta name="generator" content="Docusaurus v3.2.1"> -<title data-rh="true">Hands-on • Quantum Espresso Tutorial - - + +Hands-on • Quantum Espresso Tutorial + + -

Hands-on

Copyright © 2024 Pranab Das. All rights reserved.
+

Hands-on

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/category/setup/index.html b/category/setup/index.html index bd9e3c1e..2dca82af 100644 --- a/category/setup/index.html +++ b/category/setup/index.html @@ -2,12 +2,12 @@ - -Setup • Quantum Espresso Tutorial - - + +Setup • Quantum Espresso Tutorial + + -

Setup

Copyright © 2024 Pranab Das. All rights reserved.
+

Setup

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/category/theory/index.html b/category/theory/index.html index 46049183..6aefab89 100644 --- a/category/theory/index.html +++ b/category/theory/index.html @@ -2,12 +2,12 @@ - -Theory • Quantum Espresso Tutorial - - + +Theory • Quantum Espresso Tutorial + + -

Theory

Copyright © 2024 Pranab Das. All rights reserved.
+

Theory

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/Bi2Se3/index.html b/hands-on/Bi2Se3/index.html index 100f9fe6..2d2f327a 100644 --- a/hands-on/Bi2Se3/index.html +++ b/hands-on/Bi2Se3/index.html @@ -2,13 +2,13 @@ - -Bandstructure of topological insulating Bi2Se3 • Quantum Espresso Tutorial - - + +Bandstructure of topological insulating Bi2Se3 • Quantum Espresso Tutorial + + -

Bandstructure of topological insulating Bi2Se3

Topological insulators are a special class of material that is insulating in the +

Bandstructure of topological insulating Bi2Se3

Topological insulators are a special class of material that is insulating in the bulk, however exhibit conducting states in the surface. Bi2Se3 is such a material. Spin orbit coupling and breaking of the inversion symmetry at the surface of the crystal is crucial to @@ -33,9 +33,9 @@ mesh (25✕25✕5) was used. The signature of Dirac cone is evident from the DOS figure.

Bi2Se3-dos -

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/GaAs/index.html b/hands-on/GaAs/index.html index 458712b4..2fe25871 100644 --- a/hands-on/GaAs/index.html +++ b/hands-on/GaAs/index.html @@ -2,13 +2,13 @@ - -Bandstructure of GaAs • Quantum Espresso Tutorial - - + +Bandstructure of GaAs • Quantum Espresso Tutorial + + -

Bandstructure of GaAs

Now that we have calculated the bandstructure of silicon (semiconductor) and +

Bandstructure of GaAs

Now that we have calculated the bandstructure of silicon (semiconductor) and aluminum (metal), let us proceed with a compound which has two different atoms. We follow the steps like before:

First check the lattice constant with cell relaxation according to our chosen diff --git a/hands-on/aluminum/index.html b/hands-on/aluminum/index.html index fb0c0f11..b2b36d23 100644 --- a/hands-on/aluminum/index.html +++ b/hands-on/aluminum/index.html @@ -2,13 +2,13 @@ - -DOS and bandstructure for Aluminum (metal) • Quantum Espresso Tutorial - - + +DOS and bandstructure for Aluminum (metal) • Quantum Espresso Tutorial + + -

DOS and bandstructure for Aluminum (metal)

Variable cell relaxation​

+

DOS and bandstructure for Aluminum (metal)

Variable cell relaxation​

First we are going to relax the cell and choose appropriate lattice constant for our chosen pseudo potential. In case of metals, it is important to provide smearing parameters in the input file.

@@ -19,14 +19,14 @@

Now you may open the output file in vi editor and invoke search by pressing / and type Final enthalpy You will find the final lattice parameters below it.

-

Self consistent field (SCF) calculation​

+

Self consistent field (SCF) calculation​

We obtain relaxed lattice constant = 7.652 * 0.498611683 / 0.5 = 7.63075 Bohr. We will use this value for our next step, self consistent calculation.

src/al/al_scf.in
&CONTROL
  calculation= 'scf',
  restart_mode= 'from_scratch',
  prefix= 'al',
  outdir= '/tmp/',
  pseudo_dir= '../pseudos/'
/

&SYSTEM
  ibrav= 2,
  celldm(1) = 7.63075,
  nat= 1,
  ntyp= 1,
  ecutwfc= 50,
  ecutrho= 500,
  occupations= 'smearing',
  smearing= 'gaussian',
  degauss= 0.01
/

&ELECTRONS
  conv_thr= 1e-8
/

ATOMIC_SPECIES
  Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF

ATOMIC_POSITIONS (alat)
  Al 0.00 0.00 0.00

K_POINTS (automatic)
  10 10 10 0 0 0

We run our self consistent calculation:

pw.x < al_scf.in > al_scf.out
-

Non-self consistent field calculation​

+

Non-self consistent field calculation​

Inspect the output file, and let's proceed to next step non-self consistent calculation:

@@ -34,7 +34,7 @@ 

pw.x < al_nscf.in > al_nscf.out

-

Density of states​

+

Density of states​

Next we go ahead with our density of states calculation:

src/al/al_dos.in
&DOS
  prefix= 'al',
  outdir= '/tmp/',
  fildos= 'al_dos.dat',
  emin= -10,
  emax= 35
/
@@ -43,7 +43,7 @@

Dens

Note from our al_nscf.out that our Fermi energy is at 7.9421 eV. We plot our density of states:

al-dos -

Bandstructure calculation​

+

Bandstructure calculation​

We prepare the input file the same as the case of our previous example silicon:

src/al/al_bands.in
&CONTROL
  calculation= 'bands',
  restart_mode= 'from_scratch',
  prefix= 'al',
  outdir= '/tmp/',
  pseudo_dir= '../pseudos/'
/

&SYSTEM
  ibrav= 2,
  celldm(1) = 7.63075,
  nat= 1,
  ntyp= 1,
  ecutwfc= 50,
  ecutrho= 500,
  occupations= 'smearing',
  smearing= 'gaussian',
  degauss= 0.01
/

&ELECTRONS
  conv_thr= 1e-8
/

ATOMIC_SPECIES
  Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF

ATOMIC_POSITIONS (alat)
  Al 0.00 0.00 0.00

K_POINTS {crystal_b}
5
  00.000 0.500 00.000 20  !L
  00.000 0.000 00.000 30  !G
  -0.500 0.000 -0.500 10  !X
  -0.375 0.250 -0.375 30  !U
  00.000 0.000 00.000 20  !G
@@ -56,7 +56,7 @@ 

bands.x < al_bands_pp.in > al_bands_pp.out

We obtain the following bandstructure:

al-bands -

Importance of smearing in convergence​

+

Importance of smearing in convergence​

Smearing is a technique used for suppressing unstable electron density in the calculation of metals. Such a problem occurs in metals (and semimetals) because the valence bands that cross Fermi level are partially occupied. Due to @@ -74,6 +74,6 @@

Edit this page

Copyright © 2024 Pranab Das. All rights reserved.
+Monkhorst-Plank grid.

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/bands/index.html b/hands-on/bands/index.html index 54cf2d69..d5b1f2c8 100644 --- a/hands-on/bands/index.html +++ b/hands-on/bands/index.html @@ -2,13 +2,13 @@ - -Bandstructure Calculation • Quantum Espresso Tutorial - - + +Bandstructure Calculation • Quantum Espresso Tutorial + + -

Bandstructure Calculation

Before we can run bands calculation, we need to perform single-point self +

Bandstructure Calculation

Before we can run bands calculation, we need to perform single-point self consistent field calculation. We have our input scf file with some new parameters:

@@ -52,7 +52,7 @@ which we need to label in our band diagram, can be found in the post-processing output file (si_bands_pp.out).

Bandgap value can be determined from the highest occupied, lowest unoccupied level values printed in scf calculation output.

-

Note on bandgap​

+

Note on bandgap​

Usually, band gaps computed using common exchange-correction functionals such as LDA or GGA are severely underestimated compared to actual experimental values. This discrepancy is mainly due to (1) approximations used in the exchange @@ -61,33 +61,33 @@

Note o the system. The second contribution is larger contributor to the error. It can be partly addressed by a variety of techniques such as the GW approximation.

Strategies to improve band gap prediction at moderate to low computational cost -now been developed by several groups, including Chan and Ceder (delta-sol)1, -Heyd et al. (hybrid functionals)2, and Setyawan et al. (empirical fits)3.

-

Resources​

+now been developed by several groups, including Chan and Ceder (delta-sol)1, +Heyd et al. (hybrid functionals)2, and Setyawan et al. (empirical fits)3.

+

Resources​

-

Footnotes​

+

Footnotes​

  1. M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical -Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩

    +Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩

  2. J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of Chemical Physics 123 (2005) -https://doi.org/10.1063/1.2085170 ↩

    +https://doi.org/10.1063/1.2085170 ↩

  3. W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, High-throughput combinatorial database of electronic band structures for inorganic scintillator materials., ACS Combinatorial Science. (2011) -https://doi.org/10.1021/co200012w. ↩

    +https://doi.org/10.1021/co200012w. ↩

-
Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/convergence/index.html b/hands-on/convergence/index.html index a8098e49..54aeeb60 100644 --- a/hands-on/convergence/index.html +++ b/hands-on/convergence/index.html @@ -2,13 +2,13 @@ - -Convergence testing • Quantum Espresso Tutorial - - + +Convergence testing • Quantum Espresso Tutorial + + -

Convergence testing

Convergence with cutoff energy using PWTK​

+

Convergence testing

Convergence with cutoff energy using PWTK​

We can automate the previous self consistent calculation by varying a certain parameter. Say we want to check the total energy of the system for various values of ecutwfc. We can do that by using pwtk script.

@@ -21,7 +21,7 @@

We will use matplotlib to make the plots. Here is the python code for plotting:

notebooks/silicon-scf.ipynb
import matplotlib.pyplot as plt
from matplotlib import rcParamsDefault
import numpy as np
%matplotlib inline
plt.rcParams["figure.dpi"]=150
plt.rcParams["figure.facecolor"]="white"

x, y = np.loadtxt('../src/silicon/etot-vs-ecutwfc.dat', delimiter=' ', unpack=True)
plt.plot(x, y, "o-", markersize=5, label='Etot vs ecutwfc')
plt.xlabel('ecutwfc (Ry)')
plt.ylabel('Etot (Ry)')
plt.legend(frameon=False)
plt.show()
etot-vs-ecutwfc -

Convergence test using UNIX shell script​

+

Convergence test using UNIX shell script​

We can do the convergence test with various parameters. We can calculate the total energy of the system by varying various parameters. We will use the shell script to automate the process with different cutoff energy values.

@@ -37,7 +37,7 @@

Convergence test against the number of k-points​

+

Convergence test against the number of k-points​

We can run similar convergence test against another parameter, and choose the best value of that particular parameter. Here we will try to calculate the number of k-points in the Monkhorst-Pack mesh.

@@ -47,7 +47,7 @@ 

pwtk si_scf_kpoints.pwtk

notebooks/silicon-scf.ipynb
x, y = np.loadtxt('../src/silicon/etot-vs-kpoint.dat', delimiter=' ', unpack=True)
plt.plot(x, y, "o-", markersize=5, label='Etot vs kpoints')
plt.xlabel('# kpoints')
plt.ylabel('Etot (Ry)')
plt.legend(frameon=False)
plt.show()
etot-vs-kpoints -

Convergence against lattice constant​

+

Convergence against lattice constant​

Calculating total energy with respect to varying lattice constant.

src/silicon/si_scf_alat.pwtk
load_fromPWI pw.scf.silicon.in

# please uncomment & insert value as determined in the "ecutwfc" exercise
SYSTEM { ecutwfc = 30 }

# please uncomment & insert values as determined in the "kpoints" exercise
K_POINTS automatic { 6 6 6 1 1 1 }


set fid [open etot-vs-alat.dat w]

foreach alat { 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 } {

    set name si_scf_alat-$alat

    SYSTEM "celldm(1) = $alat"
    runPW $name.in

    set Etot [::pwtk::pwo::totene $name.out]
    puts $fid "$alat $Etot"
}

close $fid
@@ -55,7 +55,7 @@ 

pwtk si_scf_alat.pwtk

notebooks/silicon-scf.ipynb
x, y = np.loadtxt('../src/silicon/etot-vs-alat.dat', delimiter=' ', unpack=True)
plt.plot(x, y, "o-", markersize=5, label='Etot vs alat')
plt.xlabel('alat (Bohr)')
plt.ylabel('Etot (Ry)')
plt.legend(frameon=False)
plt.show()
etot-vs-alat -

Note on CPU time​

+

Note on CPU time​

  • CPU time is proportional to the number of plane waves used for the @@ -68,6 +68,6 @@

    Note

    CPU time increases as N3, where N is the number of atoms in the system.

    • -
Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/dft-u/index.html b/hands-on/dft-u/index.html index 9b3d3fe9..8b3a4ed4 100644 --- a/hands-on/dft-u/index.html +++ b/hands-on/dft-u/index.html @@ -2,13 +2,13 @@ - -DFT+U calculation • Quantum Espresso Tutorial - - + +DFT+U calculation • Quantum Espresso Tutorial + + -

DFT+U calculation

Electronic structure for transition metals (with localized dd or ff +

DFT+U calculation

Electronic structure for transition metals (with localized dd or ff electrons) is not accurately described by standard DFT, and therefore the need for DFT+U formulation.

&SYSTEM
    ...
    lda_plus_u = .TRUE.
    Hubbard_u(i) = 2.0
    ...
/
@@ -22,14 +22,14 @@ 
    ...
    lda_plus_u = .TRUE.
    lda_plus_u_kind = 1
    Hubbard_u(i) = U
    Hubbard_J(k, i) = J_{ki}
    ...
COMMON ERRORS

If you add Hubbard_u for elements that is not implemented to have UU term in QE, you might see a "pseudopotential not yet inserted" error.

-

Changes to input syntax in v7.1​

+

Changes to input syntax in v7.1​

Starting from Quantum Espresso version 7.1, there are changes to input syntax for DFT+U calculations. In the new version, instead of defining the necessary DFT+U parameters, now there is a new Hubbard card.

&system
...
-  lda_plus_u = .true.,
-  lda_plus_u_kind = 0,
-  U_projection_type = 'atomic',
-  Hubbard_U(1) = 4.6
-  Hubbard_U(2) = 4.6
...
/

+ HUBBARD (ortho-atomic)
+ U Fe1-3d 4.6
+ U Fe2-3d 4.6

Please refer to the qe-x.x/Doc/Hubbard_input.pdf for details.

-

DFT calculation for FeO​

+

DFT calculation for FeO​

We will first perform the standard DFT calculation.

  1. Perform the SCF calculation:
    2. @@ -45,7 +45,7 @@ 

    projwfc.x -in feo_projwfc.in > feo_projwfc.out

feo-pdos-dft

This gives us metallic density of states. In practice we get insulating FeO.

-

Calculating Hubbard U​

+

Calculating Hubbard U​

src/FeO/feo_hp.in
&inputhp
   prefix = 'FeO'
   outdir = './tmp/'
   nq1 = 1, nq2 = 1, nq3 = 1
/

Perform a linear-response calculation using hp.x program:

@@ -78,7 +78,7 @@

danger

The above hp.x code is not suitable for closed cell systems (e.g., fully occupied d-shell element), in such cases this linear response method gives unrealistically large UU value.

-

DFT+U calculation​

+

DFT+U calculation​

We repeat the calculation after setting in the &SYSTEM card:

Hubbard_U(1) = 4.6
Hubbard_U(2) = 4.6

We repeat the above calculation and plot the results. Now we find insulating @@ -93,10 +93,10 @@

DFT+U the contribution of dz2,dyz,dx2−z2d_{z^2}, d_{yz}, d_{x^2-z^2} ect., we can find them from the pdos columns. Also there arise important Lowdin charges information in the feo_projwfc.out file.

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/dos/index.html b/hands-on/dos/index.html index 3822953d..b7ca6a87 100644 --- a/hands-on/dos/index.html +++ b/hands-on/dos/index.html @@ -2,13 +2,13 @@ - -Density of States calculation • Quantum Espresso Tutorial - - + +Density of States calculation • Quantum Espresso Tutorial + + -

Density of States calculation

Electronic density of states is an important property of a material.

+

Density of States calculation

Electronic density of states is an important property of a material.

ρ(E)dE\rho(E)dE = number of electronic states in the energy interval (E,E+dE)(E, E + dE)

Before we can run the Density of States (DOS) calculation, we need

    diff --git a/hands-on/epsilon/index.html b/hands-on/epsilon/index.html index da76dbec..649accb7 100644 --- a/hands-on/epsilon/index.html +++ b/hands-on/epsilon/index.html @@ -2,13 +2,13 @@ - -Dielectric constant • Quantum Espresso Tutorial - - + +Dielectric constant • Quantum Espresso Tutorial + + -

    Dielectric constant

    First we perform self consistent field calculation:

    +

    Dielectric constant

    First we perform self consistent field calculation:

    mpirun -np 4 pw.x -i pw.scf.silicon_epsilon.in > pw.scf.silicon_epsilon.out
    src/silicon/pw.scf.silicon_epsilon.in
    &CONTROL
      calculation = 'scf',
      prefix = 'silicon',
      outdir = '/tmp/'
      pseudo_dir = '../pseudos/'
      verbosity = 'high'
    /

    &SYSTEM
      ibrav =  2,
      celldm(1) = 10.26,
      nat =  2,
      ntyp = 1,
      ecutwfc = 40
      nbnd = 20
      nosym = .TRUE.
      noinv = .TRUE.
    /

    &ELECTRONS
      mixing_beta = 0.6
    /

    ATOMIC_SPECIES
      Si 28.086 Si.pz-vbc.UPF

    ATOMIC_POSITIONS (alat)
      Si 0.0 0.0 0.0
      Si 0.25 0.25 0.25

    K_POINTS crystal
    216
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      0.83333333  0.66666667  0.83333333  4.629630e-03
      0.83333333  0.83333333  0.00000000  4.629630e-03
      0.83333333  0.83333333  0.16666667  4.629630e-03
      0.83333333  0.83333333  0.33333333  4.629630e-03
      0.83333333  0.83333333  0.50000000  4.629630e-03
      0.83333333  0.83333333  0.66666667  4.629630e-03
      0.83333333  0.83333333  0.83333333  4.629630e-03
    @@ -44,11 +44,11 @@ 40000 in Quantum Espresso, if we need more k-points, we can change Modules/parameters.f90 and recompile Quantum Espresso.

    -

    Resources​

    +

    Resources​

    Copyright © 2024 Pranab Das. All rights reserved.
    +
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/fe/index.html b/hands-on/fe/index.html index 408352fb..7ffb22c5 100644 --- a/hands-on/fe/index.html +++ b/hands-on/fe/index.html @@ -2,13 +2,13 @@ - -Magnetic system: bulk iron • Quantum Espresso Tutorial - - + +Magnetic system: bulk iron • Quantum Espresso Tutorial + + -

Magnetic system: bulk iron

I am following this example from the ICTP online school 2021.

+

Magnetic system: bulk iron

I am following this example from the ICTP online school 2021.

We will perform the SCF KS orbital calculations on magnetic (nspin=2) iron. Since the d-orbitals of Fe atom are localized/ hard, we will use ultra-soft pseudo potential (USPP).

@@ -34,14 +34,14 @@ ecutrho 4 times of ecutoff is not sufficient. We need to set ecutrho 8 or even 12 times that of ecutoff. We must test the convergence for our set values.

-

Convergence test for USPP​

+

Convergence test for USPP​

Below is the PWTK script file:

src/fe/fe_ecut.pwtk
# load the pw.x input from file
load_fromPWI fe_scf_fm.in

# dual is the ratio ecutrho/ecutwfc
foreach dual { 4 8 12 } {

    set fid [open etot-vs-ecutwfc.dual$dual.dat w]

    foreach ecutwfc [seq 25 5 50] {

        set name pw.Fe.scf.ecutwfc-$ecutwfc.dual-$dual

        SYSTEM "ecutwfc = $ecutwfc
                ecutrho = $ecutwfc*$dual "
        runPW $name.in

        set Etot [pwo_totene $name.out]
        puts $fid "$ecutwfc $Etot"
    }

    close $fid
}

Run the script:

pwtk fe_ecut.pwtk
fe-convergence -

Density of states calculation​

+

Density of states calculation​

PWTK script to calculate DOS and p-DOS:

src/fe/fe_dos.pwtk
load_fromPWI fe_scf_fm.in

SYSTEM " ecutwfc = 40
         ecutrho = 320 "

set name Fe

runPW pw.$name.scf.in

CONTROL { calculation = 'nscf' }
SYSTEM  { occupations = 'tetrahedra' ,
          degauss = ,  ! this is how variable is unset in PWTK
}
K_POINTS automatic {
    12 12 12   1 1 1
}
runPW pw.$name.nscf.in

DOS "
    fildos = '$name.dos.dat'
    Emin = 5.0
    Emax = 20.0,
    DeltaE = 0.1
"
runDOS dos.$name.in

PROJWFC "
    filpdos = '$name.pdos.dat'
    Emin = 5.0
    Emax = 20.0,
    DeltaE = 0.1
"
runPROJWFC projwfc.$name.in
@@ -49,14 +49,14 @@

fe-dos fe-pdos

Also see bandstructure of Fe with and without SOC.

-

Paramagnetism​

+

Paramagnetism​

Paramagnetic materials have fluctuating magnetic moments that may not be properly described DFT. One approach is to model paramagnetic materials in DFT calculation by building a large supercell and assign randomly oriented magnetic moments.

Also note that DFT assumes zero temperature, so it makes sense to perform FM or AFM calculation for magnetic systems.

-

Visualizing magnetic moments​

+

Visualizing magnetic moments​

We can use XCrySDen to visualize the orientation of magnetic moments. XCrySDen cannot directly read the Quantum Espresso output files for magnetic moment vectors, instead we need to create the input .xsf @@ -68,6 +68,6 @@

fe-magnetic-structure

Copyright © 2024 Pranab Das. All rights reserved.
+fe-magnetic-structure
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/fermi-surface/index.html b/hands-on/fermi-surface/index.html index 01747144..078fb11e 100644 --- a/hands-on/fermi-surface/index.html +++ b/hands-on/fermi-surface/index.html @@ -2,13 +2,13 @@ - -Fermi Surface • Quantum Espresso Tutorial - - + +Fermi Surface • Quantum Espresso Tutorial + + -

Fermi Surface

Here we will calculate Fermi surface of copper. First step is to perform self- +

Fermi Surface

Here we will calculate Fermi surface of copper. First step is to perform self- consistent field calculation.

src/cu/pw.scf.cu.in
&control
  calculation = "scf",
  prefix = "cu",
  pseudo_dir = "../pseudos/",
  outdir = "/tmp/cu/"
/

&system
  ibrav = 2,
  celldm(1) = 6.678,
  nat = 1,
  ntyp = 1,
  ecutwfc = 40,
  ecutrho = 300,
  occupations = "smearing",
  smearing = "mp",
  degauss = 0.01,
  nbnd = 16
/

&electrons
  conv_thr = 1e-9,
/

ATOMIC_SPECIES
Cu 63.546 Cu_ONCV_PBE-1.0.oncvpsp.upf

ATOMIC_POSITIONS alat
Cu 0.00 0.00 0.00

K_POINTS automatic
8 8 8 1 1 1
diff --git a/hands-on/graphene/index.html b/hands-on/graphene/index.html index 7ef3ca7b..456715bb 100644 --- a/hands-on/graphene/index.html +++ b/hands-on/graphene/index.html @@ -2,29 +2,29 @@ - -DOS and Bandstructure of Graphene • Quantum Espresso Tutorial - - + +DOS and Bandstructure of Graphene • Quantum Espresso Tutorial + + -

DOS and Bandstructure of Graphene

I am following this example from the ICTP online school 2021.

+

DOS and Bandstructure of Graphene

I am following this example from the ICTP online school 2021.

Graphene is single layer of carbon atoms. First perform the self consistent field calculation to obtain the Kohn-Sham orbitals. Please check the input files in GitHub repository. Run pw.x:

pw.x -i graphene_scf.in > graphene_scf.out

Next increase the k-grid, and perform the non-self-consistent field calculation.

pw.x -i graphene_nscf.in > graphene_nscf.out
-

DOS calculation​

+

DOS calculation​

dos.x -i graphene_dos.in > graphene_dos.out
graphene-dos -

Bandstructure calculation​

+

Bandstructure calculation​

First run the bands calculation for given k-path:

pw.x -i graphene_bands.in > graphene_bands.out

Followed by the postprocessing to collect the bands:

bands.x -i graphene_bands_pp.in > graphene_bands_pp.out

Make plots:

notebooks/graphene.ipynb
import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt('../src/graphene/graphene_bands.dat.gnu')

k = np.unique(data[:, 0])
bands = np.reshape(data[:, 1], (-1, len(k)))

for band in range(len(bands)):
    plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k')
plt.xlim(min(k), max(k))

# Fermi energy
plt.axhline(0.921, linestyle=(0, (8, 10)), linewidth=0.75, color='k', alpha=0.5)
# High symmetry k-points (check bands_pp.out)
plt.axvline(0.6667, linewidth=0.75, color='k', alpha=0.5)
plt.axvline(1, linewidth=0.75, color='k', alpha=0.5)
# text labels
plt.xticks(ticks= [0, 0.6667, 1, 1.5774], labels=['$\Gamma$', 'K', 'M', '$\Gamma$'])
plt.ylabel("Energy (eV)")
plt.show()
-graphene-bands
Copyright © 2024 Pranab Das. All rights reserved.
+graphene-bands
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/kpdos/index.html b/hands-on/kpdos/index.html index 4f45b521..3ecf66bb 100644 --- a/hands-on/kpdos/index.html +++ b/hands-on/kpdos/index.html @@ -2,13 +2,13 @@ - -k-resolved DOS • Quantum Espresso Tutorial - - + +k-resolved DOS • Quantum Espresso Tutorial + + -

k-resolved DOS

Here we will calculate k-resolved density of states for silicon. First we begin +

k-resolved DOS

Here we will calculate k-resolved density of states for silicon. First we begin with self consistent field calculation. Here is the input:

pw.x -inp si_scf.in > si_scf.out

Followed by the bands calculation. Note that for bands calculation I have diff --git a/hands-on/molecular-dynamics-pw/index.html b/hands-on/molecular-dynamics-pw/index.html index 4d591af3..21563f94 100644 --- a/hands-on/molecular-dynamics-pw/index.html +++ b/hands-on/molecular-dynamics-pw/index.html @@ -2,13 +2,13 @@ - -Molecular Dynamics (using pw.x) • Quantum Espresso Tutorial - - + +Molecular Dynamics (using pw.x) • Quantum Espresso Tutorial + + -

Molecular Dynamics (using pw.x)

We will start from the relaxation calculation, and use the relaxed structure for +

Molecular Dynamics (using pw.x)

We will start from the relaxation calculation, and use the relaxed structure for md calculation. Below in the input file for md calculation:

src/H2O-md-pw/pw.md.h2o.in
&control
    calculation  = 'md'
    restart_mode = 'from_scratch'
    prefix       = 'h2o'
    outdir       = './tmp/'
    pseudo_dir   = '../pseudos/'
    tstress      = .true.
    tprnfor      = .true.
!   about 1 fs; 1 a.u. = 0.048378 fs
    dt           = 20
    nstep        = 100
/

&system
    ibrav     = 1
    celldm(1) = 15
    nat       = 3
    ntyp      = 2,
    ecutwfc   = 40
    nosym     = .true.
/

&electrons
    conv_thr = 1e-8
/

&ions
    pot_extrapolation = 'second-order'
    wfc_extrapolation = 'second-order'
    ion_temperature   = 'initial'
    tempw             = 300
/

ATOMIC_SPECIES
 H  1.00784  H_ONCV_PBE-1.0.oncvpsp.upf
 O  15.999   O.pbe-n-kjpaw_psl.0.1.UPF

! relaxed structure
ATOMIC_POSITIONS (angstrom)
O             5.0000068025        4.8011777008        4.9999667189
H             4.9999962341        5.3994076541        5.7670041300
H             4.9999969634        5.3994146451        4.2330291511

K_POINTS automatic
  1 1 1 0 0 0
diff --git a/hands-on/ni/index.html b/hands-on/ni/index.html index fa4d7ebe..5b05a8f8 100644 --- a/hands-on/ni/index.html +++ b/hands-on/ni/index.html @@ -2,13 +2,13 @@ - -Spin polarized bandstructure calculation for nickel • Quantum Espresso Tutorial - - + +Spin polarized bandstructure calculation for nickel • Quantum Espresso Tutorial + + -

Spin polarized bandstructure calculation for nickel

We prepare the input file pw_scf_ni.in and run the calculation:

+

Spin polarized bandstructure calculation for nickel

We prepare the input file pw_scf_ni.in and run the calculation:

mpirun -np 8 pw.x -i pw_scf_ni.in > pw_scf_ni.out

Prepare the input file for bands calculation pw_bands_ni.in with our desired k-path and run:

diff --git a/hands-on/pdos/index.html b/hands-on/pdos/index.html index 81f93556..af59ae00 100644 --- a/hands-on/pdos/index.html +++ b/hands-on/pdos/index.html @@ -2,13 +2,13 @@ - -Projected Density of States • Quantum Espresso Tutorial - - + +Projected Density of States • Quantum Espresso Tutorial + + -

Projected Density of States

Here we continue with our Aluminum example. +

Projected Density of States

Here we continue with our Aluminum example. Often it is needed to know the contribution from each individual atoms and/or each of their orbital contributions. We can achieve that using projwfc.x code. First, we must perform the self consistent field calculation followed by diff --git a/hands-on/phonon/index.html b/hands-on/phonon/index.html index a3c48099..34bcd222 100644 --- a/hands-on/phonon/index.html +++ b/hands-on/phonon/index.html @@ -2,13 +2,13 @@ - -Phonon dispersion • Quantum Espresso Tutorial - - + +Phonon dispersion • Quantum Espresso Tutorial + + -

Phonon dispersion

In Quantum Espresso, phonon dispersion is calculated using ph.x program, which +

Phonon dispersion

In Quantum Espresso, phonon dispersion is calculated using ph.x program, which is implementation of density functional perturbation theory (DFPT).

Here are the steps for calculating phonon dispersion:

(1) perform SCF calculation using pw.x

@@ -45,24 +45,24 @@

(4) Finally, perform Fourier transformation of the real space components to get the dynamical matrix at any q by using matdyn.x.

-
src/GaAs-phonon/matdyn.GaAs.in
&INPUT
  asr = 'crystal'
  flfrc = 'GaAs.fc'
  flfrq = 'GaAs.freq'
  flvec = 'GaAs.modes'
!  loto_2d = .true.
  q_in_band_form = .true.
/
5
0.500 0.500 0.500   20 ! L
0.000 0.000 0.000   20 ! G
0.500 0.000 0.500   20 ! X
0.375 0.375 0.750   20 ! K
0.000 0.000 0.000    1 ! G
+
src/GaAs-phonon/matdyn.GaAs.in
&INPUT
  asr = 'crystal'
  flfrc = 'GaAs.fc'
  flfrq = 'GaAs.freq'
  flvec = 'GaAs.modes'
!  loto_2d = .true.
  q_in_band_form = .true.
  q_in_cryst_coord = .true.
/
5
0.500 0.500 0.500   20 ! L
0.000 0.000 0.000   20 ! G
0.500 0.000 0.500   20 ! X
0.375 0.375 0.750   20 ! K
0.000 0.000 0.000    1 ! G
mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out

We can now plot the phonon dispersion of GaAs:

notebooks/GaAs-phonon.ipynb
import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt("../src/GaAs-phonon/GaAs.freq.gp")

nbands = data.shape[1] - 1
for band in range(nbands):
    plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k')
# High symmetry k-points (check matdyn.GaAs.in)
plt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5)
plt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \
           labels=['L', '$\Gamma$', 'X', 'U,K', '$\Gamma$'])
plt.ylabel("Frequency (cm$^{-1}$)")
plt.xlim(data[0, 0], data[-1, 0])
plt.ylim(0, )
plt.show()
-GaAs-phonon +GaAs-phonon
tip

We may need to lower the value of conv_thr in scf calculation for more accurate result.

-

Phonon Density of States​

+

Phonon Density of States​

Input file for phonon DOS calculation:

src/GaAs-phonon/matdyn.dos.GaAs.in
&INPUT
  asr   = 'crystal'
  flfrc = 'GaAs.fc'
  flfrq = 'GaAs.dos.freq'
  flvec = 'GaAs.dos.modes'
  dos   = .true.
  fldos = 'GaAs.dos'
  nk1   = 25
  nk2   = 25
  nk3   = 25
/

Plot phonon DOS:

notebooks/GaAs-phonon.ipynb
freq, dos, pdos_Ga, pdos_As = np.loadtxt("../src/GaAs-phonon/GaAs.dos", unpack=True)

plt.plot(freq, dos, c='k', lw=0.5, label='Total')
plt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga')
plt.plot(freq, pdos_As, c='r', lw=0.5, label='As')
plt.xlabel('$\\Omega~(cm^{-1}$)')
plt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)')
plt.legend(frameon=False, loc='upper left')
plt.xlim(freq[0], freq[-1])
plt.show()
GaAs-phonon-dos -

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/scf/index.html b/hands-on/scf/index.html index 120434e0..ab532771 100644 --- a/hands-on/scf/index.html +++ b/hands-on/scf/index.html @@ -2,13 +2,13 @@ - -Self consistent field calculation for silicon • Quantum Espresso Tutorial - - + +Self consistent field calculation for silicon • Quantum Espresso Tutorial + + -

Self consistent field calculation for silicon

We need to provide various important parameters for the self consistent +

Self consistent field calculation for silicon

We need to provide various important parameters for the self consistent calculation (solves the Kohn-Sham equation self-consistently) via an input file. In QE input files, there are NAMELISTS and INPUT_CARDS. NAMELISTS variables have default values, and new values can be provided as required for a @@ -99,10 +99,10 @@ 

number of electrons       =         8.00
number of Kohn-Sham states=            8

In our calculation we have specified the number of bands = 8. Otherwise, there would be 4 bands for 8 electrons in case of non spin-polarized systems.

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/soc/index.html b/hands-on/soc/index.html index 13a953cd..272b7b44 100644 --- a/hands-on/soc/index.html +++ b/hands-on/soc/index.html @@ -2,17 +2,17 @@ - -Spin-Orbit Coupling • Quantum Espresso Tutorial - - + +Spin-Orbit Coupling • Quantum Espresso Tutorial + + -

Spin-Orbit Coupling

In order to consider spin orbit coupling effect in our electronic structure +

Spin-Orbit Coupling

In order to consider spin orbit coupling effect in our electronic structure calculation in quantum espresso, we need to use a full relativistic pseudo potential. Following settings are needed in the &SYSTEM card:

&SYSTEM
    ...
    noncolin = .true.
    lspinorb = .true.
    ...
/
-

Non collinear spin​

+

Non collinear spin​

In simple spin polarized calculation (nspin=2), the spin quantum number (up or down) is considered in the calculation. In non-collinear case, the spin has more degrees of freedom, and can be oriented in any direction. Non-collinear @@ -30,7 +30,7 @@

Non penalty function (λ\lambda).

&SYSTEM
  ...
  angle1(i) = 0.0d0
  angle2(i) = 0.0d0
  lambda = 0.5
  ...
/

i is the index of the atom in ATOMIC_SPECIES card.

-

Strategy for convergence​

+

Strategy for convergence​

Spin-orbit coupling calculations are often hard to converge. Use a smaller mixing_beta for such calculations. First perform a collinear calculation with non-relativistic pseudopotential, and then start from the obtained charge @@ -56,7 +56,7 @@

Bandstructure of Fe with SOC​

+

Bandstructure of Fe with SOC​

src/fe/pw.scf.fe_soc.in
&control
   calculation='scf'
   pseudo_dir = '../pseudos/',
   outdir='./tmp/'
   prefix='fe'
/

&system
   ibrav = 3,
   celldm(1) = 5.39,
   nat= 1,
   ntyp= 1,
   noncolin=.true.,
   lspinorb=.true.,
   starting_magnetization(1)=0.3,
   ecutwfc = 70,
   ecutrho = 850.0,
   occupations='smearing',
   smearing='marzari-vanderbilt',
   degauss=0.02
/

&electrons
   diagonalization='david'
   conv_thr = 1.0e-8
   mixing_beta = 0.7
/

ATOMIC_SPECIES
Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF

ATOMIC_POSITIONS alat
Fe 0.0 0.0 0.0

K_POINTS AUTOMATIC
14 14 14 1 1 1

Run the scf calculation:

@@ -75,9 +75,9 @@ 

mpirun -np 8 bands.x -i pp.bands.fe_soc.in > pp.bands.fe_soc.out

fe-soc-bands -

SOC calculation for GaAs​

+

SOC calculation for GaAs​

Please check the respective input files.

mpirun -np 8 pw.x -i pw.scf.GaAs_soc.in > pw.scf.GaAs_soc.out
mpirun -np 8 pw.x -i pw.bands.GaAs_soc.in > pw.bands.GaAs_soc.out
mpirun -np 8 bands.x -i pp.bands.GaAs_soc.in > pp.bands.GaAs_soc.out
-GaAs-soc-bands
Copyright © 2024 Pranab Das. All rights reserved.
+GaAs-soc-bands
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/hands-on/structure-optimization/index.html b/hands-on/structure-optimization/index.html index 53b21dfd..ff97b0c0 100644 --- a/hands-on/structure-optimization/index.html +++ b/hands-on/structure-optimization/index.html @@ -2,13 +2,13 @@ - -Structure optimization • Quantum Espresso Tutorial - - + +Structure optimization • Quantum Espresso Tutorial + + -

Structure optimization

There are two types of structural optimization calculations in Quantum espresso: +

Structure optimization

There are two types of structural optimization calculations in Quantum espresso: (1) relax: where only the atomic positions are allowed to vary, and (2) vc-relax: which allows to vary both the atomic positions and lattice constants.

diff --git a/hands-on/wannier/index.html b/hands-on/wannier/index.html index 20e61b4d..7c778681 100644 --- a/hands-on/wannier/index.html +++ b/hands-on/wannier/index.html @@ -2,13 +2,13 @@ - -Wannier method • Quantum Espresso Tutorial - - + +Wannier method • Quantum Espresso Tutorial + + -

Wannier method

Obtain bandstructure of Silicon​

+
Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/img/GaAs-phonon.png b/img/GaAs-phonon.png index e398d175..413da127 100644 Binary files a/img/GaAs-phonon.png and b/img/GaAs-phonon.png differ diff --git a/img/GaAs-phonon.webp b/img/GaAs-phonon.webp index 5d5b544f..50ef91fb 100644 Binary files a/img/GaAs-phonon.webp and b/img/GaAs-phonon.webp differ diff --git a/index.html b/index.html index 906a68fb..ae22040a 100644 --- a/index.html +++ b/index.html @@ -2,13 +2,13 @@ - -Density Functional Theory using Quantum Espresso • Quantum Espresso Tutorial - - + +Density Functional Theory using Quantum Espresso • Quantum Espresso Tutorial + + -

Density Functional Theory using Quantum Espresso

This tutorial is result of my personal notes while trying (which I still do) to +

Density Functional Theory using Quantum Espresso

This tutorial is result of my personal notes while trying (which I still do) to learn Density Functional Theory calculations myself. I am no expert in this subject. I am sharing this notes here, just in case it helps you getting started. I will cite numerous other resources that I am following. Hope you will @@ -20,7 +20,7 @@ 

git clone https://github.com/pranabdas/espresso.git

Or, if you do not have git installed, download zipped copy of the repository here.

-

Filename conventions​

+

Filename conventions​

Lately, I decided to follow specific pattern for the filenames, but you can choose whatever works best for you. Note that all example files in this tutorial does not follow this convention yet.

@@ -28,7 +28,7 @@

F

Example: pw.bands.silicon.in → input file for the bands calculation using PWscf program for silicon.

For PWTK scripts, we will use .pwtk extension (e.g., silicon_vc_relax.pwtk).

-

Unit conversions​

+

Unit conversions​

  • 1 Bohr = 0.529177249 Å
  • 1 Rydberg (Ry) = 13.6056981 eV.
    • @@ -36,6 +36,6 @@

    Unit

    Angstrom to Bohr converter: lattice constants are often provided in angstrom, you can use following utility to convert to Bohr.

    -

     Å = 1.8897259886 Bohr. 

Copyright © 2024 Pranab Das. All rights reserved.
+

 Å = 1.8897259886 Bohr. 

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/license/index.html b/license/index.html index 5107a244..5bc32f4b 100644 --- a/license/index.html +++ b/license/index.html @@ -2,13 +2,13 @@ - -License • Quantum Espresso Tutorial - - + +License • Quantum Espresso Tutorial + + -

License

CC-BY

+

License

CC-BY

This work is licensed under a Creative Commons Attribution 4.0 International License. Any third party materials in this work are not included in the article’s Creative Commons license, and users will need to obtain permission diff --git a/resources/index.html b/resources/index.html index 7496f5e8..b37ac6f3 100644 --- a/resources/index.html +++ b/resources/index.html @@ -2,13 +2,13 @@ - -Resources • Quantum Espresso Tutorial - - + +Resources • Quantum Espresso Tutorial + + -

Resources

Copyright © 2024 Pranab Das. All rights reserved.
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tutorial is result of my personal notes while trying (which I still do) to learn Density Functional Theory calculations myself. I am no expert in this subject. I am sharing this notes here, just in case it helps you getting started. I will cite numerous other resources that I am following. Hope you will find this tutorial helpful. The quantum espresso input files, jupyter notebooks (containing python code for visualizations), and other source files related to this tutorial can be found on GitHub: pranabdas/espresso. You may clone the repository to your local machine: git clone https://github.com/pranabdas/espresso.git Or, if you do not have git installed, download zipped copy of the repository here.","s":"Density Functional Theory using Quantum Espresso","u":"/espresso/","h":"","p":1},{"i":4,"t":"Lately, I decided to follow specific pattern for the filenames, but you can choose whatever works best for you. Note that all example files in this tutorial does not follow this convention yet. {program}.{calculation}.{system}.{in, out} {program}.{calculation}.{system_description}.{in, out} {pw, pp, ...}.{scf, bands, ...}.{silicon, al_slab}.{in, out} Example: pw.bands.silicon.in → input file for the bands calculation using PWscf program for silicon. For PWTK scripts, we will use .pwtk extension (e.g., silicon_vc_relax.pwtk).","s":"Filename conventions","u":"/espresso/","h":"#filename-conventions","p":1},{"i":6,"t":"1 Bohr = 0.529177249 Å 1 Rydberg (Ry) = 13.6056981 eV. Angstrom to Bohr converter: lattice constants are often provided in angstrom, you can use following utility to convert to Bohr. Å = 1.8897259886 Bohr. Copy","s":"Unit conversions","u":"/espresso/","h":"#unit-conversions","p":1},{"i":9,"t":"First we are going to relax the cell and choose appropriate lattice constant for our chosen pseudo potential. In case of metals, it is important to provide smearing parameters in the input file. src/al/al_vc_relax.in &CONTROL calculation= 'vc-relax', prefix= 'al', outdir= '/tmp/' pseudo_dir = '../pseudos/' etot_conv_thr= 1e-6, forc_conv_thr= 1e-5 / &SYSTEM ibrav= 2, celldm(1)= 7.652, nat= 1, ntyp= 1, ecutwfc = 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / &IONS / &CELL cell_dofree= 'ibrav' / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 10 10 10 0 0 0 We run pw.x to perform variable cell relaxation calculation: pw.x < al_vc_relax.in > al_vc_relax.out Now you may open the output file in vi editor and invoke search by pressing / and type Final enthalpy You will find the final lattice parameters below it.","s":"Variable cell relaxation","u":"/espresso/hands-on/aluminum","h":"#variable-cell-relaxation","p":7},{"i":11,"t":"We obtain relaxed lattice constant = 7.652 * 0.498611683 / 0.5 = 7.63075 Bohr. We will use this value for our next step, self consistent calculation. src/al/al_scf.in &CONTROL calculation= 'scf', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 10 10 10 0 0 0 We run our self consistent calculation: pw.x < al_scf.in > al_scf.out","s":"Self consistent field (SCF) calculation","u":"/espresso/hands-on/aluminum","h":"#self-consistent-field-scf-calculation","p":7},{"i":13,"t":"Inspect the output file, and let's proceed to next step non-self consistent calculation: src/al/al_nscf.in &CONTROL calculation= 'nscf', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 40 40 40 0 0 0 Note the changes in input file. The calculation changed to nscf and we are now using a higher number of k-points grid. pw.x < al_nscf.in > al_nscf.out","s":"Non-self consistent field calculation","u":"/espresso/hands-on/aluminum","h":"#non-self-consistent-field-calculation","p":7},{"i":15,"t":"Next we go ahead with our density of states calculation: src/al/al_dos.in &DOS prefix= 'al', outdir= '/tmp/', fildos= 'al_dos.dat', emin= -10, emax= 35 / We run dos.x with DOS inputs: dos.x < al_dos.in > al_dos.out Note from our al_nscf.out that our Fermi energy is at 7.9421 eV. We plot our density of states:","s":"Density of states","u":"/espresso/hands-on/aluminum","h":"#density-of-states","p":7},{"i":17,"t":"We prepare the input file the same as the case of our previous example silicon: src/al/al_bands.in &CONTROL calculation= 'bands', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS {crystal_b} 5 00.000 0.500 00.000 20 !L 00.000 0.000 00.000 30 !G -0.500 0.000 -0.500 10 !X -0.375 0.250 -0.375 30 !U 00.000 0.000 00.000 20 !G Followed by run pw.x: pw.x < al_bands.in > al_bands.out Now we proceed with post-processing: src/al/al_bands_pp.in &BANDS prefix = 'al' outdir = '/tmp/' filband = 'al_bands.dat' / And run bands.x: bands.x < al_bands_pp.in > al_bands_pp.out We obtain the following bandstructure:","s":"Bandstructure calculation","u":"/espresso/hands-on/aluminum","h":"#bandstructure-calculation","p":7},{"i":19,"t":"Smearing is a technique used for suppressing unstable electron density in the calculation of metals. Such a problem occurs in metals (and semimetals) because the valence bands that cross Fermi level are partially occupied. Due to numerical accuracy, the electrons may occupy the unoccupied states during some iterations, making the algorithm unstable. In order to stablize the algorithm without using excessive number of k-points, smearing technique is used, which replaces the occupation number (either 0 or 1) is replaced by a smoothly varying function of energy. Such a smearing function could be Fermi Dirac distribution, instead of a step function (T = 0 K), we can use the finite temperature form. Below we will test the convergence using PWTK against the number of k-points, three different smearing functions (Gauss, Methfessel-Paxton, and Marzari-Vanderbilt), and for various smearing values. pwtk al.degauss.pwtk We see that the m-v and m-p broadening allow for faster and smother convergence while depending less on degauss value than Gaussian broadening. The number suffix next to the legend labels are number of uniform k-points in Monkhorst-Plank grid.","s":"Importance of smearing in convergence","u":"/espresso/hands-on/aluminum","h":"#importance-of-smearing-in-convergence","p":7},{"i":21,"t":"Topological insulators are a special class of material that is insulating in the bulk, however exhibit conducting states in the surface. Bi2Se3 is such a material. Spin orbit coupling and breaking of the inversion symmetry at the surface of the crystal is crucial to the existence of the Dirac surface state. Here we will calculate the bandstructure step by step: first for the bulk, next including SOC, and finally for the slab. Please check the respective input files. I followed the following steps: # SCF calculation for bulk mpirun -np 24 pw.x -i pw.scf.bi2se3_01.in > pw.scf.bi2se3_01.out # bands calculation for bulk mpirun -np 24 pw.x -i pw.bands.bi2se3_01.in > pw.bands.bi2se3_01.out # post processing for bulk bands mpirun -np 24 bands.x -i pp.bands.bi2se3_01.in > pp.bands.bi2se3_01.out # for bulk with SOC mpirun -np 24 pw.x -i pw.scf.bi2se3_02.in > pw.scf.bi2se3_02.out mpirun -np 24 pw.x -i pw.bands.bi2se3_02.in > pw.bands.bi2se3_02.out mpirun -np 24 bands.x -i pp.bands.bi2se3_02.in > pp.bands.bi2se3_02.out # slab calculation mpirun -np 24 pw.x -i pw.scf.bi2se3_03.in > pw.scf.bi2se3_03.out mpirun -np 24 pw.x -i pw.bands.bi2se3_03.in > pw.bands.bi2se3_03.out mpirun -np 24 bands.x -i pp.bands.bi2se3_03.in > pp.bands.bi2se3_03.out # DOS mpirun -np 24 pw.x -i pw.nscf.bi2se3_04.in > pw.nscf.bi2se3_04.out mpirun -np 24 dos.x -i pp.dos.bi2se3_04.in > pp.dos.bi2se3_04.out For the slab calculation the periodicity of the lattice was broken along the c-axis to artificially add 10 Å vacuum. In above calculation electronic spin was not considered (meaning the states are degenerate with spin up and down). If starting_magnetization is set to zero (or not given) the code makes a spin-orbit calculation without spin magnetization. It assumes that time reversal symmetry holds and it does not calculate the magnetization. The states are still two-component spinors but the total magnetization is zero. Notice that for the Dirac surface states the gap did not completely close at the Fermi energy. This is possibly due to finite size effect. We could repeat the calculation with larger vacuum, and see what happens. Also the Fermi energy estimation seems incorrect. In order to sample the Γ\\GammaΓ point for our DOS calculation, an odd k-grid mesh (25✕25✕5) was used. The signature of Dirac cone is evident from the DOS figure.","s":"Bandstructure of topological insulating Bi2Se3","u":"/espresso/hands-on/Bi2Se3","h":"","p":20},{"i":23,"t":"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/","s":"Resources","u":"/espresso/hands-on/Bi2Se3","h":"#resources","p":20},{"i":25,"t":"Electronic density of states is an important property of a material. ρ(E)dE\\rho(E)dEρ(E)dE = number of electronic states in the energy interval (E,E+dE)(E, E + dE)(E,E+dE) Before we can run the Density of States (DOS) calculation, we need Perform fixed-ion self consistent filed (scf) calculation. In plane-wave based DFT calculations the electronic density is expressed by functions of the form exp⁡(ik⋅r)\\exp (i \\textbf{k} \\cdot \\textbf{r})exp(ik⋅r) with energy given by E=ℏ2k2/2mE = \\hbar^2k^2/2mE=ℏ2k2/2m. Perform non-self consistent field (nscf) calculation with denser k-point grid. A large number of kkk points are required DOS calculation, as the accuracy of DOS depends on the integration in kkk space. Finally, the DOS can be determined by integrating the electron density in kkk space. I have created a new input file (pw.scf.silicon_dos.in) which is very much the same as our previous scf input file except some parameters are modified. You can find all the input files in my GitHub repository. We used the lattice constant value that we obtained from the relaxation calculation. We should not directly use the experimental/real lattice constant values. Depending on the method and pseudo-potential, it might result stress in the system. We have increased the ecutwfc to have better precision. We run the scf calculation: pw.x < pw.scf.silicon_dos.in > pw.scf.silicon_dos.out Next, we have prepared the input file for the nscf calculation. Where is have added occupations in the &system card as tetrahedra (appropriate for DOS calculation). We have increased the number of k-points to 12 × 12 × 12 with automatic option. Also specify nosym = .TRUE. to avoid generation of additional k-points in low symmetry cases. outdir and prefix must be the same as in the scf step, some of the inputs and output are read from previous step. Here we can specify a larger number of nbnd to calculate unoccupied bands. Number of occupied bands can be found in the scf output as number of Kohn-Sham states. pw.x < pw.nscf.silicon_dos.in > pw.nscf.silicon_dos.out Now our final step is to calculate the density of states. The DOS input file as follows: src/silicon/pp.dos.silicon.in &DOS prefix='silicon', outdir='./tmp/', fildos='si_dos.dat', emin=-9.0, emax=16.0 / We run: dos.x < pp.dos.silicon.in > pp.dos.silicon.out The DOS data in the si_dos.dat file that we specified in our input file. We can plot the DOS: notebooks/silicon-dos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline # load data energy, dos, idos = np.loadtxt('../src/silicon/si_dos.dat', unpack=True) # make plot plt.figure(figsize = (12, 6)) plt.plot(energy, dos, linewidth=0.75, color='red') plt.yticks([]) plt.xlabel('Energy (eV)') plt.ylabel('DOS') plt.axvline(x=6.642, linewidth=0.5, color='k', linestyle=(0, (8, 10))) plt.xlim(-6, 16) plt.ylim(0, ) plt.fill_between(energy, 0, dos, where=(energy < 6.642), facecolor='red', alpha=0.25) plt.text(6, 1.7, 'Fermi energy', fontsize= med, rotation=90) plt.show() Important For a set of calculation, we must keep the prefix same. For example, the nscf or bands calculation uses the wavefunction calculated by the scf calculation. When performing different calculations, for example you change a parameter and want to see the changes, you must use different output folder or unique prefix for different calculations so that the outputs do not get mixed. tip Sometimes it is important to sample the Γ\\GammaΓ point for DOS calculation (e.g., the conducting bands cross the Fermi surface only at Γ\\GammaΓ point). In such cases, we need to use odd k-grid (e.g., 9✕9✕5).","s":"Density of States calculation","u":"/espresso/hands-on/dos","h":"","p":24},{"i":27,"t":"Before we can run bands calculation, we need to perform single-point self consistent field calculation. We have our input scf file with some new parameters: src/silicon/pw.scf.silicon_bands.in &CONTROL calculation = 'scf', restart_mode = 'from_scratch', prefix = 'silicon', outdir = './tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &SYSTEM ibrav = 2, celldm(1) = 10.2076, nat = 2, ntyp = 1, ecutwfc = 50, ecutrho = 400, nbnd = 8, ! occupations = 'smearing', ! smearing = 'gaussian', ! degauss = 0.005 / &ELECTRONS conv_thr = 1e-8, mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 8 8 8 0 0 0 Run the scf calculation: pw.x < pw.scf.silicon_bands.in > pw.scf.silicon_bands.out Next step is our band calculation (non-self consistent field) calculation. The bands calculation is non self-consistent and reads/uses the ground state electron density, Hartree, exchange and correlation potentials obtained in the previous step (scf calculation). In case of non self-consistent calculation, the pw.x program determines the Kohn-Sham eigenfunction and eigenvalues without updating Kohn-Sham Hamiltonian at every iteration. We need to specify the k-points for which we want to calculate the eigenvalues. You may use the See-K-path tool by materials cloud to visualize the K-path. We can specify nbnd, by default it calculates half the number of valence electrons, i.e., only the occupied ground state bands. Usually we are interested also in the unoccupied bands above the Fermi energy. Number of occupied bands can be found in the scf output as number of Kohn-Sham states. Below is a sample input file for the band calculation: src/silicon/pw.bands.silicon.in &control calculation = 'bands', restart_mode = 'from_scratch', prefix = 'silicon', outdir = './tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &system ibrav = 2, celldm(1) = 10.2076, nat = 2, ntyp = 1, ecutwfc = 50, ecutrho = 400, nbnd = 8 / &electrons conv_thr = 1e-8, mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.00 0.00 0.00 Si 0.25 0.25 0.25 K_POINTS {crystal_b} 5 0.0000 0.5000 0.0000 20 !L 0.0000 0.0000 0.0000 30 !G -0.500 0.0000 -0.500 10 !X -0.375 0.2500 -0.375 30 !U 0.0000 0.0000 0.0000 20 !G Run pw.x with bands calculation input file: pw.x < pw.bands.silicon.in > pw.bands.silicon.out After the bands calculation is performed, we need some postprocessing using bands.x utility in order to obtain the data in more usable format. Input file for bands.x postprocessing: src/silicon/pp.bands.silicon.in &BANDS prefix = 'silicon' outdir = './tmp/' filband = 'si_bands.dat' / Run bands.x from post processing (PP) module: bands.x < pp.bands.silicon.in > pp.bands.silicon.out Finally, we run plotband.x to visualize bandstructure. We can either run it interactively (as described below) or provide an input file. In order to run interactively, type plotband.x in your terminal. Input file > si_bands.dat Reading 8 bands at 91 k-points Range: -5.8300 16.3420eV Emin, Emax > -6, 16 high-symmetry point: 0.5000 0.5000 0.5000 x coordinate 0.0000 high-symmetry point: 0.0000 0.0000 0.0000 x coordinate 0.8660 high-symmetry point: 1.0000 0.0000 0.0000 x coordinate 1.8660 high-symmetry point: 1.0000 0.2500 0.2500 x coordinate 2.2196 high-symmetry point: 0.0000 0.0000 0.0000 x coordinate 3.2802 output file (gnuplot/xmgr) > si_bands.gnuplot bands in gnuplot/xmgr format written to file si_bands.gnuplot output file (ps) > si_bands.ps Efermi > 6.6416 deltaE, reference E (for tics) 4, 0 bands in PostScript format written to file si_bands.ps You will have si_bands.ps with band diagram. Alternatively, you can use your favorite plotting program to make the plots. Below is an example of using Python matplotlib. notebooks/si-bands.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" plt.rcParams[\"figure.figsize\"]=(8, 6) # load data data = np.loadtxt('../src/silicon/si_bands.dat.gnu') k = np.unique(data[:, 0]) bands = np.reshape(data[:, 1], (-1, len(k))) for band in range(len(bands)): plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k') plt.xlim(min(k), max(k)) # Fermi energy plt.axhline(6.6416, linestyle=(0, (5, 5)), linewidth=0.75, color='k', alpha=0.5) # High symmetry k-points (check bands_pp.out) plt.axvline(0.8660, linewidth=0.75, color='k', alpha=0.5) plt.axvline(1.8660, linewidth=0.75, color='k', alpha=0.5) plt.axvline(2.2196, linewidth=0.75, color='k', alpha=0.5) # text labels plt.xticks(ticks= [0, 0.8660, 1.8660, 2.2196, 3.2802], \\ labels=['L', '$\\Gamma$', 'X', 'U', '$\\Gamma$']) plt.ylabel(\"Energy (eV)\") plt.text(2.3, 5.6, 'Fermi energy', fontsize= small) plt.show() info The k values corresponding to high symmetry points (such as Γ\\GammaΓ, X, U, L) which we need to label in our band diagram, can be found in the post-processing output file (si_bands_pp.out). Bandgap value can be determined from the highest occupied, lowest unoccupied level values printed in scf calculation output.","s":"Bandstructure Calculation","u":"/espresso/hands-on/bands","h":"","p":26},{"i":29,"t":"Usually, band gaps computed using common exchange-correction functionals such as LDA or GGA are severely underestimated compared to actual experimental values. This discrepancy is mainly due to (1) approximations used in the exchange correction functional and (2) a derivative discontinuity term, originating from the density functional being discontinuous with the total number of electrons in the system. The second contribution is larger contributor to the error. It can be partly addressed by a variety of techniques such as the GW approximation. Strategies to improve band gap prediction at moderate to low computational cost now been developed by several groups, including Chan and Ceder (delta-sol)1, Heyd et al. (hybrid functionals)2, and Setyawan et al. (empirical fits)3.","s":"Note on bandgap","u":"/espresso/hands-on/bands","h":"#note-on-bandgap","p":26},{"i":31,"t":"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures See K-pat online tool Footnotes​ M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩ J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of Chemical Physics 123 (2005) https://doi.org/10.1063/1.2085170 ↩ W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, High-throughput combinatorial database of electronic band structures for inorganic scintillator materials., ACS Combinatorial Science. (2011) https://doi.org/10.1021/co200012w. ↩","s":"Resources","u":"/espresso/hands-on/bands","h":"#resources","p":26},{"i":33,"t":"M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩ J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of Chemical Physics 123 (2005) https://doi.org/10.1063/1.2085170 ↩ W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, High-throughput combinatorial database of electronic band structures for inorganic scintillator materials., ACS Combinatorial Science. (2011) https://doi.org/10.1021/co200012w. ↩","s":"Footnotes","u":"/espresso/hands-on/bands","h":"#footnote-label","p":26},{"i":35,"t":"Electronic structure for transition metals (with localized ddd or fff electrons) is not accurately described by standard DFT, and therefore the need for DFT+U formulation. &SYSTEM ... lda_plus_u = .TRUE. Hubbard_u(i) = 2.0 ... / Here i refers to the atomic index in the &ATOMIC_SPECIES card corresponding to each ntyp. We can specify Hubbard_u(i) corresponding to more than one atom in separate lines. There is also Ueff=U−JU_{eff} = U - JUeff​=U−J implementation in QE. JJJ represents on-site exchange interaction. Number of JJJ terms depends on the manifold of localized electrons. For ppp, we have 1; for ddd, we have 2; and for fff, we have 3 terms. ... lda_plus_u = .TRUE. lda_plus_u_kind = 1 Hubbard_u(i) = U Hubbard_J(k, i) = J_{ki} ... COMMON ERRORS If you add Hubbard_u for elements that is not implemented to have UUU term in QE, you might see a \"pseudopotential not yet inserted\" error.","s":"DFT+U calculation","u":"/espresso/hands-on/dft-u","h":"","p":34},{"i":37,"t":"Starting from Quantum Espresso version 7.1, there are changes to input syntax for DFT+U calculations. In the new version, instead of defining the necessary DFT+U parameters, now there is a new Hubbard card. &system ... - lda_plus_u = .true., - lda_plus_u_kind = 0, - U_projection_type = 'atomic', - Hubbard_U(1) = 4.6 - Hubbard_U(2) = 4.6 ... / + HUBBARD (ortho-atomic) + U Fe1-3d 4.6 + U Fe2-3d 4.6 Please refer to the qe-x.x/Doc/Hubbard_input.pdf for details.","s":"Changes to input syntax in v7.1","u":"/espresso/hands-on/dft-u","h":"#changes-to-input-syntax-in-v71","p":34},{"i":39,"t":"We will first perform the standard DFT calculation. Perform the SCF calculation: pw.x -in feo_scf.in > feo_scf.out Perform NSCF calculation with denser k-grid: pw.x -in feo_nscf.in > feo_nscf.out Perform P-DOS calculation: projwfc.x -in feo_projwfc.in > feo_projwfc.out This gives us metallic density of states. In practice we get insulating FeO.","s":"DFT calculation for FeO","u":"/espresso/hands-on/dft-u","h":"#dft-calculation-for-feo","p":34},{"i":41,"t":"src/FeO/feo_hp.in &inputhp prefix = 'FeO' outdir = './tmp/' nq1 = 1, nq2 = 1, nq3 = 1 / Perform a linear-response calculation using hp.x program: hp.x -in feo_hp.in > feo_hp.out Check the file FeO.Hubbard_parameters.dat. info We need to check the convergence against q-mesh (as well as k-mesh in SCF calculation). Here 1×1×11\\times 1\\times 11×1×1 mesh is used. Important: lda_plus_u must be set to .true. during the SCF calculation, UUU may be set to zero. We can update the obtained UUU value in our SCF calculation, and repeat linear response calculation until we have reached self consistency in UUU value. To go even further one can check the convergence of geometry during UUU updates. There is also inter-site Hubbard correction DFT+U+V calculation. The results could be more closer to hybrid functionals like GW. The VVV can also be calculated using Quantum Espresso hp.x code. Obtained value of UUU depends on pseudopotential, Hubbard manifold (whether atomic, ortho-atomic etc.). danger The above hp.x code is not suitable for closed cell systems (e.g., fully occupied d-shell element), in such cases this linear response method gives unrealistically large UUU value.","s":"Calculating Hubbard U","u":"/espresso/hands-on/dft-u","h":"#calculating-hubbard-u","p":34},{"i":42,"t":"We repeat the calculation after setting in the &SYSTEM card: Hubbard_U(1) = 4.6 Hubbard_U(2) = 4.6 We repeat the above calculation and plot the results. Now we find insulating ground state. info U_projection_type = 'ortho-atomic' might give more realistic result than the default 'atomic'. When performing DFT+UDFT+UDFT+U calculation, the ground state might get stuck in a local minimum, in such cases we need to provide starting_ns_eigenvalue to help calculation reach desired/actual ground state. Please see these slides by Dr. Iurii Timrov for a relevant example. tip Here we have plotted the lpdos (local density of states). If we want to know the contribution of dz2,dyz,dx2−z2d_{z^2}, d_{yz}, d_{x^2-z^2}dz2​,dyz​,dx2−z2​ ect., we can find them from the pdos columns. Also there arise important Lowdin charges information in the feo_projwfc.out file.","s":"DFT+U calculation","u":"/espresso/hands-on/dft-u","h":"#dftu-calculation","p":34},{"i":44,"t":"Hands-on DFT+U by Iurii Timrov and Matteo Cococcioni Hubbard parameter calculation","s":"Resources","u":"/espresso/hands-on/dft-u","h":"#resources","p":34},{"i":47,"t":"We can automate the previous self consistent calculation by varying a certain parameter. Say we want to check the total energy of the system for various values of ecutwfc. We can do that by using pwtk script. src/silicon/si_scf_ecutoff.pwtk # load the pw.x input from file load_fromPWI pw.scf.silicon.in # open a file for writing resulting total energies set fid [open etot_vs_ecutwfc.dat w] # loop over different \"ecut\" values foreach ecut { 12 16 20 24 28 32 } { # name of I/O files: $name.in & $name.out set name si_scf_ecutwfc-$ecut # set the pw.x \"ecutwfc\" variable SYSTEM \"ecutwfc = $ecut\" # run the pw.x calculation runPW $name.in # extract the \"total energy\" and write it to file set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$ecut $Etot\" } close $fid To run the above script: pwtk si_scf_ecutoff.pwtk Now we can plot the total energy with respect to ecutwfc. The data is in etot-vs-ecutwfc.dat We will use matplotlib to make the plots. Here is the python code for plotting: notebooks/silicon-scf.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" x, y = np.loadtxt('../src/silicon/etot-vs-ecutwfc.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs ecutwfc') plt.xlabel('ecutwfc (Ry)') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence with cutoff energy using PWTK","u":"/espresso/hands-on/convergence","h":"#convergence-with-cutoff-energy-using-pwtk","p":45},{"i":49,"t":"We can do the convergence test with various parameters. We can calculate the total energy of the system by varying various parameters. We will use the shell script to automate the process with different cutoff energy values. src/silicon/si_script.sh #!/bin/sh NAME=\"ecut\" for CUTOFF in 10 15 20 25 30 35 40 do cat > ${NAME}_${CUTOFF}.in << EOF &control calculation = 'scf', prefix = 'silicon' outdir = './tmp/' pseudo_dir = './pseudos/' / &system ibrav = 2, celldm(1) = 10.0, nat = 2, ntyp = 1, ecutwfc = $CUTOFF / &electrons mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 6 6 6 1 1 1 EOF pw.x < ${NAME}_${CUTOFF}.in > ${NAME}_${CUTOFF}.out echo ${NAME}_${CUTOFF} grep ! ${NAME}_${CUTOFF}.out done Make sure the file has executable permission for the user: chmod 700 si_script.sh Run the script file: ./si_script.sh # or sh si_script.sh We can plot the energy vs cutoff energy, and choose a reasonable value. caution Initially, I had problem in running the script in macOS. The problem occurred because the script file format was set to DOS. The file format can be checked in following way: Open the file in vi editor. vi si_script.sh Now in vi editor command mode (ESC key), type :set ff? This would tell you the file format. Now to change file format, use the command :set fileformat=unix","s":"Convergence test using UNIX shell script","u":"/espresso/hands-on/convergence","h":"#convergence-test-using-unix-shell-script","p":45},{"i":51,"t":"We can run similar convergence test against another parameter, and choose the best value of that particular parameter. Here we will try to calculate the number of k-points in the Monkhorst-Pack mesh. src/silicon/si_scf_kpoints.pwtk load_fromPWI pw.scf.silicon.in set fid [open etot-vs-kpoint.dat w] foreach k { 2 4 6 8 } { set name si_scf_kpoints-$k K_POINTS automatic \"$k $k $k 1 1 1\" runPW $name.in set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$k $Etot\" } close $fid Run pwtk program: pwtk si_scf_kpoints.pwtk notebooks/silicon-scf.ipynb x, y = np.loadtxt('../src/silicon/etot-vs-kpoint.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs kpoints') plt.xlabel('# kpoints') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence test against the number of k-points","u":"/espresso/hands-on/convergence","h":"#convergence-test-against-the-number-of-k-points","p":45},{"i":53,"t":"Calculating total energy with respect to varying lattice constant. src/silicon/si_scf_alat.pwtk load_fromPWI pw.scf.silicon.in # please uncomment & insert value as determined in the \"ecutwfc\" exercise SYSTEM { ecutwfc = 30 } # please uncomment & insert values as determined in the \"kpoints\" exercise K_POINTS automatic { 6 6 6 1 1 1 } set fid [open etot-vs-alat.dat w] foreach alat { 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 } { set name si_scf_alat-$alat SYSTEM \"celldm(1) = $alat\" runPW $name.in set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$alat $Etot\" } close $fid Run the above code: pwtk si_scf_alat.pwtk notebooks/silicon-scf.ipynb x, y = np.loadtxt('../src/silicon/etot-vs-alat.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs alat') plt.xlabel('alat (Bohr)') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence against lattice constant","u":"/espresso/hands-on/convergence","h":"#convergence-against-lattice-constant","p":45},{"i":55,"t":"CPU time is proportional to the number of plane waves used for the calculation. Number of plane wave is proportional to the (ecutwfc)3/2 CPU time is proportional to the number if inequivalent k-points CPU time increases as N3, where N is the number of atoms in the system.","s":"Note on CPU time","u":"/espresso/hands-on/convergence","h":"#note-on-cpu-time","p":45},{"i":57,"t":"I am following this example from the ICTP online school 2021. We will perform the SCF KS orbital calculations on magnetic (nspin=2) iron. Since the d-orbitals of Fe atom are localized/ hard, we will use ultra-soft pseudo potential (USPP). note If we have crystal structure with only one atom per unit cell, or only one type of atoms, the only possible ordering is ferromagnetic. In such cases, we need to form supercell with more number of atoms or label multiple atoms separately, so that their magnetic orientation could be different thus having the possibility of ferro- or antiferromagnetic final states. Run the SCF calculations for both ferro- and antiferromagnetic structures. Notice that for ferromagnetic, we have BCC structure with only one type of atom, while we use simple cubic structure for antiferromagnetic case with two different atomic labels. For antiferromagnetic calculation, we need to start with opposite initial spins. pw.x -i pw.scf.fe_fm.in > pw.scf.fe_fm.out pw.x -i pw.scf.fe_afm.in > pw.scf.fe_afm.out note In case of the AFM calculation, if we have started with FM (say, for both atom types starting_magnetization=0.6 ), the calculation would still converge to AFM state as it is the true ground state for this system, albeit it would take more iteration to converge. If a system has complex potential surface with local minima, it it possible to get different final state magnetization depending on the starting magnetization. In such cases, a stricter convergence criteria might help. info In case of ultrasoft pseudo potentials, the Quantum Espresso default of ecutrho 4 times of ecutoff is not sufficient. We need to set ecutrho 8 or even 12 times that of ecutoff. We must test the convergence for our set values.","s":"Magnetic system: bulk iron","u":"/espresso/hands-on/fe","h":"","p":56},{"i":59,"t":"Below is the PWTK script file: src/fe/fe_ecut.pwtk # load the pw.x input from file load_fromPWI fe_scf_fm.in # dual is the ratio ecutrho/ecutwfc foreach dual { 4 8 12 } { set fid [open etot-vs-ecutwfc.dual$dual.dat w] foreach ecutwfc [seq 25 5 50] { set name pw.Fe.scf.ecutwfc-$ecutwfc.dual-$dual SYSTEM \"ecutwfc = $ecutwfc ecutrho = $ecutwfc*$dual \" runPW $name.in set Etot [pwo_totene $name.out] puts $fid \"$ecutwfc $Etot\" } close $fid } Run the script: pwtk fe_ecut.pwtk","s":"Convergence test for USPP","u":"/espresso/hands-on/fe","h":"#convergence-test-for-uspp","p":56},{"i":61,"t":"PWTK script to calculate DOS and p-DOS: src/fe/fe_dos.pwtk load_fromPWI fe_scf_fm.in SYSTEM \" ecutwfc = 40 ecutrho = 320 \" set name Fe runPW pw.$name.scf.in CONTROL { calculation = 'nscf' } SYSTEM { occupations = 'tetrahedra' , degauss = , ! this is how variable is unset in PWTK } K_POINTS automatic { 12 12 12 1 1 1 } runPW pw.$name.nscf.in DOS \" fildos = '$name.dos.dat' Emin = 5.0 Emax = 20.0, DeltaE = 0.1 \" runDOS dos.$name.in PROJWFC \" filpdos = '$name.pdos.dat' Emin = 5.0 Emax = 20.0, DeltaE = 0.1 \" runPROJWFC projwfc.$name.in Below is the plots of total and projected density of states. Also see bandstructure of Fe with and without SOC.","s":"Density of states calculation","u":"/espresso/hands-on/fe","h":"#density-of-states-calculation","p":56},{"i":63,"t":"Paramagnetic materials have fluctuating magnetic moments that may not be properly described DFT. One approach is to model paramagnetic materials in DFT calculation by building a large supercell and assign randomly oriented magnetic moments. Also note that DFT assumes zero temperature, so it makes sense to perform FM or AFM calculation for magnetic systems.","s":"Paramagnetism","u":"/espresso/hands-on/fe","h":"#paramagnetism","p":56},{"i":65,"t":"We can use XCrySDen to visualize the orientation of magnetic moments. XCrySDen cannot directly read the Quantum Espresso output files for magnetic moment vectors, instead we need to create the input .xsf file with magnetic moments as force vector. You can also change the background color from black from the Palette Menu which is located in the left of File menu. src/fe/fe.xsf # this is a specification for crystal structure CRYSTAL # primitive lattice vectors (in Angstroms) PRIMVEC 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 # conventional lattice vectors (in Angstroms) CONVVEC 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 # First number stands for number of atoms in primitive cell # the second number is always 1 for PRIMCOORD coordinates # followed by atomic coordinates (in Angstroms) and forces: # AtNum X Y Z Fx Fy Fz PRIMCOORD 2 1 26 0.0000000000 0.0000000000 0.0000000000 0.00 0.00 0.01 26 1.4340702350 1.4340702350 1.4340702350 0.00 0.00 -0.01 Open the file from XCrySDen Menu: File → Open Structure → Open XSF. Then go to Display menu and select Forces. If you want to adjust scaling for the force vectors, go to Modify → Force Settings and set suitable Length factor.","s":"Visualizing magnetic moments","u":"/espresso/hands-on/fe","h":"#visualizing-magnetic-moments","p":56},{"i":67,"t":"Here we will calculate Fermi surface of copper. First step is to perform self- consistent field calculation. src/cu/pw.scf.cu.in &control calculation = \"scf\", prefix = \"cu\", pseudo_dir = \"../pseudos/\", outdir = \"/tmp/cu/\" / &system ibrav = 2, celldm(1) = 6.678, nat = 1, ntyp = 1, ecutwfc = 40, ecutrho = 300, occupations = \"smearing\", smearing = \"mp\", degauss = 0.01, nbnd = 16 / &electrons conv_thr = 1e-9, / ATOMIC_SPECIES Cu 63.546 Cu_ONCV_PBE-1.0.oncvpsp.upf ATOMIC_POSITIONS alat Cu 0.00 0.00 0.00 K_POINTS automatic 8 8 8 1 1 1 mpirun -np 4 pw.x -in pw.scf.cu.in > pw.scf.cu.out Next we perform bands calculation over dense uniform k-grid: src/cu/pw.bands.cu.in &control calculation = \"bands\", prefix = \"cu\", pseudo_dir = \"../pseudos/\", outdir = \"/tmp/cu/\" / &system ibrav = 2, celldm(1) = 6.678, nat = 1, ntyp = 1, ecutwfc = 40, ecutrho = 300, occupations = \"smearing\", smearing = \"mp\", degauss = 0.01, nbnd = 16 / &electrons conv_thr = 1e-9, / ATOMIC_SPECIES Cu 63.546 Cu_ONCV_PBE-1.0.oncvpsp.upf ATOMIC_POSITIONS alat Cu 0.00 0.00 0.00 K_POINTS automatic 30 30 30 0 0 0 mpirun -np 4 pw.x -in pw.bands.cu.in > pw.bands.cu.out Finally, we process the data with fs.x post processing tool. Below is the input file: src/cu/fs.cu.in &fermi outdir = \"/tmp/cu/\" prefix = \"cu\" / mpirun -np 4 fs.x -in fs.cu.in > fs.cu.out We can visualize the output file cu_fs.bxsf using xcrysdens program: xcrysden --bxsf cu_fs.bxsf","s":"Fermi Surface","u":"/espresso/hands-on/fermi-surface","h":"","p":66},{"i":69,"t":"I am following this example from the ICTP online school 2021. Graphene is single layer of carbon atoms. First perform the self consistent field calculation to obtain the Kohn-Sham orbitals. Please check the input files in GitHub repository. Run pw.x: pw.x -i graphene_scf.in > graphene_scf.out Next increase the k-grid, and perform the non-self-consistent field calculation. pw.x -i graphene_nscf.in > graphene_nscf.out","s":"DOS and Bandstructure of Graphene","u":"/espresso/hands-on/graphene","h":"","p":68},{"i":71,"t":"dos.x -i graphene_dos.in > graphene_dos.out","s":"DOS calculation","u":"/espresso/hands-on/graphene","h":"#dos-calculation","p":68},{"i":73,"t":"First run the bands calculation for given k-path: pw.x -i graphene_bands.in > graphene_bands.out Followed by the postprocessing to collect the bands: bands.x -i graphene_bands_pp.in > graphene_bands_pp.out Make plots: notebooks/graphene.ipynb import numpy as np import matplotlib.pyplot as plt data = np.loadtxt('../src/graphene/graphene_bands.dat.gnu') k = np.unique(data[:, 0]) bands = np.reshape(data[:, 1], (-1, len(k))) for band in range(len(bands)): plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k') plt.xlim(min(k), max(k)) # Fermi energy plt.axhline(0.921, linestyle=(0, (8, 10)), linewidth=0.75, color='k', alpha=0.5) # High symmetry k-points (check bands_pp.out) plt.axvline(0.6667, linewidth=0.75, color='k', alpha=0.5) plt.axvline(1, linewidth=0.75, color='k', alpha=0.5) # text labels plt.xticks(ticks= [0, 0.6667, 1, 1.5774], labels=['$\\Gamma$', 'K', 'M', '$\\Gamma$']) plt.ylabel(\"Energy (eV)\") plt.show()","s":"Bandstructure calculation","u":"/espresso/hands-on/graphene","h":"#bandstructure-calculation","p":68},{"i":75,"t":"First we perform self consistent field calculation: mpirun -np 4 pw.x -i pw.scf.silicon_epsilon.in > pw.scf.silicon_epsilon.out src/silicon/pw.scf.silicon_epsilon.in &CONTROL calculation = 'scf', prefix = 'silicon', outdir = '/tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &SYSTEM ibrav = 2, celldm(1) = 10.26, nat = 2, ntyp = 1, ecutwfc = 40 nbnd = 20 nosym = .TRUE. noinv = .TRUE. / &ELECTRONS mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS crystal 216 0.00000000 0.00000000 0.00000000 4.629630e-03 0.00000000 0.00000000 0.16666667 4.629630e-03 0.00000000 0.00000000 0.33333333 4.629630e-03 0.00000000 0.00000000 0.50000000 4.629630e-03 0.00000000 0.00000000 0.66666667 4.629630e-03 0.00000000 0.00000000 0.83333333 4.629630e-03 0.00000000 0.16666667 0.00000000 4.629630e-03 0.00000000 0.16666667 0.16666667 4.629630e-03 0.00000000 0.16666667 0.33333333 4.629630e-03 0.00000000 0.16666667 0.50000000 4.629630e-03 0.00000000 0.16666667 0.66666667 4.629630e-03 0.00000000 0.16666667 0.83333333 4.629630e-03 0.00000000 0.33333333 0.00000000 4.629630e-03 0.00000000 0.33333333 0.16666667 4.629630e-03 0.00000000 0.33333333 0.33333333 4.629630e-03 0.00000000 0.33333333 0.50000000 4.629630e-03 0.00000000 0.33333333 0.66666667 4.629630e-03 0.00000000 0.33333333 0.83333333 4.629630e-03 0.00000000 0.50000000 0.00000000 4.629630e-03 0.00000000 0.50000000 0.16666667 4.629630e-03 0.00000000 0.50000000 0.33333333 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0.50000000 4.629630e-03 0.50000000 0.50000000 0.66666667 4.629630e-03 0.50000000 0.50000000 0.83333333 4.629630e-03 0.50000000 0.66666667 0.00000000 4.629630e-03 0.50000000 0.66666667 0.16666667 4.629630e-03 0.50000000 0.66666667 0.33333333 4.629630e-03 0.50000000 0.66666667 0.50000000 4.629630e-03 0.50000000 0.66666667 0.66666667 4.629630e-03 0.50000000 0.66666667 0.83333333 4.629630e-03 0.50000000 0.83333333 0.00000000 4.629630e-03 0.50000000 0.83333333 0.16666667 4.629630e-03 0.50000000 0.83333333 0.33333333 4.629630e-03 0.50000000 0.83333333 0.50000000 4.629630e-03 0.50000000 0.83333333 0.66666667 4.629630e-03 0.50000000 0.83333333 0.83333333 4.629630e-03 0.66666667 0.00000000 0.00000000 4.629630e-03 0.66666667 0.00000000 0.16666667 4.629630e-03 0.66666667 0.00000000 0.33333333 4.629630e-03 0.66666667 0.00000000 0.50000000 4.629630e-03 0.66666667 0.00000000 0.66666667 4.629630e-03 0.66666667 0.00000000 0.83333333 4.629630e-03 0.66666667 0.16666667 0.00000000 4.629630e-03 0.66666667 0.16666667 0.16666667 4.629630e-03 0.66666667 0.16666667 0.33333333 4.629630e-03 0.66666667 0.16666667 0.50000000 4.629630e-03 0.66666667 0.16666667 0.66666667 4.629630e-03 0.66666667 0.16666667 0.83333333 4.629630e-03 0.66666667 0.33333333 0.00000000 4.629630e-03 0.66666667 0.33333333 0.16666667 4.629630e-03 0.66666667 0.33333333 0.33333333 4.629630e-03 0.66666667 0.33333333 0.50000000 4.629630e-03 0.66666667 0.33333333 0.66666667 4.629630e-03 0.66666667 0.33333333 0.83333333 4.629630e-03 0.66666667 0.50000000 0.00000000 4.629630e-03 0.66666667 0.50000000 0.16666667 4.629630e-03 0.66666667 0.50000000 0.33333333 4.629630e-03 0.66666667 0.50000000 0.50000000 4.629630e-03 0.66666667 0.50000000 0.66666667 4.629630e-03 0.66666667 0.50000000 0.83333333 4.629630e-03 0.66666667 0.66666667 0.00000000 4.629630e-03 0.66666667 0.66666667 0.16666667 4.629630e-03 0.66666667 0.66666667 0.33333333 4.629630e-03 0.66666667 0.66666667 0.50000000 4.629630e-03 0.66666667 0.66666667 0.66666667 4.629630e-03 0.66666667 0.66666667 0.83333333 4.629630e-03 0.66666667 0.83333333 0.00000000 4.629630e-03 0.66666667 0.83333333 0.16666667 4.629630e-03 0.66666667 0.83333333 0.33333333 4.629630e-03 0.66666667 0.83333333 0.50000000 4.629630e-03 0.66666667 0.83333333 0.66666667 4.629630e-03 0.66666667 0.83333333 0.83333333 4.629630e-03 0.83333333 0.00000000 0.00000000 4.629630e-03 0.83333333 0.00000000 0.16666667 4.629630e-03 0.83333333 0.00000000 0.33333333 4.629630e-03 0.83333333 0.00000000 0.50000000 4.629630e-03 0.83333333 0.00000000 0.66666667 4.629630e-03 0.83333333 0.00000000 0.83333333 4.629630e-03 0.83333333 0.16666667 0.00000000 4.629630e-03 0.83333333 0.16666667 0.16666667 4.629630e-03 0.83333333 0.16666667 0.33333333 4.629630e-03 0.83333333 0.16666667 0.50000000 4.629630e-03 0.83333333 0.16666667 0.66666667 4.629630e-03 0.83333333 0.16666667 0.83333333 4.629630e-03 0.83333333 0.33333333 0.00000000 4.629630e-03 0.83333333 0.33333333 0.16666667 4.629630e-03 0.83333333 0.33333333 0.33333333 4.629630e-03 0.83333333 0.33333333 0.50000000 4.629630e-03 0.83333333 0.33333333 0.66666667 4.629630e-03 0.83333333 0.33333333 0.83333333 4.629630e-03 0.83333333 0.50000000 0.00000000 4.629630e-03 0.83333333 0.50000000 0.16666667 4.629630e-03 0.83333333 0.50000000 0.33333333 4.629630e-03 0.83333333 0.50000000 0.50000000 4.629630e-03 0.83333333 0.50000000 0.66666667 4.629630e-03 0.83333333 0.50000000 0.83333333 4.629630e-03 0.83333333 0.66666667 0.00000000 4.629630e-03 0.83333333 0.66666667 0.16666667 4.629630e-03 0.83333333 0.66666667 0.33333333 4.629630e-03 0.83333333 0.66666667 0.50000000 4.629630e-03 0.83333333 0.66666667 0.66666667 4.629630e-03 0.83333333 0.66666667 0.83333333 4.629630e-03 0.83333333 0.83333333 0.00000000 4.629630e-03 0.83333333 0.83333333 0.16666667 4.629630e-03 0.83333333 0.83333333 0.33333333 4.629630e-03 0.83333333 0.83333333 0.50000000 4.629630e-03 0.83333333 0.83333333 0.66666667 4.629630e-03 0.83333333 0.83333333 0.83333333 4.629630e-03 Especially, notice following changes: nbnd = 20 nosym = .true. noinv = .true. We turn off the automatic reduction of k-points that pw.x does by using crystal symmetries (nosym = .true. and noinv = .true.). This is because epsilon.x does not recognize crystal symmetries, therefore the entire list of k-points in the grid is needed. Secondly, we calculate a larger number of bands (20), since we are interested in interband transitions. Also, note that epsilon.x doesn't support the reduction of the k-points grid into the irreducible Brillouin zone, so the PW runs must be performed with a uniform k-points grid and all k-points weights must be equal to each other, i.e. in the k-points card the k-points coordinates must be given manually in crystal or alat or bohr, but not with the automatic option. However, the automatic k-points option seems to work. If necessary, we can perform nscf calculation with finer k-grid. Next step is to prepare the input file for epsilon.x: src/silicon/epsilon.si.in &inputpp outdir = \"/tmp/\" prefix = \"silicon\" calculation = \"eps\" / &energy_grid smeartype = \"gauss\" intersmear = 0.2 wmin = 0.0 wmax = 30.0 nw = 500 / The variables smeartype and intersmear define the numerical approximation used to represent the Dirac delta functions in the expression for ϵ2\\epsilon_2ϵ2​ given above. The variables wmin, wmax and nw define the energy grid for the dielectric function. All the energy variables are in eV. mpirun -np 4 epsilon.x -i epsilon.si.in > epsilon.si.out We will see the results are saved in separate .dat files. We can plot the real (ϵ1\\epsilon_1ϵ1​) and imaginary (ϵ2\\epsilon_2ϵ2​) parts of dielectric constants: import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" data_r = np.loadtxt('../src/silicon/epsr_silicon.dat') data_i = np.loadtxt('../src/silicon/epsi_silicon.dat') energy_r, epsilon_r = data_r[:, 0], data_r[:, 2] energy_i, epsilon_i = data_i[:, 0], data_i[:, 2] plt.plot(energy_r, epsilon_r, lw=1, label=\"$\\\\epsilon_1$\") plt.plot(energy_i, epsilon_i, lw=1, label=\"$\\\\epsilon_2$\") plt.xlim(0, 15) plt.xlabel(\"Energy (eV)\") plt.ylabel(\"$\\\\epsilon_1~/~\\\\epsilon_2$\") plt.legend(frameon=False) plt.show() warning Ultra-soft pseudopotentials do not work with epsilon.x. Also note that the above example is not tested against the k-mesh. We usually need finer k-mesh for ϵ\\epsilonϵ to converge. By default the maximum number of k-points is set to 40000 in Quantum Espresso, if we need more k-points, we can change Modules/parameters.f90 and recompile Quantum Espresso.","s":"Dielectric constant","u":"/espresso/hands-on/epsilon","h":"","p":74},{"i":77,"t":"Epsilon.x manual","s":"Resources","u":"/espresso/hands-on/epsilon","h":"#resources","p":74},{"i":79,"t":"Here we will calculate k-resolved density of states for silicon. First we begin with self consistent field calculation. Here is the input: pw.x -inp si_scf.in > si_scf.out Followed by the bands calculation. Note that for bands calculation I have doubled the number of k-points compared to our previous bands calculation. pw.x -inp si_bands.in > si_bands.out Calculate the orbital projections with k-resolved information: src/silicon/si_projwfc.in &projwfc outdir = './tmp/' prefix = 'silicon' ngauss = 0 degauss = 0.036748 DeltaE = 0.005 kresolveddos = .true. filpdos = 'silicon.k' / projwfc.x -inp si_projwfc.in > si_projwfc.out This will give separate orbital projections, as well as total sum for k-resolved DOS. Make plots: notebooks/silicon-kpdos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np import zipfile %matplotlib inline # data file was compressed to reduce file size zipobj = zipfile.ZipFile('../src/silicon/silicon.k.pdos_tot.zip', 'r') zipdata = zipobj.open('silicon.k.pdos_tot') data = np.loadtxt(zipdata) k = np.unique(data[:, 0]) # k values e = np.unique(data[:, 1]) # dos energy values dos = np.zeros([len(k), len(e)]) for i in range(len(data)): e_index = int(i % len(e)) k_index = int(data[i][0] - 1) dos[k_index, e_index] = data[i][2] plt.pcolormesh(k, e, dos.T, cmap='magma', shading='auto') # plt.ylim(-2, 10) plt.xticks([]) plt.ylabel('Energy (eV)') plt.xticks([]) plt.gcf().text(0.12, 0.06, 'L', fontsize=16, fontweight='normal') plt.gcf().text(0.29, 0.06, '$\\Gamma$', fontsize=16, fontweight='normal') plt.gcf().text(0.55, 0.06, 'X', fontsize=16, fontweight='normal') plt.gcf().text(0.63, 0.06, 'U', fontsize=16, fontweight='normal') plt.gcf().text(0.892, 0.06, '$\\Gamma$', fontsize=16, fontweight='normal') plt.axvline(21, c='yellow', lw=1, alpha=0.5) plt.axvline(51, c='yellow', lw=1, alpha=0.5) plt.axvline(61, c='yellow', lw=1, alpha=0.5) plt.show() info If you are using ibrav=0, you can calculate projwfc with lsym=.false. option. If we have contribution from multiple orbitals, we can sum desired projections using sumpdos.x program. For example: sumpdos.x *\\(Cl\\)*\\(p\\) > Cl_2p_tot.dat This way we can plot different orbital projections along with energy and k-resolution.","s":"k-resolved DOS","u":"/espresso/hands-on/kpdos","h":"","p":78},{"i":81,"t":"We will start from the relaxation calculation, and use the relaxed structure for md calculation. Below in the input file for md calculation: src/H2O-md-pw/pw.md.h2o.in &control calculation = 'md' restart_mode = 'from_scratch' prefix = 'h2o' outdir = './tmp/' pseudo_dir = '../pseudos/' tstress = .true. tprnfor = .true. ! about 1 fs; 1 a.u. = 0.048378 fs dt = 20 nstep = 100 / &system ibrav = 1 celldm(1) = 15 nat = 3 ntyp = 2, ecutwfc = 40 nosym = .true. / &electrons conv_thr = 1e-8 / &ions pot_extrapolation = 'second-order' wfc_extrapolation = 'second-order' ion_temperature = 'initial' tempw = 300 / ATOMIC_SPECIES H 1.00784 H_ONCV_PBE-1.0.oncvpsp.upf O 15.999 O.pbe-n-kjpaw_psl.0.1.UPF ! relaxed structure ATOMIC_POSITIONS (angstrom) O 5.0000068025 4.8011777008 4.9999667189 H 4.9999962341 5.3994076541 5.7670041300 H 4.9999969634 5.3994146451 4.2330291511 K_POINTS automatic 1 1 1 0 0 0 Quantum ESPRESSO output file can be loaded in Xcrysden for visualization.","s":"Molecular Dynamics (using pw.x)","u":"/espresso/hands-on/molecular-dynamics-pw","h":"","p":80},{"i":83,"t":"Now that we have calculated the bandstructure of silicon (semiconductor) and aluminum (metal), let us proceed with a compound which has two different atoms. We follow the steps like before: First check the lattice constant with cell relaxation according to our chosen pseudo potential. We use that lattice constant in our next steps. Our lattice constant = 10.6867 * 0.508176602 / 0.5 = 10.861462. pw.x < pw.relax.GaAs.in > pw.relax.GaAs.out Perform self consistent field calculation: pw.x < pw.scf.GaAs.in > pw.scf.GaAs.out Give denser k-points and perform non-self consistent calculation. This step is only necessary if you need to obtain density of states. pw.x < pw.nscf.GaAs.in > pw.nscf.GaAs.out Perform bands calculation pw.x < pw.bands.GaAs.in > pw.bands.GaAs.out Post process the data and plot the bandstructure. bands.x < pp.bands.GaAs.in > pp.bands.GaAs.out If everything goes well, you will get the bandstructure as below: Warning Sometimes a calculation with the same inputs converges in one computer, while fails in another due to library configuration or even due to floating point approximations. The final output numbers will always vary slightly for different machines, or even among different runs in the same machine. Also check the Quantum Espresso version for reproducibility. Also see the bandstructure of GaAs with SOC.","s":"Bandstructure of GaAs","u":"/espresso/hands-on/GaAs","h":"","p":82},{"i":85,"t":"We prepare the input file pw_scf_ni.in and run the calculation: mpirun -np 8 pw.x -i pw_scf_ni.in > pw_scf_ni.out Prepare the input file for bands calculation pw_bands_ni.in with our desired k-path and run: mpirun -np 8 pw.x -i pw_bands_ni.in > pw_bands_ni.out Now we perform the bands.x calculation with spin_component=1 to process only the spin up bands: src/ni/bands_ni_up.in &BANDS outdir='./tmp/', prefix='ni', filband='ni_bands_up.dat', spin_component = 1, / Run the calculation: mpirun -np 8 bands.x -i bands_ni_up.in > bands_ni_up.out Similarly, we process the spin down bands spin_component=2 and plot them.","s":"Spin polarized bandstructure calculation for nickel","u":"/espresso/hands-on/ni","h":"","p":84},{"i":87,"t":"Here we continue with our Aluminum example. Often it is needed to know the contribution from each individual atoms and/or each of their orbital contributions. We can achieve that using projwfc.x code. First, we must perform the self consistent field calculation followed by the non-self consistent field calculation with denser k-points. pw.x < al_scf.in > al_scf.out pw.x < al_nscf.in > al_nscf.out Then we prepare the input file for projwfc.x: src/al/al_projwfc.in &PROJWFC prefix= 'al', outdir= '/tmp/', filpdos= 'al_pdos.dat' / Perform the calculation: projwfc.x < al_projwfc.in > al_projwfc.out Output data format: the DOS values are written in the file {filpdos}.pdos_atm#N(X)_wfc#M(l), where N is atom number, X is atom symbol, M is wfc number, and l=s,p,d,f one file for each atomic wavefunction read from pseudopotential file. The header of file looks like (for spin polarized calculations, we have separate up and down columns): E LDOS(E) PDOS_1(E) ... PDOS_{2l+1}(E) LDOS=∑m=12l+1PDOSm(E)LDOS = \\sum\\limits_{m=1}^{2l+1} PDOS_m (E)LDOS=m=1∑2l+1​PDOSm​(E) PDOSm(E)→PDOS_m (E) \\rightarrowPDOSm​(E)→ projected DOS on atomic wfc with component mmm. Orbital order: for l=1l=1l=1: pz (m=0)p_z~(m=0)pz​ (m=0) pxp_xpx​ (real combination of m=±1m=\\pm 1m=±1 with cosine) pyp_ypy​ (real combination of m=±1m=\\pm 1m=±1 with sine) for l=2l=2l=2: dz2 (m=0)d_{z^2}~(m=0)dz2​ (m=0) dzxd_{zx}dzx​ (real combination of m=±1m=\\pm 1m=±1 with cosine) dzyd_{zy}dzy​ (real combination of m=±1m=\\pm 1m=±1 with sine) dx2−y2d_{x^2-y^2}dx2−y2​ (real combination of m=±2m=\\pm 2m=±2 with cosine) dxyd_{xy}dxy​ (real combination of m=±2m=\\pm 2m=±2 with sine) For more details and PROJWFC output format, please consult the documentation here. Let's create our plots: src/notebooks/al-pdos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline # load data def data_loader(fname): import numpy as np data = np.loadtxt(fname) energy = data[:, 0] pdos = data[:, 1] # ldos col, total contribution for a given orbital return energy, pdos energy, pdos_s = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#1(s)') _, pdos_p = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#2(p)') _, pdos_tot = data_loader('../src/al/al_pdos.dat.pdos_tot') # make plots plt.figure(figsize = (8, 4)) plt.plot(energy, pdos_s, linewidth=0.75, color='#006699', label='s-orbital') plt.plot(energy, pdos_p, linewidth=0.75, color='r', label='p-orbital') plt.plot(energy, pdos_tot, linewidth=0.75, color='k', label='total') plt.yticks([]) plt.xlabel('Energy (eV)') plt.ylabel('DOS') plt.axvline(x= 7.9421, linewidth=0.5, color='k', linestyle=(0, (8, 10))) plt.xlim(-5, 27) plt.ylim(0, ) plt.fill_between(energy, 0, pdos_s, where=(energy < 7.9421), facecolor='#006699', alpha=0.25) plt.fill_between(energy, 0, pdos_p, where=(energy < 7.9421), facecolor='r', alpha=0.25) plt.fill_between(energy, 0, pdos_tot, where=(energy < 7.9421), facecolor='k', alpha=0.25) # plt.text(6.5, 0.52, 'Fermi energy', fontsize= small, rotation=90) plt.legend(frameon=False) plt.show() Here is how our projected density of states plot looks like: We can perform sums of specific atom or orbital contributions using sumpdos.x code if there are multiple sss or ppp orbitals: sumpdos.x *\\(Al\\)* > atom_Al_tot.dat sumpdos.x *\\(Al\\)*\\(s\\) > atom_Al_s.dat sumpdos.x *\\(Al\\)*\\(p\\) > atom_Al_p.dat","s":"Projected Density of States","u":"/espresso/hands-on/pdos","h":"","p":86},{"i":89,"t":"In Quantum Espresso, phonon dispersion is calculated using ph.x program, which is implementation of density functional perturbation theory (DFPT). Here are the steps for calculating phonon dispersion: (1) perform SCF calculation using pw.x src/GaAs-phonon/pw.scf.GaAs.in &control calculation = 'scf' prefix = 'GaAs' pseudo_dir = '../pseudos/' outdir = './tmp/' verbosity = 'high' wf_collect = .true. / &system ibrav = 2 celldm(1) = 10.861462 nat = 2 ntyp = 2 ecutwfc = 80 ecutrho = 640 / &electrons mixing_mode = 'plain' mixing_beta = 0.7 conv_thr = 1.0e-8 / ATOMIC_SPECIES Ga 69.723 Ga.pbe-dn-kjpaw_psl.1.0.0.UPF As 74.921595 As.nc.z_15.oncvpsp3.dojo.v4-std.upf ATOMIC_POSITIONS Ga 0.00 0.00 0.00 As 0.25 0.25 0.25 K_POINTS {automatic} 8 8 8 0 0 0 We perform the SCF calculation: mpirun -np 4 pw.x -i pw.scf.GaAs.in > pw.scf.GaAs.out info Usually higher energy cutoff values are used for phonon calculation to get better accuracy. In case of two dimensional systems, use assume_isolated = '2D' in the SYSTEM namelist to avoid negative or imaginary acoustic frequencies near Γ\\GammaΓ point. Read more here. (2) calculate the dynamical matrix on a uniform mesh of q-points using ph.x src/GaAs-phonon/ph.GaAs.in &INPUTPH outdir = './tmp/' prefix = 'GaAs' tr2_ph = 1d-14 ldisp = .true. ! recover = .true. nq1 = 6 nq2 = 6 nq3 = 6 fildyn = 'GaAs.dyn' / Run the calculation: mpirun -np 4 ph.x -i ph.GaAs.in > ph.GaAs.out The above calculation is computationally demanding. Our example calculation took about a whole day on a 2.6 GHz quad core processor. info You can restart an interrupted ph.x calculation with recover = .true. in the INPUTPH namelist. You can cleanly exit an ongoing calculation by creating an empty file with name {prefix}.EXIT. (3) perform inverse Fourier transform of the dynamical matrix to obtain inverse Fourier components in real space using q2r.x. Below is our input file: src/GaAs-phonon/q2r.GaAs.in &INPUT fildyn = 'GaAs.dyn' zasr = 'crystal' flfrc = 'GaAs.fc' / mpirun -np 4 q2r.x -i q2r.GaAs.in > q2r.GaAs.out (4) Finally, perform Fourier transformation of the real space components to get the dynamical matrix at any q by using matdyn.x. src/GaAs-phonon/matdyn.GaAs.in &INPUT asr = 'crystal' flfrc = 'GaAs.fc' flfrq = 'GaAs.freq' flvec = 'GaAs.modes' ! loto_2d = .true. q_in_band_form = .true. / 5 0.500 0.500 0.500 20 ! L 0.000 0.000 0.000 20 ! G 0.500 0.000 0.500 20 ! X 0.375 0.375 0.750 20 ! K 0.000 0.000 0.000 1 ! G mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out We can now plot the phonon dispersion of GaAs: notebooks/GaAs-phonon.ipynb import numpy as np import matplotlib.pyplot as plt data = np.loadtxt(\"../src/GaAs-phonon/GaAs.freq.gp\") nbands = data.shape[1] - 1 for band in range(nbands): plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k') # High symmetry k-points (check matdyn.GaAs.in) plt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5) plt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \\ labels=['L', '$\\Gamma$', 'X', 'U,K', '$\\Gamma$']) plt.ylabel(\"Frequency (cm$^{-1}$)\") plt.xlim(data[0, 0], data[-1, 0]) plt.ylim(0, ) plt.show() tip We may need to lower the value of conv_thr in scf calculation for more accurate result.","s":"Phonon dispersion","u":"/espresso/hands-on/phonon","h":"","p":88},{"i":91,"t":"Input file for phonon DOS calculation: src/GaAs-phonon/matdyn.dos.GaAs.in &INPUT asr = 'crystal' flfrc = 'GaAs.fc' flfrq = 'GaAs.dos.freq' flvec = 'GaAs.dos.modes' dos = .true. fldos = 'GaAs.dos' nk1 = 25 nk2 = 25 nk3 = 25 / Plot phonon DOS: notebooks/GaAs-phonon.ipynb freq, dos, pdos_Ga, pdos_As = np.loadtxt(\"../src/GaAs-phonon/GaAs.dos\", unpack=True) plt.plot(freq, dos, c='k', lw=0.5, label='Total') plt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga') plt.plot(freq, pdos_As, c='r', lw=0.5, label='As') plt.xlabel('$\\\\Omega~(cm^{-1}$)') plt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)') plt.legend(frameon=False, loc='upper left') plt.xlim(freq[0], freq[-1]) plt.show()","s":"Phonon Density of States","u":"/espresso/hands-on/phonon","h":"#phonon-density-of-states","p":88},{"i":93,"t":"School on Electron-Phonon Physics from First Principles (2018) (Video lectures on YouTube) https://github.com/nguyen-group/QE-SSP","s":"Resources","u":"/espresso/hands-on/phonon","h":"#resources","p":88},{"i":95,"t":"We need to provide various important parameters for the self consistent calculation (solves the Kohn-Sham equation self-consistently) via an input file. In QE input files, there are NAMELISTS and INPUT_CARDS. NAMELISTS variables have default values, and new values can be provided as required for a specific calculation. The variables can be declared in any specific order. On the other hand, the variables in the INPUT_CARDS has always to be specified and in specific order. Logically independent INPUT_CARDS may be organized in any order. There are three mandatory NAMELISTS in PWscf: (1) &CONTROL: specifies the flux of computation, (2) &SYSTEM: specifies the system, and (3) &ELECTRONS: specifies the algorithms used to solve the Kohn-Sham equation. There are two other NAMELISTS: &IONS and &CELLS, which need to be specified depending on the calculation. Three INPUT_CARDS: ATOMIC_SPECIES, ATOMIC_POSITIONS, and K_POINTS in PWscf are mandatory. There are few others that must be provided in certain calculations. Below is our input file pw.scf.silicon.in for silicon in standard diamond (FCC) structure. Note that Quantum ESPRESSO uses primitive unit cell when CELL_PARAMETERS are not provided. One can use any other type of cell e.g., conventional unit cell or supercell by specifying corresponding CELL_PARAMETERS and ATOMIC_POSITIONS.The input files are typically named with .in prefix, while output files are named with .out prefix for their easier identification. The input parameters are organized in &namelists followed by their fields or cards. The &control, &system, and &electrons namelists are required. There are also optional &cell and &ions, you must provide them if your calculation require them. Most parameters in the namelists have default values (which may or may not suit your needs), however some variables you must always provide. Comment lines can be added with lines starting with a ! like in FORTRAN. Also, parameter names are not case-sensitive as in FORTRAN, i.e., &control and &CONTROL are the same. src/silicon/pw.scf.silicon.in &CONTROL ! we want to perform self consistent field calculation calculation = 'scf', ! prefix is reference to the output files prefix = 'silicon', ! output directory. Note that it is deprecated. outdir = './tmp/' ! directory for the pseudo potential directory pseudo_dir = '../pseudos/' ! verbosity high will give more details on the output file verbosity = 'high' / &SYSTEM ! Bravais lattice index, which is 2 for FCC structure ibrav = 2, ! Lattice constant in BOHR celldm(1) = 10.26, ! number of atoms in an unit cell nat = 2, ! number of different types of atom in the cell ntyp = 1, ! kinetic energy cutoff for wavefunction in Ry ecutwfc = 30 ! number of bands to calculate nbnd = 8 / &ELECTRONS ! Mixing factor used in the self-consistent method mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 6 6 6 0 0 0 I am using the pseudo potential file (Si.pz-vbc.UPF) downloaded from Quantum Espresso Website. You must read the PWscf user manual for in-depth understanding. Check the qe-x.x/PW/Doc/ folder under your installation directory. Also see INPUT_PW.html describing various input parameters. PW stands for plane waves. Run pw.x in self consistent mode for silicon. pw.x < pw.scf.silicon.in > pw.scf.silicon.out # For parallel execution mpirun -np 4 pw.x -inp pw.scf.silicon.in > pw.scf.silicon.out note I have added the Quantum ESPRESSO executable directory to the PATH environment variable in bash/zsh profile, otherwise we have to type the full path of pw.x executable location. Now let's look at the output file pw.scf.silicon.out and see how the convergence is reached: grep -e 'total energy' -e estimate pw.scf.silicon.out and you should see something like this: total energy = -15.85014573 Ry Harris-Foulkes estimate = -15.86899637 Ry estimated scf accuracy < 0.06093037 Ry total energy = -15.85194177 Ry Harris-Foulkes estimate = -15.85292281 Ry estimated scf accuracy < 0.00462014 Ry total energy = -15.85218359 Ry Harris-Foulkes estimate = -15.85220235 Ry estimated scf accuracy < 0.00011293 Ry ! total energy = -15.85219789 Ry Harris-Foulkes estimate = -15.85219831 Ry estimated scf accuracy < 0.00000099 Ry The total energy is the sum of the following terms: It is important to note that the absolute value of DFT total energy is not with respect to the vacuum reference, and depends on the chosen pseudopotential. The meaningful measure is the difference in total energy, where various offsets cancel out. note In the above calculation, if you check the output file pw.scf.silicon.out, you will find: highest occupied, lowest unoccupied level (eV): 6.2117 6.8442. Therefore, the bandgap is 0.6325 eV, which is an underestimation of actual bandgap (1.12 eV). Tips on convergence Reduce mixing_beta value, especially if there is an oscillation around the convergence energy. If it is a metallic system, use smearing and degauss. In this case, the SCF accuracy gradually goes down then suddenly increases (due to slight change in Fermi energy highest occupied/ lowest unoccupied levels change). Increase energy and charge density cutoffs (make sure they are sufficient). Certain pseudo potential files have issues, you may try with pseudo potentials from different libraries. Suggested values for the conv_thr: for energy and eigenvalues (scf calculation) 1.0d-7, for forces (relax calculation) 1.0d-8, for stress (vc-relax calculation) 1.0d-9 Ry. For certain calculation convergence might be very slow for the first iteration, one can start the calculation with a higher threshold, after few iterations reduce it and restart the calculation. There are several other important information is printed on the output file. Exchange correlation used in the calculation: Exchange-correlation= SLA PZ NOGX NOGC Where SLA → Slater exchange; PZ → Perdew-Zunger parametrization of the LDA; NOGX and NOGC indicates that density gradients are not taken into account. We can see the total number of plane waves (1067) uses in our calculation: Parallelization info -------------------- sticks: dense smooth PW G-vecs: dense smooth PW Min 108 108 34 1489 1489 266 Max 109 109 35 1492 1492 267 Sum 433 433 139 5961 5961 1067 Number of Kohn-Sham states: number of electrons = 8.00 number of Kohn-Sham states= 8 In our calculation we have specified the number of bands = 8. Otherwise, there would be 4 bands for 8 electrons in case of non spin-polarized systems.","s":"Self consistent field calculation for silicon","u":"/espresso/hands-on/scf","h":"","p":94},{"i":97,"t":"https://www.quantum-espresso.org/Doc/pw_user_guide/ Quantum Espresso Input Generator (can help creating QE input files)","s":"Resources","u":"/espresso/hands-on/scf","h":"#resources","p":94},{"i":100,"t":"Perform scf calculation using Quantum Espresso pw.x QE_PATH=\"/workspaces/q-e-qe-7.2/bin\" mpirun -np 4 ${QE_PATH}/pw.x -i pw.scf.silicon.in > pw.scf.silicon.out Perform nscf calculation using pw.x. Instead of automatic k-grid, we need to provide explicit list of k-points. Such explicit list of k-points can be generated using perl script included in the Wannier package under utility. WANNIER_PATH=\"/workspaces/wannier90-3.1.0\" # directly append the k-points to the input file ${WANNIER_PATH}/utility/kmesh.pl 4 4 4 >> pw.nscf.silicon.in Run nscf calculation: mpirun -np 4 ${QE_PATH}/pw.x -i pw.nscf.silicon.in > pw.nscf.silicon.out Prepare input file for wannier90 (silicon.win). Here we need the k-points list without the weights: ${WANNIER_PATH}/utility/kmesh.pl 4 4 4 wan Generate nnkp input: # we can just provide the seedname or seedname.win ${WANNIER_PATH}/wannier90.x -pp silicon Create input file for pw2wan, and generate initial projections: mpirun -np 4 ${WANNIER_PATH}/pw2wannier90.x -i pw2wan.silicon.in > pw2 wan.silicon.out Run wannier calculation: mpirun -np 4 ${WANNIER_PATH}/wannier90.x silicon","s":"Obtain bandstructure of Silicon","u":"/espresso/hands-on/wannier","h":"#obtain-bandstructure-of-silicon","p":98},{"i":102,"t":"https://sites.google.com/view/hubbard-koopmans/program","s":"Resources","u":"/espresso/hands-on/wannier","h":"#resources","p":98},{"i":104,"t":"In order to consider spin orbit coupling effect in our electronic structure calculation in quantum espresso, we need to use a full relativistic pseudo potential. Following settings are needed in the &SYSTEM card: &SYSTEM ... noncolin = .true. lspinorb = .true. ... /","s":"Spin-Orbit Coupling","u":"/espresso/hands-on/soc","h":"","p":103},{"i":106,"t":"In simple spin polarized calculation (nspin=2), the spin quantum number (up or down) is considered in the calculation. In non-collinear case, the spin has more degrees of freedom, and can be oriented in any direction. Non-collinear magnetism is quite common in nature, where the spins are not parallel (ferromagnetic) or anti-parallel (antiferromagnetic), rather they orient in spirals, helicoids, canted or disordered. Non-collinear magnetism can occur because of geometric frustration of magnetic interaction. It can also occur due to the magnetocrystalline anisotropy which is the result of interaction between the spin and lattice interaction. This relativistic effect comes via spin-orbit coupling. We can constrain the magnetic moment: &SYSTEM ... constrained_magnetization = 'atomic direction' ... / Starting magnetization can be specified by angle1 (angle with zzz axis) and angle2 (angle of projection in xyxyxy-plane and with xxx-axis). Also check the penalty function (λ\\lambdaλ). &SYSTEM ... angle1(i) = 0.0d0 angle2(i) = 0.0d0 lambda = 0.5 ... / i is the index of the atom in ATOMIC_SPECIES card.","s":"Non collinear spin","u":"/espresso/hands-on/soc","h":"#non-collinear-spin","p":103},{"i":108,"t":"Spin-orbit coupling calculations are often hard to converge. Use a smaller mixing_beta for such calculations. First perform a collinear calculation with non-relativistic pseudopotential, and then start from the obtained charge density to perform non-colinear spin orbit calculation. &ELECTRONS ... mixing_beta = 1.0000000000d-01 startingpot = 'file' / When starting with non-collinear calculation from an existing charge density file from a collinear lsda calculation, we need to set lforcet=.true.. It assumes previous density points in z direction, and rotates in the direction specified by angle1 (initial magnetization angle with zzz-axis in degrees), and angle2 (angle in degrees for projections in xyxyxy-plane and with xxx-axis). &SYSTEM ... angle1(i) = 0.0 angle2(i) = 0.0 lforcet = .true. / Also, make sure that energy and charge density cutoffs are sufficient. Certain pseudo potentials might have issues, try with pseudo potentials from a different library. In case of metallic systems, remember to apply smearing. Common Errors S matrix not positive definite: This error might appear due to numerical instability from overlapping atoms. Check atomic positions carefully. In one my calculations, this error was resolved after setting higher ecutrho. Simplified LDA+U not implemented with noncol magnetism, use lda_plus_u_kind=1.","s":"Strategy for convergence","u":"/espresso/hands-on/soc","h":"#strategy-for-convergence","p":103},{"i":110,"t":"src/fe/pw.scf.fe_soc.in &control calculation='scf' pseudo_dir = '../pseudos/', outdir='./tmp/' prefix='fe' / &system ibrav = 3, celldm(1) = 5.39, nat= 1, ntyp= 1, noncolin=.true., lspinorb=.true., starting_magnetization(1)=0.3, ecutwfc = 70, ecutrho = 850.0, occupations='smearing', smearing='marzari-vanderbilt', degauss=0.02 / &electrons diagonalization='david' conv_thr = 1.0e-8 mixing_beta = 0.7 / ATOMIC_SPECIES Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS alat Fe 0.0 0.0 0.0 K_POINTS AUTOMATIC 14 14 14 1 1 1 Run the scf calculation: mpirun -np 8 pw.x -i pw.scf.fe_soc.in > pw.scf.fe_soc.out Prepare the input file for nscf bands calculation: src/fe/pw.bands.fe_soc.in &control calculation='bands' pseudo_dir = '../pseudos/', outdir='./tmp/' prefix='fe' / &system ibrav = 3, celldm(1) = 5.39, nat= 1, ntyp= 1, noncolin=.true., lspinorb=.true., starting_magnetization(1)=0.3, ecutwfc = 70, ecutrho = 850.0, occupations='smearing', smearing='marzari-vanderbilt', degauss=0.02 / &electrons diagonalization='david' conv_thr = 1.0e-8 mixing_beta = 0.7 / ATOMIC_SPECIES Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS alat Fe 0.0 0.0 0.0 K_POINTS tpiba_b 6 0.000 0.000 0.000 40 !gamma 0.000 1.000 0.000 40 !H 0.500 0.500 0.000 30 !N 0.000 0.000 0.000 30 !gamma 0.500 0.500 0.500 30 !P 0.000 1.000 0.000 1 !H Run the bands calculation: mpirun -np 8 pw.x -i pw.bands.fe_soc.in > pw.bands.fe_soc.out Finally post process the bandstructure data: src/fe/pp.bands.fe_soc.in &BANDS outdir='./tmp/', prefix='fe', filband='fe_bands_soc.dat', / In this case spin_component has been removed and we add lsigma(3)=.true. that instructs the program to compute the expectation value for the z component of the spin operator for each eigenfunction and save all values in the file fe.noncolin.data.3. All values in this case are either +1/2 or -1/2. mpirun -np 8 bands.x -i pp.bands.fe_soc.in > pp.bands.fe_soc.out","s":"Bandstructure of Fe with SOC","u":"/espresso/hands-on/soc","h":"#bandstructure-of-fe-with-soc","p":103},{"i":112,"t":"Please check the respective input files. mpirun -np 8 pw.x -i pw.scf.GaAs_soc.in > pw.scf.GaAs_soc.out mpirun -np 8 pw.x -i pw.bands.GaAs_soc.in > pw.bands.GaAs_soc.out mpirun -np 8 bands.x -i pp.bands.GaAs_soc.in > pp.bands.GaAs_soc.out","s":"SOC calculation for GaAs","u":"/espresso/hands-on/soc","h":"#soc-calculation-for-gaas","p":103},{"i":114,"t":"There are two types of structural optimization calculations in Quantum espresso: (1) relax: where only the atomic positions are allowed to vary, and (2) vc-relax: which allows to vary both the atomic positions and lattice constants. src/silicon/si_relax.in &control calculation = 'vc-relax' prefix = 'silicon' outdir = './tmp/' pseudo_dir = './pseudos/' etot_conv_thr = 1e-5 forc_conv_thr = 1e-4 / &system ibrav=2, celldm(1) =14, nat=2, ntyp=1, ecutwfc=30 / &electrons conv_thr=1e-8 / &ions / &cell cell_dofree='ibrav' / ATOMIC_SPECIES Si 28.0855 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.00 0.00 0.00 0 0 0 Si 0.25 0.25 0.25 0 0 0 K_POINTS (automatic) 6 6 6 1 1 1 Perform the plane wave calculation: pw.x -inp si_relax.in > si_relax.out This produces following output (see the si_relax.out for more details, look for \"Final enthalpy\"): Final enthalpy = -15.8536258868 Ry Begin final coordinates new unit-cell volume = 265.89380 a.u.^3 ( 39.40140 Ang^3 ) density = 2.36728 g/cm^3 CELL_PARAMETERS (alat= 14.00000000) -0.364556379 0.000000000 0.364556379 0.000000000 0.364556379 0.364556379 -0.364556379 0.364556379 0.000000000 ATOMIC_POSITIONS (alat) Si 0.0000000000 0.0000000000 0.0000000000 0 0 0 Si 0.1822781896 0.1822781896 0.1822781896 0 0 0 End final coordinates Lattice constant = 0.364556379 * 14 / 0.5 = 10.2076 Bohr.","s":"Structure optimization","u":"/espresso/hands-on/structure-optimization","h":"","p":113},{"i":116,"t":"This work is licensed under a Creative Commons Attribution 4.0 International License. Any third party materials in this work are not included in the article’s Creative Commons license, and users will need to obtain permission from the respective license holder to reproduce such materials. You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. Notices: No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material. To view full copy of this license, visit http://creativecommons.org/licenses/by/4.0/","s":"License","u":"/espresso/license","h":"","p":115},{"i":118,"t":"Quantum Espresso Tutorials ICTP Quantum Espresso workshop 2021 Ljubljana QE summer school 2019 MASTANI Summer School, IISER Pune 2014 (archive) Examples included in Quantum Espresso (qe-x.x/PW/examples/). QE mailing list archive Materials square blog Cornell PARADIM Summer School School on Electron-Phonon Physics from First Principles (2018)","s":"Resources","u":"/espresso/resources","h":"","p":117},{"i":120,"t":"QUANTUM ESPRESSO for quantum simulations of materials Advanced capabilities for materials modelling with QE Hubbard parameters from density-functional perturbation theory Self-consistent Hubbard parameters from DFPT","s":"Papers describing DFT implementations in QE","u":"/espresso/resources","h":"#papers-describing-dft-implementations-in-qe","p":117},{"i":122,"t":"A bird's–eye view of DFT Density Functional Theory: A Practical Introduction by Sholl and Steckel Materials Modelling using Density Functional Theory by Feliciano Giustino Electronic Structure: Basic Theory and Practical Method by Richard M. Martin Electronic Structure Calculations for Solids and Molecules by Jorge Kohanoff PhD Thesis of Dominik Bogdan Jochym","s":"Books","u":"/espresso/resources","h":"#books","p":117},{"i":124,"t":"In order to perform computationally heavy calculations, we would require access to high performance computing facilities.","s":"High Performance Computing","u":"/espresso/setup/hpc","h":"","p":123},{"i":126,"t":"Connect to a login node via ssh: ssh {username}@atlas9.nus.edu.sg Secure copy files between local and remote machines: scp {username}@10.10.0.2:/remote/file.txt /local/directory scp local/file.txt {username}@10.10.0.2:/remote/directory Check disk usage: du -hs . du -hs /path/ Rsync to synchronize two folders: rsync -azhv --delete /source/my_project/ /destination/my_project","s":"Useful UNIX commands","u":"/espresso/setup/hpc","h":"#useful-unix-commands","p":123},{"i":128,"t":"Check your storage quota: hpc s PBS commands: hpc pbs summary Example scrips for job submissions: hpc pbs script parallel20 hpc pbs vasp List available modules: module avail Load a module: module load {module-name} Purge loaded modules: module purge Quantum Espresso is already installed in NUS HPC clusters. Here is a sample job script for NUS HPC clusters: scripts/pbs_job.sh #!/bin/bash #PBS -q parallel24 #PBS -l select=2:ncpus=24:mpiprocs=24:mem=96GB #PBS -j eo #PBS -N qe-project-xx source /etc/profile.d/rec_modules.sh module load espresso6.5-intel_18 ## module load espresso6.5-Centos6_Intel cd $PBS_O_WORKDIR; np=$( cat ${PBS_NODEFILE} | wc -l ); mpirun -np $np -f ${PBS_NODEFILE} pw.x -inp qe-scf.in > qe-scf.out info Notice that the lines beginning with #PBS are actually PBS commands, not comments. For comments, I am using ##. Query about a queue system: qstat -q Check status of a particular queue system: qstat -Qx parallel24 Submitting a job: qsub pbs_job.sh Check running jobs: qstat Details about a job: qstat -f {job-id} Stopping a job: qdel {job-id}","s":"Running jobs at NUS HPC","u":"/espresso/setup/hpc","h":"#running-jobs-at-nus-hpc","p":123},{"i":130,"t":"If you need to modify certain parameters while the program is running, e.g., you want to change the mixing_beta value because SCF accuracy is oscillation without any sign of convergence. Create an empty file named {prefix}.EXIT in the directory where you have the input file or in the outdir as set in the &CONTROL card of input file. touch {prefix}.EXIT That will stop the program on the next iteration, and save the state. In order to restart, set the restart_mode in &CONTROL card to 'restart' and re-run after necessary changes. You must re-submit the job with the same number of processors. &CONTROL ... restart_mode = 'restart' ... /","s":"Abort and restart a calculation","u":"/espresso/setup/hpc","h":"#abort-and-restart-a-calculation","p":123},{"i":132,"t":"If you need a newer or specific version of Quantum Espresso that is not installed in the NUS clusters or you have modified the source codes yourself, here are the steps that I followed to successfully compile. info Quantum Espresso project is primarily hosted on GitLab, and its mirror is maintained at GitHub. You may check their repository at GitLab for more up to date information. The releases via GitLab can be found under: https://gitlab.com/QEF/q-e/-/releases Download and decompress the source files. wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz tar -zxvf q-e-qe-7.2.tar.gz Load the necessary modules (applicable for NUS clusters, last checked in Jun 2022): module load xe_2018 module load fftw/3.3.7 Go to QE directory and run configure: cd q-e-qe-7.2 ./configure You will see output something like: ... BLAS_LIBS= -lmkl_intel_lp64 -lmkl_sequential -lmkl_core LAPACK_LIBS= FFT_LIBS= ... For me, the LAPACK_LIBS and FFT_LIBS libs were not automatically detected. We need to specify them manually. First, get the link libraries line specific to your version of MKL and other configurations from the Intel link advisor. For my case, the link line was: -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl We need to insert the link for BLAS_LIBS, LAPACK_LIBS, and SCALAPACK_LIBS. We also need to find out where is the FFTW lib located. In NUS HPC, we can use module avail command to see where a particular module is located, usually under /app1/modules/. Open make.inc and make the following changes: make.inc # ... CFLAGS = -O2 $(DFLAGS) $(IFLAGS) CFLAGS = -O3 $(DFLAGS) $(IFLAGS) F90FLAGS = $(FFLAGS) -nomodule -fpp $(FDFLAGS) $(CUDA_F90FLAGS) $(IFLAGS) $(MODFLAGS) # compiler flags with and without optimization for fortran-77 # the latter is NEEDED to properly compile dlamch.f, used by lapack - FFLAGS = -O2 -assume byterecl -g -traceback + FFLAGS = -O3 -assume byterecl -g -traceback FFLAGS_NOOPT = -O0 -assume byterecl -g -traceback # ... # If you have nothing better, use the local copy # BLAS_LIBS = $(TOPDIR)/LAPACK/libblas.a - BLAS_LIBS = -lmkl_intel_lp64 -lmkl_sequential -lmkl_core + BLAS_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl # If you have nothing better, use the local copy # LAPACK = liblapack # LAPACK_LIBS = $(TOPDIR)/external/lapack/liblapack.a - LAPACK = + LAPACK = liblapack - LAPACK_LIBS = + LAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl - SCALAPACK_LIBS = + SCALAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl # nothing is needed here if the internal copy of FFTW is compiled # (needs -D__FFTW in DFLAGS) - FFT_LIBS = + FFT_LIBS = -L/app1/centos6.3/gnu/fftw/3.3.7/lib/ -lmpi # ... Now we are ready to compile: make -j8 all I am parallelizing with 8 processors to speed things up. You may add the q-e-qe-7.2/bin path to your .bashrc: echo 'export PATH=\"/home/svu/{username}/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc And don't forget to load dependencies before calling QE executables. module load xe_2018 module load fftw/3.3.7 note If you are submitting job via PBS queue, you need to provide full path of the QE executables, e.g., /home/svu/{username}/q-e-qe-7.2/bin/pw.x. PBS system won't read your bash settings, neither the relative paths of your login node would apply.","s":"Compiling Quantum Espresso using Intel® Math Kernel Library (MKL)","u":"/espresso/setup/hpc","h":"#compiling-quantum-espresso-using-intel-math-kernel-library-mkl","p":123},{"i":134,"t":"If you need to install Intel oneAPI libraries yourself, following instructions might be useful. Please refer to Intel website for up to date information. Intel oneAPI Base Toolkit:​ wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/992857b9-624c-45de-9701-f6445d845359/l_BaseKit_p_2023.2.0.49397_offline.sh # requires gnu-awk sudo apt update && sudo apt install -y --no-install-recommends gawk gcc g++ # interactive cli installation sudo apt install -y --no-install-recommends ncurses-term sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --cli # list components included in oneAPI Base Toolkit sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --list-components # install a subset of components with silent/unattended option sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --silent --eula accept --components intel.oneapi.lin.dpcpp-cpp-compiler:intel.oneapi.lin.mkl.devel note If you install oneAPI without sudo privilege, it will be installed under the user directory: /home/{username}/intel/oneapi/. After installation is completed, the setup script will print the installation location. HPC Toolkit​ wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/0722521a-34b5-4c41-af3f-d5d14e88248d/l_HPCKit_p_2023.2.0.49440_offline.sh sudo sh ./l_HPCKit_p_2023.2.0.49440_offline.sh -a --silent --eula accept Intel MKL library​ Installing individual components: wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/adb8a02c-4ee7-4882-97d6-a524150da358/l_onemkl_p_2023.2.0.49497_offline.sh sudo sh ./l_onemkl_p_2023.2.0.49497_offline.sh -a --silent --eula accept After installation, do not forget to source the environment variables before using: source /opt/intel/oneapi/setvars.sh Compile quantum espresso: wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz tar -zxvf q-e-qe-7.2.tar.gz rm q-e-qe-7.2.tar.gz cd q-e-qe-7.2 ./configure \\ F90=mpiifort \\ MPIF90=mpiifort \\ CC=mpicc CXX=icc \\ F77=mpiifort \\ FFLAGS=\"-O3 -assume byterecl -g -traceback\" \\ LAPACK_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" \\ BLAS_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" \\ SCALAPACK_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" make -j4 all","s":"Installing Intel oneAPI libraries","u":"/espresso/setup/hpc","h":"#installing-intel-oneapi-libraries","p":123},{"i":136,"t":"Please check out the official documentation for more details. It requires cmake version 3.14 or later. apt update && apt install autoconf cmake gawk gcc g++ make I used following steps to successfully compile Quantum Espresso using 2023 versions of Intel libraries in Ubuntu 22.04 system: cd q-e-qe-7.2 mkdir build && cd build cmake -DCMAKE_C_COMPILER=mpiicc -DCMAKE_Fortran_COMPILER=mpiifort -DQE_ENABLE_SCALAPACK=ON .. make -j4 mv bin .. cd .. rm -rf build","s":"Compiling Quantum Espresso with CMake","u":"/espresso/setup/hpc","h":"#compiling-quantum-espresso-with-cmake","p":123},{"i":138,"t":"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/ https://help.nscc.sg/pbspro-quickstartguide/ https://www.youtube.com/watch?v=doudMLEaq3w","s":"Resources","u":"/espresso/setup/hpc","h":"#resources","p":123},{"i":140,"t":"We can install Quantum Espresso on our personal laptops or desktops to run relatively less computationally intensive calculations. If we intend to perform computationally heavy tasks, we would need access to better computing resources with large number of CPU (or GPU) cores, memory, bandwidth, and disc IO. Throughout this tutorial, I will be using a Ubuntu system for smaller calculations while other computationally intensive calculations will be done in HPC clusters. Perhaps the easiest way to install Quantum Espresso is from the package manager of respective Linux distribution. This should work fine for us and this is recommended option. Following commands are for Ubuntu/Debian. First make sure your system is up-to-date. sudo apt update && sudo apt upgrade Install Quantum Espresso from apt repository: sudo apt install --no-install-recommends \\ libfftw3-dev \\ quantum-espresso tip Pre-built binaries of Quantum ESPRESSO for Ubuntu is included in my GitHub repository releases for easy installation. Please refer to the release notes for more details on how to install. If you want to compile from the source yourself, here are the installation steps for the Quantum Espresso version 7.2 in a Ubuntu (LTS 22.04) system. I will be compiling for single processor. First install the recommended libraries and dependencies: sudo apt install --no-install-recommends \\ autoconf \\ build-essential \\ ca-certificates \\ gfortran \\ libblas3 \\ libc6 \\ libfftw3-dev \\ libgcc-s1 \\ liblapack-dev \\ wget If you want to compile for parallel processing, you also need to install: sudo apt install --no-install-recommends \\ libopenmpi-dev \\ libscalapack-openmpi-dev \\ libelpa17 # use libelpa4 on Ubuntu 20.04 Download Quantum Espresso (latest version 7.2 at the time of writing): wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz Un-tar the source files: tar -zxvf q-e-qe-7.2.tar.gz Go to the qe directory and issue configure: cd q-e-qe-7.2 ./configure Here we can provide various configuration options. Read the manual in oder to properly understand. But in most cases we will be just fine with the defaults, it should detect the system configuration automatically, in case you don't get what you want, try the various configuration flags with configure. caution Note that certain programs/utilities bundled with Quantum Espresso might not work correctly in parallel compilation, so we may need serial compilation for those by ./configure --disable-parallel option in case parallel option is automatically detected. Finally, compile the source files and create the binary executables: # compile individual packages make pw # or compile everything make all # we can parallelize e.g., below command uses 4 CPUs make -j4 all Now, the binary files or their symbolic links (shortcuts) would be placed in the bin directory. It would be good idea to include the executable path to your .bashrc (or .zshrc or whatever shell you use) file: # use the correct path if it differs from mine echo 'export PATH=\"/root/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc Finally, you may need to restart your terminal or source .bashrc. source ~/.bashrc You can compile the documentation by going to particular directory (e.g., PW or PP) and execute (you need to have LaTeX installed in your system): make doc If you want docs in PDF format, you can use latex commands to create them as well: pdflatex filename.tex We are now ready to run Quantum Espresso pw.x (or any other program) using mpirun by following command: pw.x -inp inputfile > outputfile # For parallel version mpirun -np 12 pw.x -inp inputfile > outputfile Where -np 12 specifies the number of processors. -inp stands for input file. Alternatively, we can use -i, or -in, or -input, or even standard input redirect <. But beware some systems may not interpret all the different options, I think safe option is to use -i. Once installation is completed, optionally we can run tests if everything went OK. Go to the test-suite directory and run make run-tests If all is well, we will see Passed messages and we are good to go. caution Note that the above installation steps may not be the most optimal way to run Quantum Espresso in your computer. There are multiple implementations of same library. For example, you can replace openmpi libraries with Intel MKL or MPICH implementations. Please do research yourself or ask help from someone who has knowledge about high performance computing.","s":"Quantum Espresso installation","u":"/espresso/setup/install","h":"","p":139},{"i":142,"t":"We will install a very hand scripting package PWscf Toolkit (PWTK). First we need to install following dependencies: sudo apt install tcl tcllib Download the file from - http://pwtk.ijs.si/download/pwtk-2.0.tar.gz wget \"http://pwtk.ijs.si/download/pwtk-2.0.tar.gz\" Above command will download and save the file to your current directory. Next we need to just un-tar (no need to compile): tar -zxvf pwtk-2.0.tar.gz Add the path (modify below as appropriate) to .bashrc: echo 'export PATH=\"/root/pwtk-2.0:$PATH\"' >> ~/.bashrc source ~/.bashrc","s":"Installing PWTK","u":"/espresso/setup/install","h":"#installing-pwtk","p":139},{"i":144,"t":"There are several ways you can run Jupyterlab in your computer.","s":"Jupyter notebooks","u":"/espresso/setup/jupyter","h":"","p":143},{"i":146,"t":"Install Python 3 in your computer # on ubuntu / debian apt install python3 python3-pip Install the required python packages on your computer pip3 install --upgrade -r requirements.txt # or pip3 install --upgrade numpy scipy matplotlib jupyterlab Run Jupyterlab jupyter-lab # or the classic jupyter notebook jupyter-notebook","s":"1. Install on your computer","u":"/espresso/setup/jupyter","h":"#1-install-on-your-computer","p":143},{"i":148,"t":"Install Python 3 and virtualenv on your computer pip3 install --upgrade virtualenv create virtual environment in the project directory cd qe-dft virtualenv venv activate virtual env source venv/bin/activate Install required python packages under virtualenv Launch Jupyterlab Once done, deactivate virtualenv deactivate","s":"2. Install python packages via virtualenv","u":"/espresso/setup/jupyter","h":"#2-install-python-packages-via-virtualenv","p":143},{"i":150,"t":"Install Docker Create an image with Python and the required packages installed # build using the Dockerfile included in my github repo: # https://github.com/pranabdas/espresso # (adjust the Dockerfile according to your needs) docker build -t espresso . Run a container with port forwarding docker run -it --rm -p 8888:8888 -v ${PWD}:/home espresso bash Launch Jupyterlab jupyter-lab","s":"3. Run on a container","u":"/espresso/setup/jupyter","h":"#3-run-on-a-container","p":143},{"i":153,"t":"Density functional theory (DFT) calculations are ab-initio meaning the calculation is done from the scratch based on given input parameters. We need to provide the crystal structure in order to calculate DFT. Crystal structures are widely available in Crystallographic Information File (.CIF) format. There are several databases where you can look for crystal structures. http://crystallography.net/cod/ https://materialsproject.org https://mpds.io/ https://icsd.fiz-karlsruhe.de/index.xhtml http://aflowlib.org/CrystalDatabase/ http://crystdb.nims.go.jp/crystdb/search-materials In Quantum Espresso, the structure information is provided by ibrav number, and corresponding celldm values or lattice constants and cosines of angle between the axes. It is also possible to set ibrav=0 and provide lattice vectors in CELL_PARAMETERS. danger When set ibrav=0, the lattice vectors must be provided with sufficiently large number of decimal accuracy, otherwise symmetry detection may fail and strange problems may arrise. ibrav numbers for different lattice types: ibrav Lattice type 1 Simple cubic 2 Face centered cubic 3,-3 Body centered cubic 4 Hexagonal 5 Trigonal with c as 3-fold axis -5 Trigonal with <111> as 3-fold axis 6 Simple tetragonal 7 Centered tetragonal 8 Simple orthorhombic 9,-9,91 One-face centered orthorhombic 10 Face centered orthorhombic 11 Body centered orthorhombic 12 Simple monoclinic, c unique -12 Simple monoclinic, b unique 13 One base centered monoclinic, c unique -13 One base centered monoclinic, b unique 14 Triclinic","s":"Structure databases","u":"/espresso/setup/crystal-structure","h":"#structure-databases","p":151},{"i":155,"t":"Vesta - https://jp-minerals.org/vesta/en/. It helps you visualize crystal structure, create and modify supercells, crystal structures, and many other useful functionalities. We can prepare our Quantum Espresso input file using cif2cell utility. If you do not have cif2cell installed, you can use pip to install: sudo pip3 install cif2cell You may need to add it to the path in your .bashrc manually: export PATH=\"/home/pranab/.local/lib/python3.8/site-packages/:$PATH\" Running cif2cell command: cif2cell file.cif -p quantum-espresso -o inputfile.in","s":"Useful tools:","u":"/espresso/setup/crystal-structure","h":"#useful-tools","p":151},{"i":157,"t":"You can explore the crystal structure, find out k-path and many more using Xcrysdens application - http://www.xcrysden.org For certain functionality, Xcrysdens requires basic calculator program. On Ubuntu/ Debian: sudo apt update sudo apt install bc xcrysden Manual installation: # install dependencies sudo apt install --no-install-recommends bc tk libglu1-mesa libtogl2 \\ libfftw3-3 libxmu6 imagemagick openbabel libgfortran5 # download the latest version of xcrysden and extract wget http://www.xcrysden.org/download/xcrysden-1.6.2-linux_x86_64-shared.tar.gz tar -zxvf xcrysden-1.6.2-linux_x86_64-shared.tar.gz # launch (provided you extracted under your home directory) ~/xcrysden-1.6.2-bin-shared/xcrysden If you are on WSL, you need to install X-server (X-ming for Windows) on the host and set export DISPLAY=:0 in your WSL instance.","s":"Xcrysdens","u":"/espresso/setup/crystal-structure","h":"#xcrysdens","p":151},{"i":159,"t":"You can generate PWscf input files using tools in this website as well https://www.materialscloud.org/work/tools/qeinputgenerator The same website also has a tool for k-path visualization and generation https://www.materialscloud.org/work/tools/seekpath","s":"QE Input generator","u":"/espresso/setup/crystal-structure","h":"#qe-input-generator","p":151},{"i":161,"t":"Supercell construction using Vesta","s":"Resources","u":"/espresso/setup/crystal-structure","h":"#resources","p":151},{"i":163,"t":"In Quantum Espresso, pseudopotential replaces the actual electron-ion interaction. The pseudopotential describes the atomic nucleus and all the electrons except the outermost valence shell. The rapidly changing potential field near the atomic core is replaced by a smoother function that simulates the potential field far from the core very well. By doing so, it requires less number plane wave basis for wavefunction expansion. tip You may try my Pseudos Web-App, where you can look for pseudopotentials by element name, and download them. Currently, Standard Solid State Pseudopotentials (SSSP) and GBRV pseudopotentials are included. We can choose form various pseudopotential libraries. Choice of pseudopotential depends on the problem we are investigating, e.g., if there is a heavy element present in our system and we are interested in the spin-orbit coupling effects, we should choose a full relativistic pseudopotential. We need to be careful whether our chosen pseudopotential correctly reproduces physical properties. Various pseudopotential libraries: https://www.quantum-espresso.org/pseudopotentials https://www.materialscloud.org/discover/sssp/table/efficiency http://www.pseudo-dojo.org https://www.physics.rutgers.edu/gbrv/ https://nninc.cnf.cornell.edu http://www.quantum-simulation.org/potentials/ BLYP pseudopotentials SCAN pseudopotentials Pseudopotential naming conventions in PSLibrary: an example pseudopotential filename is O.rel-pbe-n-rrkjus_psl.1.0.0.UPF. O → denotes the atomic species rel → full relativistic (optional) pbe → exchange correlation functional n → non-linear core correction (optional) rrkjus → pseudopotential type Exchange correlation functionals: Identifier Functional pz Perdew-Zunger (LDA) pbe Perdew-Burke-Ernzerhof (GGA) pw91 Perdew-Wang 91 (GGA) blyp Becke-Lee-Yang-Parr (GGA) Pseudopotential types: Identifier PP types ae all-electron rrkj Rappe-Rabe-Kaxiras-Joannopoulos (Norm conserving) rrkjus Rappe-Rabe-Kaxiras-Joannopoulos (Ultrasoft) kjpaw Kresse-Joubert (PAW) Ultra soft pseudopotentials are computationally efficient than the norm conserving pseudopotentials. You will find the recommended ecutwfc in the header of each pseudopotential file. If you choose an ultra-soft pseudopotential, you will need ecutrho about 8 times the value of ecutwfc. The default ecutrho is 4 times ecutwfc in Quantum Espresso code, which is a good choice for norm conserving pseudopotentials. You should check energy convergence against ecutwfc for your system. By using pseudopotential, we want to get rid of the core electrons that do not participate in the chemical properties of material. This is known also as rigid core approximation. Instead of accounting the nucleus and core electrons separately, we want to have a pseudopotential that interacts in a similar way with the valence electrons. info We can mix different types of pseudo potentials (e.g., norm conserving, ultra-soft, or PAW), but we cannot mix different exchange correlation functional (e.g., PBE and LDA). Exchange correlation functional can be read from the pseudopotential file or be provided via input_dft parameter in Quantum Espresso. \"sol\" in PBE-sol stands for solid. For bulk systems PBE-sol should be used, while PBE is appropriate for molecules. In case of 2D materials generally PBE is chosen, but one can check PBE-sol. Common error If you mix PBE with PBE-sol type, it results in Error: conflicting values for igcx. However, it is allowed to mix those two types of pseudo. We can set desired exchange correlation functional via input_dft instead of reading from the pseudopotential file.","s":"Pseudo potentials","u":"/espresso/setup/pseudo-potential","h":"","p":162},{"i":165,"t":"Naming convention for PP files","s":"Resources","u":"/espresso/setup/pseudo-potential","h":"#resources","p":162},{"i":167,"t":"Hatree-Fock theory is foundational to many subsequent electronic structure theories. It is an independent particle model or mean filed theory. Consider we have two non-interacting electrons. In that case, the Hamiltonian would be separable, and the total wavefunction Ψ(r1,r2)\\Psi(\\textbf{r}_1, \\textbf{r}_2)Ψ(r1​,r2​) would be product of the individual wave function. Now if we consider two electrons are forming a single system, then there are two issues. (1) We can no longer ignore the electron-electron interaction. (2) The wavefunction describing fermions must be antisymmetric with respect to the interchange of any set of space-spin coordinates. A simple Hartree product fails to satisfy that condition: ΨHP(r1,r2,⋯ ,rN)=ϕ1(r1)ϕ2(r2)⋯ϕN(rN)\\Psi_{HP}(\\textbf{r}_1, \\textbf{r}_2, \\cdots, \\textbf{r}_N) = \\phi_1(\\textbf{r}_1) \\phi_2(\\textbf{r}_2) \\cdots \\phi_N(\\textbf{r}_N)ΨHP​(r1​,r2​,⋯,rN​)=ϕ1​(r1​)ϕ2​(r2​)⋯ϕN​(rN​) In order to satisfy the antisymmetry condition, for our two electron system we can formulate a total wavefunction of the form: Ψ(r1,r2)=12[χ1(r1)χ2(r2)−χ1(r2)χ2(r1)]\\Psi(\\textbf{r}_1, \\textbf{r}_2) = \\frac{1}{\\sqrt{2}} [\\chi_1(\\textbf{r}_1) \\chi_2(\\textbf{r}_2) - \\chi_1(\\textbf{r}_2)\\chi_2(\\textbf{r}_1)]Ψ(r1​,r2​)=2​1​[χ1​(r1​)χ2​(r2​)−χ1​(r2​)χ2​(r1​)]","s":"Hartree-Fock Theory","u":"/espresso/theory/hartree-fock","h":"","p":166},{"i":169,"t":"The above equation can be written as: Ψ(r1,r2)=12∣χ1(r1)χ2(r1)χ1(r2)χ2(r2)∣\\Psi(\\textbf{r}_1, \\textbf{r}_2) = \\frac{1}{\\sqrt{2}} \\begin{vmatrix} \\chi_1(\\textbf{r}_1) & \\chi_2(\\textbf{r}_1) \\\\ \\chi_1(\\textbf{r}_2) & \\chi_2(\\textbf{r}_2) \\end{vmatrix}Ψ(r1​,r2​)=2​1​​χ1​(r1​)χ1​(r2​)​χ2​(r1​)χ2​(r2​)​​ Now what happens if we have more than two electrons? We can generalize the above determinant form to NNN electrons: Ψ=1N!∣χ1(r1)χ2(r1)⋯χN(r1)χ1(r2)χ2(r2)⋯χN(r2)⋮⋮⋱⋮χ1(rN)χ2(rN)⋯χN(rN)∣\\Psi = \\frac{1}{\\sqrt{N!}} \\begin{vmatrix} \\chi_1(\\textbf{r}_1) & \\chi_2(\\textbf{r}_1) & \\cdots & \\chi_N(\\textbf{r}_1) \\\\ \\chi_1(\\textbf{r}_2) & \\chi_2(\\textbf{r}_2) & \\cdots & \\chi_N(\\textbf{r}_2) \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\chi_1(\\textbf{r}_N) & \\chi_2(\\textbf{r}_N) & \\cdots & \\chi_N(\\textbf{r}_N) \\end{vmatrix}Ψ=N!​1​​χ1​(r1​)χ1​(r2​)⋮χ1​(rN​)​χ2​(r1​)χ2​(r2​)⋮χ2​(rN​)​⋯⋯⋱⋯​χN​(r1​)χN​(r2​)⋮χN​(rN​)​​ The above antisymmetrized product can describe electrons that move independently of each other while they experience an average (mean-field) Coulomb force.","s":"Slater determinant","u":"/espresso/theory/hartree-fock","h":"#slater-determinant","p":166},{"i":171,"t":"http://vergil.chemistry.gatech.edu/notes/hf-intro/hf-intro.html","s":"Resources","u":"/espresso/theory/hartree-fock","h":"#resources","p":166},{"i":173,"t":"We want to calculate the electronic structure of real materials and their physical properties by ab-initio method. Electrons are microscopic particle, hence their dynamics is governed by the laws of quantum mechanics. Quantum particles are described by the wave function. λ⋅p=h\\lambda \\cdot p = hλ⋅p=h where hhh is the Plank constant. The Wavefunction of an electron in a potential filed (V)(V)(V) is calculated by solving the Schrödinger equation: −ℏ22m∇2Ψ(r,t)+V(r,t)=iℏ∂Ψ(r,t)∂t-\\frac{\\hbar^2}{2m} \\nabla^2 \\Psi(\\textbf{r}, t) + V(\\textbf{r}, t) = i\\hbar \\frac{\\partial\\Psi(\\textbf{r}, t)}{\\partial t}−2mℏ2​∇2Ψ(r,t)+V(r,t)=iℏ∂t∂Ψ(r,t)​ Fortunately, in most practical purposes, the potential field is not a function of time (t)(t)(t), or even if it is a function of time, they changes relatively slowly compared to the dynamics we are interested in. For example, the electrons inside a material are subjected to the Coulomb field of the nucleus. The nucleus is heavy and their motion is much slower than the motion of the electrons. In such situation, we can separate out the spatial and temporal parts of the wave function: Ψ(r,t)=ψ(r)f(t)\\Psi(\\textbf{r}, t) = \\psi(\\textbf{r}) f(t)Ψ(r,t)=ψ(r)f(t) That reduces our task to solving only time independent Schrödinger equation: [−ℏ2∇22m+v(r)]ψ(r)=ϵψ(r)\\left[-\\frac{\\hbar^2 \\nabla^2}{2m} + v(\\textbf{r})\\right] \\psi(\\textbf{r}) = \\epsilon \\psi(\\textbf{r})[−2mℏ2∇2​+v(r)]ψ(r)=ϵψ(r) Once we have the wavefunction, we can calculate the observables by taking the expectation values. ⟨ψi∣ψj⟩=δij\\braket{\\psi_i | \\psi_j} = \\delta_{ij}⟨ψi​∣ψj​⟩=δij​⟨ψi∣H^∣ψi⟩=ϵi\\braket{\\psi_i | \\hat{H} | \\psi_i} = \\epsilon_i⟨ψi​∣H^∣ψi​⟩=ϵi​ However, the challenge is to solve the Schrödinger equation as a real physical system is consists of a large number of atoms. The Schrödinger equation becomes coupled many-body equation. [−ℏ2m∑i=1N∇i2+∑i=1NV(ri)+∑i=1N∑j 0) is hopping or off-diagonal term.","s":"Introduction","u":"/espresso/theory/wannier","h":"#introduction","p":197},{"i":201,"t":"The choice of Wannier function is not unique. One such option could be the set that maximizes localization. Two different sets of Wannier basis are connected via unitary transformation. MLWFs can be considered as a generalization of localized molecular orbitals (LMOs) to periodic systems.","s":"Maximally Localized Wannier Function","u":"/espresso/theory/wannier","h":"#maximally-localized-wannier-function","p":197},{"i":203,"t":"Introduction to Wannier Basis lecture by Vijay A. Singh Maximally localized generalized Wannier functions for composite energy bands, Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997) Maximally localized Wannier functions for entangled energy bands, Souza, Marzari and Vanderbilt, Phys. Rev. B 65, 035109 (2001) Maximally localized Wannier functions: Theory and applications, Marzari et. al., Rev. Mod. Phys. 84, 1419 (2012) Introduction to Maximally Localized Wannier Functions, Ambrosetti and Silvestrelli, Reviews in Computational Chemistry, Ch. 6, pp. 327 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pw.scf.bi2se3_01.out # bands calculation for bulk mpirun -np 24 pw.x -i pw.bands.bi2se3_01.in > pw.bands.bi2se3_01.out # post processing for bulk bands mpirun -np 24 bands.x -i pp.bands.bi2se3_01.in > pp.bands.bi2se3_01.out # for bulk with SOC mpirun -np 24 pw.x -i pw.scf.bi2se3_02.in > pw.scf.bi2se3_02.out mpirun -np 24 pw.x -i pw.bands.bi2se3_02.in > pw.bands.bi2se3_02.out mpirun -np 24 bands.x -i pp.bands.bi2se3_02.in > pp.bands.bi2se3_02.out # slab calculation mpirun -np 24 pw.x -i pw.scf.bi2se3_03.in > pw.scf.bi2se3_03.out mpirun -np 24 pw.x -i pw.bands.bi2se3_03.in > pw.bands.bi2se3_03.out mpirun -np 24 bands.x -i pp.bands.bi2se3_03.in > pp.bands.bi2se3_03.out # DOS mpirun -np 24 pw.x -i pw.nscf.bi2se3_04.in > pw.nscf.bi2se3_04.out mpirun -np 24 dos.x -i pp.dos.bi2se3_04.in > pp.dos.bi2se3_04.out For the slab calculation the periodicity of the lattice was broken along the c-axis to artificially add 10 Å vacuum. In above calculation electronic spin was not considered (meaning the states are degenerate with spin up and down). If starting_magnetization is set to zero (or not given) the code makes a spin-orbit calculation without spin magnetization. It assumes that time reversal symmetry holds and it does not calculate the magnetization. The states are still two-component spinors but the total magnetization is zero. Notice that for the Dirac surface states the gap did not completely close at the Fermi energy. This is possibly due to finite size effect. We could repeat the calculation with larger vacuum, and see what happens. Also the Fermi energy estimation seems incorrect. In order to sample the Γ\\GammaΓ point for our DOS calculation, an odd k-grid mesh (25✕25✕5) was used. The signature of Dirac cone is evident from the DOS figure.","s":"Bandstructure of topological insulating Bi2Se3","u":"/espresso/hands-on/Bi2Se3","h":"","p":1},{"i":4,"t":"https://docs.quantumatk.com/tutorials/topological_insulator_bi2se3/","s":"Resources","u":"/espresso/hands-on/Bi2Se3","h":"#resources","p":1},{"i":7,"t":"First we are going to relax the cell and choose appropriate lattice constant for our chosen pseudo potential. In case of metals, it is important to provide smearing parameters in the input file. src/al/al_vc_relax.in &CONTROL calculation= 'vc-relax', prefix= 'al', outdir= '/tmp/' pseudo_dir = '../pseudos/' etot_conv_thr= 1e-6, forc_conv_thr= 1e-5 / &SYSTEM ibrav= 2, celldm(1)= 7.652, nat= 1, ntyp= 1, ecutwfc = 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / &IONS / &CELL cell_dofree= 'ibrav' / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 10 10 10 0 0 0 We run pw.x to perform variable cell relaxation calculation: pw.x < al_vc_relax.in > al_vc_relax.out Now you may open the output file in vi editor and invoke search by pressing / and type Final enthalpy You will find the final lattice parameters below it.","s":"Variable cell relaxation","u":"/espresso/hands-on/aluminum","h":"#variable-cell-relaxation","p":5},{"i":9,"t":"We obtain relaxed lattice constant = 7.652 * 0.498611683 / 0.5 = 7.63075 Bohr. We will use this value for our next step, self consistent calculation. src/al/al_scf.in &CONTROL calculation= 'scf', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 10 10 10 0 0 0 We run our self consistent calculation: pw.x < al_scf.in > al_scf.out","s":"Self consistent field (SCF) calculation","u":"/espresso/hands-on/aluminum","h":"#self-consistent-field-scf-calculation","p":5},{"i":11,"t":"Inspect the output file, and let's proceed to next step non-self consistent calculation: src/al/al_nscf.in &CONTROL calculation= 'nscf', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS (automatic) 40 40 40 0 0 0 Note the changes in input file. The calculation changed to nscf and we are now using a higher number of k-points grid. pw.x < al_nscf.in > al_nscf.out","s":"Non-self consistent field calculation","u":"/espresso/hands-on/aluminum","h":"#non-self-consistent-field-calculation","p":5},{"i":13,"t":"Next we go ahead with our density of states calculation: src/al/al_dos.in &DOS prefix= 'al', outdir= '/tmp/', fildos= 'al_dos.dat', emin= -10, emax= 35 / We run dos.x with DOS inputs: dos.x < al_dos.in > al_dos.out Note from our al_nscf.out that our Fermi energy is at 7.9421 eV. We plot our density of states:","s":"Density of states","u":"/espresso/hands-on/aluminum","h":"#density-of-states","p":5},{"i":15,"t":"We prepare the input file the same as the case of our previous example silicon: src/al/al_bands.in &CONTROL calculation= 'bands', restart_mode= 'from_scratch', prefix= 'al', outdir= '/tmp/', pseudo_dir= '../pseudos/' / &SYSTEM ibrav= 2, celldm(1) = 7.63075, nat= 1, ntyp= 1, ecutwfc= 50, ecutrho= 500, occupations= 'smearing', smearing= 'gaussian', degauss= 0.01 / &ELECTRONS conv_thr= 1e-8 / ATOMIC_SPECIES Al 26.981539 Al.pbe-n-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS (alat) Al 0.00 0.00 0.00 K_POINTS {crystal_b} 5 00.000 0.500 00.000 20 !L 00.000 0.000 00.000 30 !G -0.500 0.000 -0.500 10 !X -0.375 0.250 -0.375 30 !U 00.000 0.000 00.000 20 !G Followed by run pw.x: pw.x < al_bands.in > al_bands.out Now we proceed with post-processing: src/al/al_bands_pp.in &BANDS prefix = 'al' outdir = '/tmp/' filband = 'al_bands.dat' / And run bands.x: bands.x < al_bands_pp.in > al_bands_pp.out We obtain the following bandstructure:","s":"Bandstructure calculation","u":"/espresso/hands-on/aluminum","h":"#bandstructure-calculation","p":5},{"i":17,"t":"Smearing is a technique used for suppressing unstable electron density in the calculation of metals. Such a problem occurs in metals (and semimetals) because the valence bands that cross Fermi level are partially occupied. Due to numerical accuracy, the electrons may occupy the unoccupied states during some iterations, making the algorithm unstable. In order to stablize the algorithm without using excessive number of k-points, smearing technique is used, which replaces the occupation number (either 0 or 1) is replaced by a smoothly varying function of energy. Such a smearing function could be Fermi Dirac distribution, instead of a step function (T = 0 K), we can use the finite temperature form. Below we will test the convergence using PWTK against the number of k-points, three different smearing functions (Gauss, Methfessel-Paxton, and Marzari-Vanderbilt), and for various smearing values. pwtk al.degauss.pwtk We see that the m-v and m-p broadening allow for faster and smother convergence while depending less on degauss value than Gaussian broadening. The number suffix next to the legend labels are number of uniform k-points in Monkhorst-Plank grid.","s":"Importance of smearing in convergence","u":"/espresso/hands-on/aluminum","h":"#importance-of-smearing-in-convergence","p":5},{"i":19,"t":"Before we can run bands calculation, we need to perform single-point self consistent field calculation. We have our input scf file with some new parameters: src/silicon/pw.scf.silicon_bands.in &CONTROL calculation = 'scf', restart_mode = 'from_scratch', prefix = 'silicon', outdir = './tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &SYSTEM ibrav = 2, celldm(1) = 10.2076, nat = 2, ntyp = 1, ecutwfc = 50, ecutrho = 400, nbnd = 8, ! occupations = 'smearing', ! smearing = 'gaussian', ! degauss = 0.005 / &ELECTRONS conv_thr = 1e-8, mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 8 8 8 0 0 0 Run the scf calculation: pw.x < pw.scf.silicon_bands.in > pw.scf.silicon_bands.out Next step is our band calculation (non-self consistent field) calculation. The bands calculation is non self-consistent and reads/uses the ground state electron density, Hartree, exchange and correlation potentials obtained in the previous step (scf calculation). In case of non self-consistent calculation, the pw.x program determines the Kohn-Sham eigenfunction and eigenvalues without updating Kohn-Sham Hamiltonian at every iteration. We need to specify the k-points for which we want to calculate the eigenvalues. You may use the See-K-path tool by materials cloud to visualize the K-path. We can specify nbnd, by default it calculates half the number of valence electrons, i.e., only the occupied ground state bands. Usually we are interested also in the unoccupied bands above the Fermi energy. Number of occupied bands can be found in the scf output as number of Kohn-Sham states. Below is a sample input file for the band calculation: src/silicon/pw.bands.silicon.in &control calculation = 'bands', restart_mode = 'from_scratch', prefix = 'silicon', outdir = './tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &system ibrav = 2, celldm(1) = 10.2076, nat = 2, ntyp = 1, ecutwfc = 50, ecutrho = 400, nbnd = 8 / &electrons conv_thr = 1e-8, mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.00 0.00 0.00 Si 0.25 0.25 0.25 K_POINTS {crystal_b} 5 0.0000 0.5000 0.0000 20 !L 0.0000 0.0000 0.0000 30 !G -0.500 0.0000 -0.500 10 !X -0.375 0.2500 -0.375 30 !U 0.0000 0.0000 0.0000 20 !G Run pw.x with bands calculation input file: pw.x < pw.bands.silicon.in > pw.bands.silicon.out After the bands calculation is performed, we need some postprocessing using bands.x utility in order to obtain the data in more usable format. Input file for bands.x postprocessing: src/silicon/pp.bands.silicon.in &BANDS prefix = 'silicon' outdir = './tmp/' filband = 'si_bands.dat' / Run bands.x from post processing (PP) module: bands.x < pp.bands.silicon.in > pp.bands.silicon.out Finally, we run plotband.x to visualize bandstructure. We can either run it interactively (as described below) or provide an input file. In order to run interactively, type plotband.x in your terminal. Input file > si_bands.dat Reading 8 bands at 91 k-points Range: -5.8300 16.3420eV Emin, Emax > -6, 16 high-symmetry point: 0.5000 0.5000 0.5000 x coordinate 0.0000 high-symmetry point: 0.0000 0.0000 0.0000 x coordinate 0.8660 high-symmetry point: 1.0000 0.0000 0.0000 x coordinate 1.8660 high-symmetry point: 1.0000 0.2500 0.2500 x coordinate 2.2196 high-symmetry point: 0.0000 0.0000 0.0000 x coordinate 3.2802 output file (gnuplot/xmgr) > si_bands.gnuplot bands in gnuplot/xmgr format written to file si_bands.gnuplot output file (ps) > si_bands.ps Efermi > 6.6416 deltaE, reference E (for tics) 4, 0 bands in PostScript format written to file si_bands.ps You will have si_bands.ps with band diagram. Alternatively, you can use your favorite plotting program to make the plots. Below is an example of using Python matplotlib. notebooks/si-bands.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" plt.rcParams[\"figure.figsize\"]=(8, 6) # load data data = np.loadtxt('../src/silicon/si_bands.dat.gnu') k = np.unique(data[:, 0]) bands = np.reshape(data[:, 1], (-1, len(k))) for band in range(len(bands)): plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k') plt.xlim(min(k), max(k)) # Fermi energy plt.axhline(6.6416, linestyle=(0, (5, 5)), linewidth=0.75, color='k', alpha=0.5) # High symmetry k-points (check bands_pp.out) plt.axvline(0.8660, linewidth=0.75, color='k', alpha=0.5) plt.axvline(1.8660, linewidth=0.75, color='k', alpha=0.5) plt.axvline(2.2196, linewidth=0.75, color='k', alpha=0.5) # text labels plt.xticks(ticks= [0, 0.8660, 1.8660, 2.2196, 3.2802], \\ labels=['L', '$\\Gamma$', 'X', 'U', '$\\Gamma$']) plt.ylabel(\"Energy (eV)\") plt.text(2.3, 5.6, 'Fermi energy', fontsize= small) plt.show() info The k values corresponding to high symmetry points (such as Γ\\GammaΓ, X, U, L) which we need to label in our band diagram, can be found in the post-processing output file (si_bands_pp.out). Bandgap value can be determined from the highest occupied, lowest unoccupied level values printed in scf calculation output.","s":"Bandstructure Calculation","u":"/espresso/hands-on/bands","h":"","p":18},{"i":21,"t":"Usually, band gaps computed using common exchange-correction functionals such as LDA or GGA are severely underestimated compared to actual experimental values. This discrepancy is mainly due to (1) approximations used in the exchange correction functional and (2) a derivative discontinuity term, originating from the density functional being discontinuous with the total number of electrons in the system. The second contribution is larger contributor to the error. It can be partly addressed by a variety of techniques such as the GW approximation. Strategies to improve band gap prediction at moderate to low computational cost now been developed by several groups, including Chan and Ceder (delta-sol)1, Heyd et al. (hybrid functionals)2, and Setyawan et al. (empirical fits)3.","s":"Note on bandgap","u":"/espresso/hands-on/bands","h":"#note-on-bandgap","p":18},{"i":23,"t":"https://docs.materialsproject.org/methodology/materials-methodology/electronic-structure#accuracy-of-band-structures See K-pat online tool Footnotes​ M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩ J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of Chemical Physics 123 (2005) https://doi.org/10.1063/1.2085170 ↩ W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, High-throughput combinatorial database of electronic band structures for inorganic scintillator materials., ACS Combinatorial Science. (2011) https://doi.org/10.1021/co200012w. ↩","s":"Resources","u":"/espresso/hands-on/bands","h":"#resources","p":18},{"i":25,"t":"M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, Physical Review Letters 19 (2010) https://doi.org/10.1103/PhysRevLett.105.196403 ↩ J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of Chemical Physics 123 (2005) https://doi.org/10.1063/1.2085170 ↩ W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, High-throughput combinatorial database of electronic band structures for inorganic scintillator materials., ACS Combinatorial Science. (2011) https://doi.org/10.1021/co200012w. ↩","s":"Footnotes","u":"/espresso/hands-on/bands","h":"#footnote-label","p":18},{"i":28,"t":"We can automate the previous self consistent calculation by varying a certain parameter. Say we want to check the total energy of the system for various values of ecutwfc. We can do that by using pwtk script. src/silicon/si_scf_ecutoff.pwtk # load the pw.x input from file load_fromPWI pw.scf.silicon.in # open a file for writing resulting total energies set fid [open etot_vs_ecutwfc.dat w] # loop over different \"ecut\" values foreach ecut { 12 16 20 24 28 32 } { # name of I/O files: $name.in & $name.out set name si_scf_ecutwfc-$ecut # set the pw.x \"ecutwfc\" variable SYSTEM \"ecutwfc = $ecut\" # run the pw.x calculation runPW $name.in # extract the \"total energy\" and write it to file set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$ecut $Etot\" } close $fid To run the above script: pwtk si_scf_ecutoff.pwtk Now we can plot the total energy with respect to ecutwfc. The data is in etot-vs-ecutwfc.dat We will use matplotlib to make the plots. Here is the python code for plotting: notebooks/silicon-scf.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" x, y = np.loadtxt('../src/silicon/etot-vs-ecutwfc.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs ecutwfc') plt.xlabel('ecutwfc (Ry)') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence with cutoff energy using PWTK","u":"/espresso/hands-on/convergence","h":"#convergence-with-cutoff-energy-using-pwtk","p":26},{"i":30,"t":"We can do the convergence test with various parameters. We can calculate the total energy of the system by varying various parameters. We will use the shell script to automate the process with different cutoff energy values. src/silicon/si_script.sh #!/bin/sh NAME=\"ecut\" for CUTOFF in 10 15 20 25 30 35 40 do cat > ${NAME}_${CUTOFF}.in << EOF &control calculation = 'scf', prefix = 'silicon' outdir = './tmp/' pseudo_dir = './pseudos/' / &system ibrav = 2, celldm(1) = 10.0, nat = 2, ntyp = 1, ecutwfc = $CUTOFF / &electrons mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 6 6 6 1 1 1 EOF pw.x < ${NAME}_${CUTOFF}.in > ${NAME}_${CUTOFF}.out echo ${NAME}_${CUTOFF} grep ! ${NAME}_${CUTOFF}.out done Make sure the file has executable permission for the user: chmod 700 si_script.sh Run the script file: ./si_script.sh # or sh si_script.sh We can plot the energy vs cutoff energy, and choose a reasonable value. caution Initially, I had problem in running the script in macOS. The problem occurred because the script file format was set to DOS. The file format can be checked in following way: Open the file in vi editor. vi si_script.sh Now in vi editor command mode (ESC key), type :set ff? This would tell you the file format. Now to change file format, use the command :set fileformat=unix","s":"Convergence test using UNIX shell script","u":"/espresso/hands-on/convergence","h":"#convergence-test-using-unix-shell-script","p":26},{"i":32,"t":"We can run similar convergence test against another parameter, and choose the best value of that particular parameter. Here we will try to calculate the number of k-points in the Monkhorst-Pack mesh. src/silicon/si_scf_kpoints.pwtk load_fromPWI pw.scf.silicon.in set fid [open etot-vs-kpoint.dat w] foreach k { 2 4 6 8 } { set name si_scf_kpoints-$k K_POINTS automatic \"$k $k $k 1 1 1\" runPW $name.in set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$k $Etot\" } close $fid Run pwtk program: pwtk si_scf_kpoints.pwtk notebooks/silicon-scf.ipynb x, y = np.loadtxt('../src/silicon/etot-vs-kpoint.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs kpoints') plt.xlabel('# kpoints') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence test against the number of k-points","u":"/espresso/hands-on/convergence","h":"#convergence-test-against-the-number-of-k-points","p":26},{"i":34,"t":"Calculating total energy with respect to varying lattice constant. src/silicon/si_scf_alat.pwtk load_fromPWI pw.scf.silicon.in # please uncomment & insert value as determined in the \"ecutwfc\" exercise SYSTEM { ecutwfc = 30 } # please uncomment & insert values as determined in the \"kpoints\" exercise K_POINTS automatic { 6 6 6 1 1 1 } set fid [open etot-vs-alat.dat w] foreach alat { 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 } { set name si_scf_alat-$alat SYSTEM \"celldm(1) = $alat\" runPW $name.in set Etot [::pwtk::pwo::totene $name.out] puts $fid \"$alat $Etot\" } close $fid Run the above code: pwtk si_scf_alat.pwtk notebooks/silicon-scf.ipynb x, y = np.loadtxt('../src/silicon/etot-vs-alat.dat', delimiter=' ', unpack=True) plt.plot(x, y, \"o-\", markersize=5, label='Etot vs alat') plt.xlabel('alat (Bohr)') plt.ylabel('Etot (Ry)') plt.legend(frameon=False) plt.show()","s":"Convergence against lattice constant","u":"/espresso/hands-on/convergence","h":"#convergence-against-lattice-constant","p":26},{"i":36,"t":"CPU time is proportional to the number of plane waves used for the calculation. Number of plane wave is proportional to the (ecutwfc)3/2 CPU time is proportional to the number if inequivalent k-points CPU time increases as N3, where N is the number of atoms in the system.","s":"Note on CPU time","u":"/espresso/hands-on/convergence","h":"#note-on-cpu-time","p":26},{"i":38,"t":"Electronic density of states is an important property of a material. ρ(E)dE\\rho(E)dEρ(E)dE = number of electronic states in the energy interval (E,E+dE)(E, E + dE)(E,E+dE) Before we can run the Density of States (DOS) calculation, we need Perform fixed-ion self consistent filed (scf) calculation. In plane-wave based DFT calculations the electronic density is expressed by functions of the form exp⁡(ik⋅r)\\exp (i \\textbf{k} \\cdot \\textbf{r})exp(ik⋅r) with energy given by E=ℏ2k2/2mE = \\hbar^2k^2/2mE=ℏ2k2/2m. Perform non-self consistent field (nscf) calculation with denser k-point grid. A large number of kkk points are required DOS calculation, as the accuracy of DOS depends on the integration in kkk space. Finally, the DOS can be determined by integrating the electron density in kkk space. I have created a new input file (pw.scf.silicon_dos.in) which is very much the same as our previous scf input file except some parameters are modified. You can find all the input files in my GitHub repository. We used the lattice constant value that we obtained from the relaxation calculation. We should not directly use the experimental/real lattice constant values. Depending on the method and pseudo-potential, it might result stress in the system. We have increased the ecutwfc to have better precision. We run the scf calculation: pw.x < pw.scf.silicon_dos.in > pw.scf.silicon_dos.out Next, we have prepared the input file for the nscf calculation. Where is have added occupations in the &system card as tetrahedra (appropriate for DOS calculation). We have increased the number of k-points to 12 × 12 × 12 with automatic option. Also specify nosym = .TRUE. to avoid generation of additional k-points in low symmetry cases. outdir and prefix must be the same as in the scf step, some of the inputs and output are read from previous step. Here we can specify a larger number of nbnd to calculate unoccupied bands. Number of occupied bands can be found in the scf output as number of Kohn-Sham states. pw.x < pw.nscf.silicon_dos.in > pw.nscf.silicon_dos.out Now our final step is to calculate the density of states. The DOS input file as follows: src/silicon/pp.dos.silicon.in &DOS prefix='silicon', outdir='./tmp/', fildos='si_dos.dat', emin=-9.0, emax=16.0 / We run: dos.x < pp.dos.silicon.in > pp.dos.silicon.out The DOS data in the si_dos.dat file that we specified in our input file. We can plot the DOS: notebooks/silicon-dos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline # load data energy, dos, idos = np.loadtxt('../src/silicon/si_dos.dat', unpack=True) # make plot plt.figure(figsize = (12, 6)) plt.plot(energy, dos, linewidth=0.75, color='red') plt.yticks([]) plt.xlabel('Energy (eV)') plt.ylabel('DOS') plt.axvline(x=6.642, linewidth=0.5, color='k', linestyle=(0, (8, 10))) plt.xlim(-6, 16) plt.ylim(0, ) plt.fill_between(energy, 0, dos, where=(energy < 6.642), facecolor='red', alpha=0.25) plt.text(6, 1.7, 'Fermi energy', fontsize= med, rotation=90) plt.show() Important For a set of calculation, we must keep the prefix same. For example, the nscf or bands calculation uses the wavefunction calculated by the scf calculation. When performing different calculations, for example you change a parameter and want to see the changes, you must use different output folder or unique prefix for different calculations so that the outputs do not get mixed. tip Sometimes it is important to sample the Γ\\GammaΓ point for DOS calculation (e.g., the conducting bands cross the Fermi surface only at Γ\\GammaΓ point). In such cases, we need to use odd k-grid (e.g., 9✕9✕5).","s":"Density of States calculation","u":"/espresso/hands-on/dos","h":"","p":37},{"i":40,"t":"I am following this example from the ICTP online school 2021. We will perform the SCF KS orbital calculations on magnetic (nspin=2) iron. Since the d-orbitals of Fe atom are localized/ hard, we will use ultra-soft pseudo potential (USPP). note If we have crystal structure with only one atom per unit cell, or only one type of atoms, the only possible ordering is ferromagnetic. In such cases, we need to form supercell with more number of atoms or label multiple atoms separately, so that their magnetic orientation could be different thus having the possibility of ferro- or antiferromagnetic final states. Run the SCF calculations for both ferro- and antiferromagnetic structures. Notice that for ferromagnetic, we have BCC structure with only one type of atom, while we use simple cubic structure for antiferromagnetic case with two different atomic labels. For antiferromagnetic calculation, we need to start with opposite initial spins. pw.x -i pw.scf.fe_fm.in > pw.scf.fe_fm.out pw.x -i pw.scf.fe_afm.in > pw.scf.fe_afm.out note In case of the AFM calculation, if we have started with FM (say, for both atom types starting_magnetization=0.6 ), the calculation would still converge to AFM state as it is the true ground state for this system, albeit it would take more iteration to converge. If a system has complex potential surface with local minima, it it possible to get different final state magnetization depending on the starting magnetization. In such cases, a stricter convergence criteria might help. info In case of ultrasoft pseudo potentials, the Quantum Espresso default of ecutrho 4 times of ecutoff is not sufficient. We need to set ecutrho 8 or even 12 times that of ecutoff. We must test the convergence for our set values.","s":"Magnetic system: bulk iron","u":"/espresso/hands-on/fe","h":"","p":39},{"i":42,"t":"Below is the PWTK script file: src/fe/fe_ecut.pwtk # load the pw.x input from file load_fromPWI fe_scf_fm.in # dual is the ratio ecutrho/ecutwfc foreach dual { 4 8 12 } { set fid [open etot-vs-ecutwfc.dual$dual.dat w] foreach ecutwfc [seq 25 5 50] { set name pw.Fe.scf.ecutwfc-$ecutwfc.dual-$dual SYSTEM \"ecutwfc = $ecutwfc ecutrho = $ecutwfc*$dual \" runPW $name.in set Etot [pwo_totene $name.out] puts $fid \"$ecutwfc $Etot\" } close $fid } Run the script: pwtk fe_ecut.pwtk","s":"Convergence test for USPP","u":"/espresso/hands-on/fe","h":"#convergence-test-for-uspp","p":39},{"i":44,"t":"PWTK script to calculate DOS and p-DOS: src/fe/fe_dos.pwtk load_fromPWI fe_scf_fm.in SYSTEM \" ecutwfc = 40 ecutrho = 320 \" set name Fe runPW pw.$name.scf.in CONTROL { calculation = 'nscf' } SYSTEM { occupations = 'tetrahedra' , degauss = , ! this is how variable is unset in PWTK } K_POINTS automatic { 12 12 12 1 1 1 } runPW pw.$name.nscf.in DOS \" fildos = '$name.dos.dat' Emin = 5.0 Emax = 20.0, DeltaE = 0.1 \" runDOS dos.$name.in PROJWFC \" filpdos = '$name.pdos.dat' Emin = 5.0 Emax = 20.0, DeltaE = 0.1 \" runPROJWFC projwfc.$name.in Below is the plots of total and projected density of states. Also see bandstructure of Fe with and without SOC.","s":"Density of states calculation","u":"/espresso/hands-on/fe","h":"#density-of-states-calculation","p":39},{"i":46,"t":"Paramagnetic materials have fluctuating magnetic moments that may not be properly described DFT. One approach is to model paramagnetic materials in DFT calculation by building a large supercell and assign randomly oriented magnetic moments. Also note that DFT assumes zero temperature, so it makes sense to perform FM or AFM calculation for magnetic systems.","s":"Paramagnetism","u":"/espresso/hands-on/fe","h":"#paramagnetism","p":39},{"i":48,"t":"We can use XCrySDen to visualize the orientation of magnetic moments. XCrySDen cannot directly read the Quantum Espresso output files for magnetic moment vectors, instead we need to create the input .xsf file with magnetic moments as force vector. You can also change the background color from black from the Palette Menu which is located in the left of File menu. src/fe/fe.xsf # this is a specification for crystal structure CRYSTAL # primitive lattice vectors (in Angstroms) PRIMVEC 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 # conventional lattice vectors (in Angstroms) CONVVEC 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 0.0000000000 0.0000000000 0.0000000000 2.8681404710 # First number stands for number of atoms in primitive cell # the second number is always 1 for PRIMCOORD coordinates # followed by atomic coordinates (in Angstroms) and forces: # AtNum X Y Z Fx Fy Fz PRIMCOORD 2 1 26 0.0000000000 0.0000000000 0.0000000000 0.00 0.00 0.01 26 1.4340702350 1.4340702350 1.4340702350 0.00 0.00 -0.01 Open the file from XCrySDen Menu: File → Open Structure → Open XSF. Then go to Display menu and select Forces. If you want to adjust scaling for the force vectors, go to Modify → Force Settings and set suitable Length factor.","s":"Visualizing magnetic moments","u":"/espresso/hands-on/fe","h":"#visualizing-magnetic-moments","p":39},{"i":50,"t":"First we perform self consistent field calculation: mpirun -np 4 pw.x -i pw.scf.silicon_epsilon.in > pw.scf.silicon_epsilon.out src/silicon/pw.scf.silicon_epsilon.in &CONTROL calculation = 'scf', prefix = 'silicon', outdir = '/tmp/' pseudo_dir = '../pseudos/' verbosity = 'high' / &SYSTEM ibrav = 2, celldm(1) = 10.26, nat = 2, ntyp = 1, ecutwfc = 40 nbnd = 20 nosym = .TRUE. noinv = .TRUE. / &ELECTRONS mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS crystal 216 0.00000000 0.00000000 0.00000000 4.629630e-03 0.00000000 0.00000000 0.16666667 4.629630e-03 0.00000000 0.00000000 0.33333333 4.629630e-03 0.00000000 0.00000000 0.50000000 4.629630e-03 0.00000000 0.00000000 0.66666667 4.629630e-03 0.00000000 0.00000000 0.83333333 4.629630e-03 0.00000000 0.16666667 0.00000000 4.629630e-03 0.00000000 0.16666667 0.16666667 4.629630e-03 0.00000000 0.16666667 0.33333333 4.629630e-03 0.00000000 0.16666667 0.50000000 4.629630e-03 0.00000000 0.16666667 0.66666667 4.629630e-03 0.00000000 0.16666667 0.83333333 4.629630e-03 0.00000000 0.33333333 0.00000000 4.629630e-03 0.00000000 0.33333333 0.16666667 4.629630e-03 0.00000000 0.33333333 0.33333333 4.629630e-03 0.00000000 0.33333333 0.50000000 4.629630e-03 0.00000000 0.33333333 0.66666667 4.629630e-03 0.00000000 0.33333333 0.83333333 4.629630e-03 0.00000000 0.50000000 0.00000000 4.629630e-03 0.00000000 0.50000000 0.16666667 4.629630e-03 0.00000000 0.50000000 0.33333333 4.629630e-03 0.00000000 0.50000000 0.50000000 4.629630e-03 0.00000000 0.50000000 0.66666667 4.629630e-03 0.00000000 0.50000000 0.83333333 4.629630e-03 0.00000000 0.66666667 0.00000000 4.629630e-03 0.00000000 0.66666667 0.16666667 4.629630e-03 0.00000000 0.66666667 0.33333333 4.629630e-03 0.00000000 0.66666667 0.50000000 4.629630e-03 0.00000000 0.66666667 0.66666667 4.629630e-03 0.00000000 0.66666667 0.83333333 4.629630e-03 0.00000000 0.83333333 0.00000000 4.629630e-03 0.00000000 0.83333333 0.16666667 4.629630e-03 0.00000000 0.83333333 0.33333333 4.629630e-03 0.00000000 0.83333333 0.50000000 4.629630e-03 0.00000000 0.83333333 0.66666667 4.629630e-03 0.00000000 0.83333333 0.83333333 4.629630e-03 0.16666667 0.00000000 0.00000000 4.629630e-03 0.16666667 0.00000000 0.16666667 4.629630e-03 0.16666667 0.00000000 0.33333333 4.629630e-03 0.16666667 0.00000000 0.50000000 4.629630e-03 0.16666667 0.00000000 0.66666667 4.629630e-03 0.16666667 0.00000000 0.83333333 4.629630e-03 0.16666667 0.16666667 0.00000000 4.629630e-03 0.16666667 0.16666667 0.16666667 4.629630e-03 0.16666667 0.16666667 0.33333333 4.629630e-03 0.16666667 0.16666667 0.50000000 4.629630e-03 0.16666667 0.16666667 0.66666667 4.629630e-03 0.16666667 0.16666667 0.83333333 4.629630e-03 0.16666667 0.33333333 0.00000000 4.629630e-03 0.16666667 0.33333333 0.16666667 4.629630e-03 0.16666667 0.33333333 0.33333333 4.629630e-03 0.16666667 0.33333333 0.50000000 4.629630e-03 0.16666667 0.33333333 0.66666667 4.629630e-03 0.16666667 0.33333333 0.83333333 4.629630e-03 0.16666667 0.50000000 0.00000000 4.629630e-03 0.16666667 0.50000000 0.16666667 4.629630e-03 0.16666667 0.50000000 0.33333333 4.629630e-03 0.16666667 0.50000000 0.50000000 4.629630e-03 0.16666667 0.50000000 0.66666667 4.629630e-03 0.16666667 0.50000000 0.83333333 4.629630e-03 0.16666667 0.66666667 0.00000000 4.629630e-03 0.16666667 0.66666667 0.16666667 4.629630e-03 0.16666667 0.66666667 0.33333333 4.629630e-03 0.16666667 0.66666667 0.50000000 4.629630e-03 0.16666667 0.66666667 0.66666667 4.629630e-03 0.16666667 0.66666667 0.83333333 4.629630e-03 0.16666667 0.83333333 0.00000000 4.629630e-03 0.16666667 0.83333333 0.16666667 4.629630e-03 0.16666667 0.83333333 0.33333333 4.629630e-03 0.16666667 0.83333333 0.50000000 4.629630e-03 0.16666667 0.83333333 0.66666667 4.629630e-03 0.16666667 0.83333333 0.83333333 4.629630e-03 0.33333333 0.00000000 0.00000000 4.629630e-03 0.33333333 0.00000000 0.16666667 4.629630e-03 0.33333333 0.00000000 0.33333333 4.629630e-03 0.33333333 0.00000000 0.50000000 4.629630e-03 0.33333333 0.00000000 0.66666667 4.629630e-03 0.33333333 0.00000000 0.83333333 4.629630e-03 0.33333333 0.16666667 0.00000000 4.629630e-03 0.33333333 0.16666667 0.16666667 4.629630e-03 0.33333333 0.16666667 0.33333333 4.629630e-03 0.33333333 0.16666667 0.50000000 4.629630e-03 0.33333333 0.16666667 0.66666667 4.629630e-03 0.33333333 0.16666667 0.83333333 4.629630e-03 0.33333333 0.33333333 0.00000000 4.629630e-03 0.33333333 0.33333333 0.16666667 4.629630e-03 0.33333333 0.33333333 0.33333333 4.629630e-03 0.33333333 0.33333333 0.50000000 4.629630e-03 0.33333333 0.33333333 0.66666667 4.629630e-03 0.33333333 0.33333333 0.83333333 4.629630e-03 0.33333333 0.50000000 0.00000000 4.629630e-03 0.33333333 0.50000000 0.16666667 4.629630e-03 0.33333333 0.50000000 0.33333333 4.629630e-03 0.33333333 0.50000000 0.50000000 4.629630e-03 0.33333333 0.50000000 0.66666667 4.629630e-03 0.33333333 0.50000000 0.83333333 4.629630e-03 0.33333333 0.66666667 0.00000000 4.629630e-03 0.33333333 0.66666667 0.16666667 4.629630e-03 0.33333333 0.66666667 0.33333333 4.629630e-03 0.33333333 0.66666667 0.50000000 4.629630e-03 0.33333333 0.66666667 0.66666667 4.629630e-03 0.33333333 0.66666667 0.83333333 4.629630e-03 0.33333333 0.83333333 0.00000000 4.629630e-03 0.33333333 0.83333333 0.16666667 4.629630e-03 0.33333333 0.83333333 0.33333333 4.629630e-03 0.33333333 0.83333333 0.50000000 4.629630e-03 0.33333333 0.83333333 0.66666667 4.629630e-03 0.33333333 0.83333333 0.83333333 4.629630e-03 0.50000000 0.00000000 0.00000000 4.629630e-03 0.50000000 0.00000000 0.16666667 4.629630e-03 0.50000000 0.00000000 0.33333333 4.629630e-03 0.50000000 0.00000000 0.50000000 4.629630e-03 0.50000000 0.00000000 0.66666667 4.629630e-03 0.50000000 0.00000000 0.83333333 4.629630e-03 0.50000000 0.16666667 0.00000000 4.629630e-03 0.50000000 0.16666667 0.16666667 4.629630e-03 0.50000000 0.16666667 0.33333333 4.629630e-03 0.50000000 0.16666667 0.50000000 4.629630e-03 0.50000000 0.16666667 0.66666667 4.629630e-03 0.50000000 0.16666667 0.83333333 4.629630e-03 0.50000000 0.33333333 0.00000000 4.629630e-03 0.50000000 0.33333333 0.16666667 4.629630e-03 0.50000000 0.33333333 0.33333333 4.629630e-03 0.50000000 0.33333333 0.50000000 4.629630e-03 0.50000000 0.33333333 0.66666667 4.629630e-03 0.50000000 0.33333333 0.83333333 4.629630e-03 0.50000000 0.50000000 0.00000000 4.629630e-03 0.50000000 0.50000000 0.16666667 4.629630e-03 0.50000000 0.50000000 0.33333333 4.629630e-03 0.50000000 0.50000000 0.50000000 4.629630e-03 0.50000000 0.50000000 0.66666667 4.629630e-03 0.50000000 0.50000000 0.83333333 4.629630e-03 0.50000000 0.66666667 0.00000000 4.629630e-03 0.50000000 0.66666667 0.16666667 4.629630e-03 0.50000000 0.66666667 0.33333333 4.629630e-03 0.50000000 0.66666667 0.50000000 4.629630e-03 0.50000000 0.66666667 0.66666667 4.629630e-03 0.50000000 0.66666667 0.83333333 4.629630e-03 0.50000000 0.83333333 0.00000000 4.629630e-03 0.50000000 0.83333333 0.16666667 4.629630e-03 0.50000000 0.83333333 0.33333333 4.629630e-03 0.50000000 0.83333333 0.50000000 4.629630e-03 0.50000000 0.83333333 0.66666667 4.629630e-03 0.50000000 0.83333333 0.83333333 4.629630e-03 0.66666667 0.00000000 0.00000000 4.629630e-03 0.66666667 0.00000000 0.16666667 4.629630e-03 0.66666667 0.00000000 0.33333333 4.629630e-03 0.66666667 0.00000000 0.50000000 4.629630e-03 0.66666667 0.00000000 0.66666667 4.629630e-03 0.66666667 0.00000000 0.83333333 4.629630e-03 0.66666667 0.16666667 0.00000000 4.629630e-03 0.66666667 0.16666667 0.16666667 4.629630e-03 0.66666667 0.16666667 0.33333333 4.629630e-03 0.66666667 0.16666667 0.50000000 4.629630e-03 0.66666667 0.16666667 0.66666667 4.629630e-03 0.66666667 0.16666667 0.83333333 4.629630e-03 0.66666667 0.33333333 0.00000000 4.629630e-03 0.66666667 0.33333333 0.16666667 4.629630e-03 0.66666667 0.33333333 0.33333333 4.629630e-03 0.66666667 0.33333333 0.50000000 4.629630e-03 0.66666667 0.33333333 0.66666667 4.629630e-03 0.66666667 0.33333333 0.83333333 4.629630e-03 0.66666667 0.50000000 0.00000000 4.629630e-03 0.66666667 0.50000000 0.16666667 4.629630e-03 0.66666667 0.50000000 0.33333333 4.629630e-03 0.66666667 0.50000000 0.50000000 4.629630e-03 0.66666667 0.50000000 0.66666667 4.629630e-03 0.66666667 0.50000000 0.83333333 4.629630e-03 0.66666667 0.66666667 0.00000000 4.629630e-03 0.66666667 0.66666667 0.16666667 4.629630e-03 0.66666667 0.66666667 0.33333333 4.629630e-03 0.66666667 0.66666667 0.50000000 4.629630e-03 0.66666667 0.66666667 0.66666667 4.629630e-03 0.66666667 0.66666667 0.83333333 4.629630e-03 0.66666667 0.83333333 0.00000000 4.629630e-03 0.66666667 0.83333333 0.16666667 4.629630e-03 0.66666667 0.83333333 0.33333333 4.629630e-03 0.66666667 0.83333333 0.50000000 4.629630e-03 0.66666667 0.83333333 0.66666667 4.629630e-03 0.66666667 0.83333333 0.83333333 4.629630e-03 0.83333333 0.00000000 0.00000000 4.629630e-03 0.83333333 0.00000000 0.16666667 4.629630e-03 0.83333333 0.00000000 0.33333333 4.629630e-03 0.83333333 0.00000000 0.50000000 4.629630e-03 0.83333333 0.00000000 0.66666667 4.629630e-03 0.83333333 0.00000000 0.83333333 4.629630e-03 0.83333333 0.16666667 0.00000000 4.629630e-03 0.83333333 0.16666667 0.16666667 4.629630e-03 0.83333333 0.16666667 0.33333333 4.629630e-03 0.83333333 0.16666667 0.50000000 4.629630e-03 0.83333333 0.16666667 0.66666667 4.629630e-03 0.83333333 0.16666667 0.83333333 4.629630e-03 0.83333333 0.33333333 0.00000000 4.629630e-03 0.83333333 0.33333333 0.16666667 4.629630e-03 0.83333333 0.33333333 0.33333333 4.629630e-03 0.83333333 0.33333333 0.50000000 4.629630e-03 0.83333333 0.33333333 0.66666667 4.629630e-03 0.83333333 0.33333333 0.83333333 4.629630e-03 0.83333333 0.50000000 0.00000000 4.629630e-03 0.83333333 0.50000000 0.16666667 4.629630e-03 0.83333333 0.50000000 0.33333333 4.629630e-03 0.83333333 0.50000000 0.50000000 4.629630e-03 0.83333333 0.50000000 0.66666667 4.629630e-03 0.83333333 0.50000000 0.83333333 4.629630e-03 0.83333333 0.66666667 0.00000000 4.629630e-03 0.83333333 0.66666667 0.16666667 4.629630e-03 0.83333333 0.66666667 0.33333333 4.629630e-03 0.83333333 0.66666667 0.50000000 4.629630e-03 0.83333333 0.66666667 0.66666667 4.629630e-03 0.83333333 0.66666667 0.83333333 4.629630e-03 0.83333333 0.83333333 0.00000000 4.629630e-03 0.83333333 0.83333333 0.16666667 4.629630e-03 0.83333333 0.83333333 0.33333333 4.629630e-03 0.83333333 0.83333333 0.50000000 4.629630e-03 0.83333333 0.83333333 0.66666667 4.629630e-03 0.83333333 0.83333333 0.83333333 4.629630e-03 Especially, notice following changes: nbnd = 20 nosym = .true. noinv = .true. We turn off the automatic reduction of k-points that pw.x does by using crystal symmetries (nosym = .true. and noinv = .true.). This is because epsilon.x does not recognize crystal symmetries, therefore the entire list of k-points in the grid is needed. Secondly, we calculate a larger number of bands (20), since we are interested in interband transitions. Also, note that epsilon.x doesn't support the reduction of the k-points grid into the irreducible Brillouin zone, so the PW runs must be performed with a uniform k-points grid and all k-points weights must be equal to each other, i.e. in the k-points card the k-points coordinates must be given manually in crystal or alat or bohr, but not with the automatic option. However, the automatic k-points option seems to work. If necessary, we can perform nscf calculation with finer k-grid. Next step is to prepare the input file for epsilon.x: src/silicon/epsilon.si.in &inputpp outdir = \"/tmp/\" prefix = \"silicon\" calculation = \"eps\" / &energy_grid smeartype = \"gauss\" intersmear = 0.2 wmin = 0.0 wmax = 30.0 nw = 500 / The variables smeartype and intersmear define the numerical approximation used to represent the Dirac delta functions in the expression for ϵ2\\epsilon_2ϵ2​ given above. The variables wmin, wmax and nw define the energy grid for the dielectric function. All the energy variables are in eV. mpirun -np 4 epsilon.x -i epsilon.si.in > epsilon.si.out We will see the results are saved in separate .dat files. We can plot the real (ϵ1\\epsilon_1ϵ1​) and imaginary (ϵ2\\epsilon_2ϵ2​) parts of dielectric constants: import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline plt.rcParams[\"figure.dpi\"]=150 plt.rcParams[\"figure.facecolor\"]=\"white\" data_r = np.loadtxt('../src/silicon/epsr_silicon.dat') data_i = np.loadtxt('../src/silicon/epsi_silicon.dat') energy_r, epsilon_r = data_r[:, 0], data_r[:, 2] energy_i, epsilon_i = data_i[:, 0], data_i[:, 2] plt.plot(energy_r, epsilon_r, lw=1, label=\"$\\\\epsilon_1$\") plt.plot(energy_i, epsilon_i, lw=1, label=\"$\\\\epsilon_2$\") plt.xlim(0, 15) plt.xlabel(\"Energy (eV)\") plt.ylabel(\"$\\\\epsilon_1~/~\\\\epsilon_2$\") plt.legend(frameon=False) plt.show() warning Ultra-soft pseudopotentials do not work with epsilon.x. Also note that the above example is not tested against the k-mesh. We usually need finer k-mesh for ϵ\\epsilonϵ to converge. By default the maximum number of k-points is set to 40000 in Quantum Espresso, if we need more k-points, we can change Modules/parameters.f90 and recompile Quantum Espresso.","s":"Dielectric constant","u":"/espresso/hands-on/epsilon","h":"","p":49},{"i":52,"t":"Epsilon.x manual","s":"Resources","u":"/espresso/hands-on/epsilon","h":"#resources","p":49},{"i":54,"t":"Electronic structure for transition metals (with localized ddd or fff electrons) is not accurately described by standard DFT, and therefore the need for DFT+U formulation. &SYSTEM ... lda_plus_u = .TRUE. Hubbard_u(i) = 2.0 ... / Here i refers to the atomic index in the &ATOMIC_SPECIES card corresponding to each ntyp. We can specify Hubbard_u(i) corresponding to more than one atom in separate lines. There is also Ueff=U−JU_{eff} = U - JUeff​=U−J implementation in QE. JJJ represents on-site exchange interaction. Number of JJJ terms depends on the manifold of localized electrons. For ppp, we have 1; for ddd, we have 2; and for fff, we have 3 terms. ... lda_plus_u = .TRUE. lda_plus_u_kind = 1 Hubbard_u(i) = U Hubbard_J(k, i) = J_{ki} ... COMMON ERRORS If you add Hubbard_u for elements that is not implemented to have UUU term in QE, you might see a \"pseudopotential not yet inserted\" error.","s":"DFT+U calculation","u":"/espresso/hands-on/dft-u","h":"","p":53},{"i":56,"t":"Starting from Quantum Espresso version 7.1, there are changes to input syntax for DFT+U calculations. In the new version, instead of defining the necessary DFT+U parameters, now there is a new Hubbard card. &system ... - lda_plus_u = .true., - lda_plus_u_kind = 0, - U_projection_type = 'atomic', - Hubbard_U(1) = 4.6 - Hubbard_U(2) = 4.6 ... / + HUBBARD (ortho-atomic) + U Fe1-3d 4.6 + U Fe2-3d 4.6 Please refer to the qe-x.x/Doc/Hubbard_input.pdf for details.","s":"Changes to input syntax in v7.1","u":"/espresso/hands-on/dft-u","h":"#changes-to-input-syntax-in-v71","p":53},{"i":58,"t":"We will first perform the standard DFT calculation. Perform the SCF calculation: pw.x -in feo_scf.in > feo_scf.out Perform NSCF calculation with denser k-grid: pw.x -in feo_nscf.in > feo_nscf.out Perform P-DOS calculation: projwfc.x -in feo_projwfc.in > feo_projwfc.out This gives us metallic density of states. In practice we get insulating FeO.","s":"DFT calculation for FeO","u":"/espresso/hands-on/dft-u","h":"#dft-calculation-for-feo","p":53},{"i":60,"t":"src/FeO/feo_hp.in &inputhp prefix = 'FeO' outdir = './tmp/' nq1 = 1, nq2 = 1, nq3 = 1 / Perform a linear-response calculation using hp.x program: hp.x -in feo_hp.in > feo_hp.out Check the file FeO.Hubbard_parameters.dat. info We need to check the convergence against q-mesh (as well as k-mesh in SCF calculation). Here 1×1×11\\times 1\\times 11×1×1 mesh is used. Important: lda_plus_u must be set to .true. during the SCF calculation, UUU may be set to zero. We can update the obtained UUU value in our SCF calculation, and repeat linear response calculation until we have reached self consistency in UUU value. To go even further one can check the convergence of geometry during UUU updates. There is also inter-site Hubbard correction DFT+U+V calculation. The results could be more closer to hybrid functionals like GW. The VVV can also be calculated using Quantum Espresso hp.x code. Obtained value of UUU depends on pseudopotential, Hubbard manifold (whether atomic, ortho-atomic etc.). danger The above hp.x code is not suitable for closed cell systems (e.g., fully occupied d-shell element), in such cases this linear response method gives unrealistically large UUU value.","s":"Calculating Hubbard U","u":"/espresso/hands-on/dft-u","h":"#calculating-hubbard-u","p":53},{"i":61,"t":"We repeat the calculation after setting in the &SYSTEM card: Hubbard_U(1) = 4.6 Hubbard_U(2) = 4.6 We repeat the above calculation and plot the results. Now we find insulating ground state. info U_projection_type = 'ortho-atomic' might give more realistic result than the default 'atomic'. When performing DFT+UDFT+UDFT+U calculation, the ground state might get stuck in a local minimum, in such cases we need to provide starting_ns_eigenvalue to help calculation reach desired/actual ground state. Please see these slides by Dr. Iurii Timrov for a relevant example. tip Here we have plotted the lpdos (local density of states). If we want to know the contribution of dz2,dyz,dx2−z2d_{z^2}, d_{yz}, d_{x^2-z^2}dz2​,dyz​,dx2−z2​ ect., we can find them from the pdos columns. Also there arise important Lowdin charges information in the feo_projwfc.out file.","s":"DFT+U calculation","u":"/espresso/hands-on/dft-u","h":"#dftu-calculation","p":53},{"i":63,"t":"Hands-on DFT+U by Iurii Timrov and Matteo Cococcioni Hubbard parameter calculation","s":"Resources","u":"/espresso/hands-on/dft-u","h":"#resources","p":53},{"i":65,"t":"Here we will calculate Fermi surface of copper. First step is to perform self- consistent field calculation. src/cu/pw.scf.cu.in &control calculation = \"scf\", prefix = \"cu\", pseudo_dir = \"../pseudos/\", outdir = \"/tmp/cu/\" / &system ibrav = 2, celldm(1) = 6.678, nat = 1, ntyp = 1, ecutwfc = 40, ecutrho = 300, occupations = \"smearing\", smearing = \"mp\", degauss = 0.01, nbnd = 16 / &electrons conv_thr = 1e-9, / ATOMIC_SPECIES Cu 63.546 Cu_ONCV_PBE-1.0.oncvpsp.upf ATOMIC_POSITIONS alat Cu 0.00 0.00 0.00 K_POINTS automatic 8 8 8 1 1 1 mpirun -np 4 pw.x -in pw.scf.cu.in > pw.scf.cu.out Next we perform bands calculation over dense uniform k-grid: src/cu/pw.bands.cu.in &control calculation = \"bands\", prefix = \"cu\", pseudo_dir = \"../pseudos/\", outdir = \"/tmp/cu/\" / &system ibrav = 2, celldm(1) = 6.678, nat = 1, ntyp = 1, ecutwfc = 40, ecutrho = 300, occupations = \"smearing\", smearing = \"mp\", degauss = 0.01, nbnd = 16 / &electrons conv_thr = 1e-9, / ATOMIC_SPECIES Cu 63.546 Cu_ONCV_PBE-1.0.oncvpsp.upf ATOMIC_POSITIONS alat Cu 0.00 0.00 0.00 K_POINTS automatic 30 30 30 0 0 0 mpirun -np 4 pw.x -in pw.bands.cu.in > pw.bands.cu.out Finally, we process the data with fs.x post processing tool. Below is the input file: src/cu/fs.cu.in &fermi outdir = \"/tmp/cu/\" prefix = \"cu\" / mpirun -np 4 fs.x -in fs.cu.in > fs.cu.out We can visualize the output file cu_fs.bxsf using xcrysdens program: xcrysden --bxsf cu_fs.bxsf","s":"Fermi Surface","u":"/espresso/hands-on/fermi-surface","h":"","p":64},{"i":67,"t":"Now that we have calculated the bandstructure of silicon (semiconductor) and aluminum (metal), let us proceed with a compound which has two different atoms. We follow the steps like before: First check the lattice constant with cell relaxation according to our chosen pseudo potential. We use that lattice constant in our next steps. Our lattice constant = 10.6867 * 0.508176602 / 0.5 = 10.861462. pw.x < pw.relax.GaAs.in > pw.relax.GaAs.out Perform self consistent field calculation: pw.x < pw.scf.GaAs.in > pw.scf.GaAs.out Give denser k-points and perform non-self consistent calculation. This step is only necessary if you need to obtain density of states. pw.x < pw.nscf.GaAs.in > pw.nscf.GaAs.out Perform bands calculation pw.x < pw.bands.GaAs.in > pw.bands.GaAs.out Post process the data and plot the bandstructure. bands.x < pp.bands.GaAs.in > pp.bands.GaAs.out If everything goes well, you will get the bandstructure as below: Warning Sometimes a calculation with the same inputs converges in one computer, while fails in another due to library configuration or even due to floating point approximations. The final output numbers will always vary slightly for different machines, or even among different runs in the same machine. Also check the Quantum Espresso version for reproducibility. Also see the bandstructure of GaAs with SOC.","s":"Bandstructure of GaAs","u":"/espresso/hands-on/GaAs","h":"","p":66},{"i":69,"t":"Here we will calculate k-resolved density of states for silicon. First we begin with self consistent field calculation. Here is the input: pw.x -inp si_scf.in > si_scf.out Followed by the bands calculation. Note that for bands calculation I have doubled the number of k-points compared to our previous bands calculation. pw.x -inp si_bands.in > si_bands.out Calculate the orbital projections with k-resolved information: src/silicon/si_projwfc.in &projwfc outdir = './tmp/' prefix = 'silicon' ngauss = 0 degauss = 0.036748 DeltaE = 0.005 kresolveddos = .true. filpdos = 'silicon.k' / projwfc.x -inp si_projwfc.in > si_projwfc.out This will give separate orbital projections, as well as total sum for k-resolved DOS. Make plots: notebooks/silicon-kpdos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np import zipfile %matplotlib inline # data file was compressed to reduce file size zipobj = zipfile.ZipFile('../src/silicon/silicon.k.pdos_tot.zip', 'r') zipdata = zipobj.open('silicon.k.pdos_tot') data = np.loadtxt(zipdata) k = np.unique(data[:, 0]) # k values e = np.unique(data[:, 1]) # dos energy values dos = np.zeros([len(k), len(e)]) for i in range(len(data)): e_index = int(i % len(e)) k_index = int(data[i][0] - 1) dos[k_index, e_index] = data[i][2] plt.pcolormesh(k, e, dos.T, cmap='magma', shading='auto') # plt.ylim(-2, 10) plt.xticks([]) plt.ylabel('Energy (eV)') plt.xticks([]) plt.gcf().text(0.12, 0.06, 'L', fontsize=16, fontweight='normal') plt.gcf().text(0.29, 0.06, '$\\Gamma$', fontsize=16, fontweight='normal') plt.gcf().text(0.55, 0.06, 'X', fontsize=16, fontweight='normal') plt.gcf().text(0.63, 0.06, 'U', fontsize=16, fontweight='normal') plt.gcf().text(0.892, 0.06, '$\\Gamma$', fontsize=16, fontweight='normal') plt.axvline(21, c='yellow', lw=1, alpha=0.5) plt.axvline(51, c='yellow', lw=1, alpha=0.5) plt.axvline(61, c='yellow', lw=1, alpha=0.5) plt.show() info If you are using ibrav=0, you can calculate projwfc with lsym=.false. option. If we have contribution from multiple orbitals, we can sum desired projections using sumpdos.x program. For example: sumpdos.x *\\(Cl\\)*\\(p\\) > Cl_2p_tot.dat This way we can plot different orbital projections along with energy and k-resolution.","s":"k-resolved DOS","u":"/espresso/hands-on/kpdos","h":"","p":68},{"i":71,"t":"I am following this example from the ICTP online school 2021. Graphene is single layer of carbon atoms. First perform the self consistent field calculation to obtain the Kohn-Sham orbitals. Please check the input files in GitHub repository. Run pw.x: pw.x -i graphene_scf.in > graphene_scf.out Next increase the k-grid, and perform the non-self-consistent field calculation. pw.x -i graphene_nscf.in > graphene_nscf.out","s":"DOS and Bandstructure of Graphene","u":"/espresso/hands-on/graphene","h":"","p":70},{"i":73,"t":"dos.x -i graphene_dos.in > graphene_dos.out","s":"DOS calculation","u":"/espresso/hands-on/graphene","h":"#dos-calculation","p":70},{"i":75,"t":"First run the bands calculation for given k-path: pw.x -i graphene_bands.in > graphene_bands.out Followed by the postprocessing to collect the bands: bands.x -i graphene_bands_pp.in > graphene_bands_pp.out Make plots: notebooks/graphene.ipynb import numpy as np import matplotlib.pyplot as plt data = np.loadtxt('../src/graphene/graphene_bands.dat.gnu') k = np.unique(data[:, 0]) bands = np.reshape(data[:, 1], (-1, len(k))) for band in range(len(bands)): plt.plot(k, bands[band, :], linewidth=1, alpha=0.5, color='k') plt.xlim(min(k), max(k)) # Fermi energy plt.axhline(0.921, linestyle=(0, (8, 10)), linewidth=0.75, color='k', alpha=0.5) # High symmetry k-points (check bands_pp.out) plt.axvline(0.6667, linewidth=0.75, color='k', alpha=0.5) plt.axvline(1, linewidth=0.75, color='k', alpha=0.5) # text labels plt.xticks(ticks= [0, 0.6667, 1, 1.5774], labels=['$\\Gamma$', 'K', 'M', '$\\Gamma$']) plt.ylabel(\"Energy (eV)\") plt.show()","s":"Bandstructure calculation","u":"/espresso/hands-on/graphene","h":"#bandstructure-calculation","p":70},{"i":77,"t":"We will start from the relaxation calculation, and use the relaxed structure for md calculation. Below in the input file for md calculation: src/H2O-md-pw/pw.md.h2o.in &control calculation = 'md' restart_mode = 'from_scratch' prefix = 'h2o' outdir = './tmp/' pseudo_dir = '../pseudos/' tstress = .true. tprnfor = .true. ! about 1 fs; 1 a.u. = 0.048378 fs dt = 20 nstep = 100 / &system ibrav = 1 celldm(1) = 15 nat = 3 ntyp = 2, ecutwfc = 40 nosym = .true. / &electrons conv_thr = 1e-8 / &ions pot_extrapolation = 'second-order' wfc_extrapolation = 'second-order' ion_temperature = 'initial' tempw = 300 / ATOMIC_SPECIES H 1.00784 H_ONCV_PBE-1.0.oncvpsp.upf O 15.999 O.pbe-n-kjpaw_psl.0.1.UPF ! relaxed structure ATOMIC_POSITIONS (angstrom) O 5.0000068025 4.8011777008 4.9999667189 H 4.9999962341 5.3994076541 5.7670041300 H 4.9999969634 5.3994146451 4.2330291511 K_POINTS automatic 1 1 1 0 0 0 Quantum ESPRESSO output file can be loaded in Xcrysden for visualization.","s":"Molecular Dynamics (using pw.x)","u":"/espresso/hands-on/molecular-dynamics-pw","h":"","p":76},{"i":79,"t":"We prepare the input file pw_scf_ni.in and run the calculation: mpirun -np 8 pw.x -i pw_scf_ni.in > pw_scf_ni.out Prepare the input file for bands calculation pw_bands_ni.in with our desired k-path and run: mpirun -np 8 pw.x -i pw_bands_ni.in > pw_bands_ni.out Now we perform the bands.x calculation with spin_component=1 to process only the spin up bands: src/ni/bands_ni_up.in &BANDS outdir='./tmp/', prefix='ni', filband='ni_bands_up.dat', spin_component = 1, / Run the calculation: mpirun -np 8 bands.x -i bands_ni_up.in > bands_ni_up.out Similarly, we process the spin down bands spin_component=2 and plot them.","s":"Spin polarized bandstructure calculation for nickel","u":"/espresso/hands-on/ni","h":"","p":78},{"i":81,"t":"Here we continue with our Aluminum example. Often it is needed to know the contribution from each individual atoms and/or each of their orbital contributions. We can achieve that using projwfc.x code. First, we must perform the self consistent field calculation followed by the non-self consistent field calculation with denser k-points. pw.x < al_scf.in > al_scf.out pw.x < al_nscf.in > al_nscf.out Then we prepare the input file for projwfc.x: src/al/al_projwfc.in &PROJWFC prefix= 'al', outdir= '/tmp/', filpdos= 'al_pdos.dat' / Perform the calculation: projwfc.x < al_projwfc.in > al_projwfc.out Output data format: the DOS values are written in the file {filpdos}.pdos_atm#N(X)_wfc#M(l), where N is atom number, X is atom symbol, M is wfc number, and l=s,p,d,f one file for each atomic wavefunction read from pseudopotential file. The header of file looks like (for spin polarized calculations, we have separate up and down columns): E LDOS(E) PDOS_1(E) ... PDOS_{2l+1}(E) LDOS=∑m=12l+1PDOSm(E)LDOS = \\sum\\limits_{m=1}^{2l+1} PDOS_m (E)LDOS=m=1∑2l+1​PDOSm​(E) PDOSm(E)→PDOS_m (E) \\rightarrowPDOSm​(E)→ projected DOS on atomic wfc with component mmm. Orbital order: for l=1l=1l=1: pz (m=0)p_z~(m=0)pz​ (m=0) pxp_xpx​ (real combination of m=±1m=\\pm 1m=±1 with cosine) pyp_ypy​ (real combination of m=±1m=\\pm 1m=±1 with sine) for l=2l=2l=2: dz2 (m=0)d_{z^2}~(m=0)dz2​ (m=0) dzxd_{zx}dzx​ (real combination of m=±1m=\\pm 1m=±1 with cosine) dzyd_{zy}dzy​ (real combination of m=±1m=\\pm 1m=±1 with sine) dx2−y2d_{x^2-y^2}dx2−y2​ (real combination of m=±2m=\\pm 2m=±2 with cosine) dxyd_{xy}dxy​ (real combination of m=±2m=\\pm 2m=±2 with sine) For more details and PROJWFC output format, please consult the documentation here. Let's create our plots: src/notebooks/al-pdos.ipynb import matplotlib.pyplot as plt from matplotlib import rcParamsDefault import numpy as np %matplotlib inline # load data def data_loader(fname): import numpy as np data = np.loadtxt(fname) energy = data[:, 0] pdos = data[:, 1] # ldos col, total contribution for a given orbital return energy, pdos energy, pdos_s = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#1(s)') _, pdos_p = data_loader('../src/al/al_pdos.dat.pdos_atm#1(Al)_wfc#2(p)') _, pdos_tot = data_loader('../src/al/al_pdos.dat.pdos_tot') # make plots plt.figure(figsize = (8, 4)) plt.plot(energy, pdos_s, linewidth=0.75, color='#006699', label='s-orbital') plt.plot(energy, pdos_p, linewidth=0.75, color='r', label='p-orbital') plt.plot(energy, pdos_tot, linewidth=0.75, color='k', label='total') plt.yticks([]) plt.xlabel('Energy (eV)') plt.ylabel('DOS') plt.axvline(x= 7.9421, linewidth=0.5, color='k', linestyle=(0, (8, 10))) plt.xlim(-5, 27) plt.ylim(0, ) plt.fill_between(energy, 0, pdos_s, where=(energy < 7.9421), facecolor='#006699', alpha=0.25) plt.fill_between(energy, 0, pdos_p, where=(energy < 7.9421), facecolor='r', alpha=0.25) plt.fill_between(energy, 0, pdos_tot, where=(energy < 7.9421), facecolor='k', alpha=0.25) # plt.text(6.5, 0.52, 'Fermi energy', fontsize= small, rotation=90) plt.legend(frameon=False) plt.show() Here is how our projected density of states plot looks like: We can perform sums of specific atom or orbital contributions using sumpdos.x code if there are multiple sss or ppp orbitals: sumpdos.x *\\(Al\\)* > atom_Al_tot.dat sumpdos.x *\\(Al\\)*\\(s\\) > atom_Al_s.dat sumpdos.x *\\(Al\\)*\\(p\\) > atom_Al_p.dat","s":"Projected Density of States","u":"/espresso/hands-on/pdos","h":"","p":80},{"i":83,"t":"We need to provide various important parameters for the self consistent calculation (solves the Kohn-Sham equation self-consistently) via an input file. In QE input files, there are NAMELISTS and INPUT_CARDS. NAMELISTS variables have default values, and new values can be provided as required for a specific calculation. The variables can be declared in any specific order. On the other hand, the variables in the INPUT_CARDS has always to be specified and in specific order. Logically independent INPUT_CARDS may be organized in any order. There are three mandatory NAMELISTS in PWscf: (1) &CONTROL: specifies the flux of computation, (2) &SYSTEM: specifies the system, and (3) &ELECTRONS: specifies the algorithms used to solve the Kohn-Sham equation. There are two other NAMELISTS: &IONS and &CELLS, which need to be specified depending on the calculation. Three INPUT_CARDS: ATOMIC_SPECIES, ATOMIC_POSITIONS, and K_POINTS in PWscf are mandatory. There are few others that must be provided in certain calculations. Below is our input file pw.scf.silicon.in for silicon in standard diamond (FCC) structure. Note that Quantum ESPRESSO uses primitive unit cell when CELL_PARAMETERS are not provided. One can use any other type of cell e.g., conventional unit cell or supercell by specifying corresponding CELL_PARAMETERS and ATOMIC_POSITIONS.The input files are typically named with .in prefix, while output files are named with .out prefix for their easier identification. The input parameters are organized in &namelists followed by their fields or cards. The &control, &system, and &electrons namelists are required. There are also optional &cell and &ions, you must provide them if your calculation require them. Most parameters in the namelists have default values (which may or may not suit your needs), however some variables you must always provide. Comment lines can be added with lines starting with a ! like in FORTRAN. Also, parameter names are not case-sensitive as in FORTRAN, i.e., &control and &CONTROL are the same. src/silicon/pw.scf.silicon.in &CONTROL ! we want to perform self consistent field calculation calculation = 'scf', ! prefix is reference to the output files prefix = 'silicon', ! output directory. Note that it is deprecated. outdir = './tmp/' ! directory for the pseudo potential directory pseudo_dir = '../pseudos/' ! verbosity high will give more details on the output file verbosity = 'high' / &SYSTEM ! Bravais lattice index, which is 2 for FCC structure ibrav = 2, ! Lattice constant in BOHR celldm(1) = 10.26, ! number of atoms in an unit cell nat = 2, ! number of different types of atom in the cell ntyp = 1, ! kinetic energy cutoff for wavefunction in Ry ecutwfc = 30 ! number of bands to calculate nbnd = 8 / &ELECTRONS ! Mixing factor used in the self-consistent method mixing_beta = 0.6 / ATOMIC_SPECIES Si 28.086 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.0 0.0 0.0 Si 0.25 0.25 0.25 K_POINTS (automatic) 6 6 6 0 0 0 I am using the pseudo potential file (Si.pz-vbc.UPF) downloaded from Quantum Espresso Website. You must read the PWscf user manual for in-depth understanding. Check the qe-x.x/PW/Doc/ folder under your installation directory. Also see INPUT_PW.html describing various input parameters. PW stands for plane waves. Run pw.x in self consistent mode for silicon. pw.x < pw.scf.silicon.in > pw.scf.silicon.out # For parallel execution mpirun -np 4 pw.x -inp pw.scf.silicon.in > pw.scf.silicon.out note I have added the Quantum ESPRESSO executable directory to the PATH environment variable in bash/zsh profile, otherwise we have to type the full path of pw.x executable location. Now let's look at the output file pw.scf.silicon.out and see how the convergence is reached: grep -e 'total energy' -e estimate pw.scf.silicon.out and you should see something like this: total energy = -15.85014573 Ry Harris-Foulkes estimate = -15.86899637 Ry estimated scf accuracy < 0.06093037 Ry total energy = -15.85194177 Ry Harris-Foulkes estimate = -15.85292281 Ry estimated scf accuracy < 0.00462014 Ry total energy = -15.85218359 Ry Harris-Foulkes estimate = -15.85220235 Ry estimated scf accuracy < 0.00011293 Ry ! total energy = -15.85219789 Ry Harris-Foulkes estimate = -15.85219831 Ry estimated scf accuracy < 0.00000099 Ry The total energy is the sum of the following terms: It is important to note that the absolute value of DFT total energy is not with respect to the vacuum reference, and depends on the chosen pseudopotential. The meaningful measure is the difference in total energy, where various offsets cancel out. note In the above calculation, if you check the output file pw.scf.silicon.out, you will find: highest occupied, lowest unoccupied level (eV): 6.2117 6.8442. Therefore, the bandgap is 0.6325 eV, which is an underestimation of actual bandgap (1.12 eV). Tips on convergence Reduce mixing_beta value, especially if there is an oscillation around the convergence energy. If it is a metallic system, use smearing and degauss. In this case, the SCF accuracy gradually goes down then suddenly increases (due to slight change in Fermi energy highest occupied/ lowest unoccupied levels change). Increase energy and charge density cutoffs (make sure they are sufficient). Certain pseudo potential files have issues, you may try with pseudo potentials from different libraries. Suggested values for the conv_thr: for energy and eigenvalues (scf calculation) 1.0d-7, for forces (relax calculation) 1.0d-8, for stress (vc-relax calculation) 1.0d-9 Ry. For certain calculation convergence might be very slow for the first iteration, one can start the calculation with a higher threshold, after few iterations reduce it and restart the calculation. There are several other important information is printed on the output file. Exchange correlation used in the calculation: Exchange-correlation= SLA PZ NOGX NOGC Where SLA → Slater exchange; PZ → Perdew-Zunger parametrization of the LDA; NOGX and NOGC indicates that density gradients are not taken into account. We can see the total number of plane waves (1067) uses in our calculation: Parallelization info -------------------- sticks: dense smooth PW G-vecs: dense smooth PW Min 108 108 34 1489 1489 266 Max 109 109 35 1492 1492 267 Sum 433 433 139 5961 5961 1067 Number of Kohn-Sham states: number of electrons = 8.00 number of Kohn-Sham states= 8 In our calculation we have specified the number of bands = 8. Otherwise, there would be 4 bands for 8 electrons in case of non spin-polarized systems.","s":"Self consistent field calculation for silicon","u":"/espresso/hands-on/scf","h":"","p":82},{"i":85,"t":"https://www.quantum-espresso.org/Doc/pw_user_guide/ Quantum Espresso Input Generator (can help creating QE input files)","s":"Resources","u":"/espresso/hands-on/scf","h":"#resources","p":82},{"i":87,"t":"In Quantum Espresso, phonon dispersion is calculated using ph.x program, which is implementation of density functional perturbation theory (DFPT). Here are the steps for calculating phonon dispersion: (1) perform SCF calculation using pw.x src/GaAs-phonon/pw.scf.GaAs.in &control calculation = 'scf' prefix = 'GaAs' pseudo_dir = '../pseudos/' outdir = './tmp/' verbosity = 'high' wf_collect = .true. / &system ibrav = 2 celldm(1) = 10.861462 nat = 2 ntyp = 2 ecutwfc = 80 ecutrho = 640 / &electrons mixing_mode = 'plain' mixing_beta = 0.7 conv_thr = 1.0e-8 / ATOMIC_SPECIES Ga 69.723 Ga.pbe-dn-kjpaw_psl.1.0.0.UPF As 74.921595 As.nc.z_15.oncvpsp3.dojo.v4-std.upf ATOMIC_POSITIONS Ga 0.00 0.00 0.00 As 0.25 0.25 0.25 K_POINTS {automatic} 8 8 8 0 0 0 We perform the SCF calculation: mpirun -np 4 pw.x -i pw.scf.GaAs.in > pw.scf.GaAs.out info Usually higher energy cutoff values are used for phonon calculation to get better accuracy. In case of two dimensional systems, use assume_isolated = '2D' in the SYSTEM namelist to avoid negative or imaginary acoustic frequencies near Γ\\GammaΓ point. Read more here. (2) calculate the dynamical matrix on a uniform mesh of q-points using ph.x src/GaAs-phonon/ph.GaAs.in &INPUTPH outdir = './tmp/' prefix = 'GaAs' tr2_ph = 1d-14 ldisp = .true. ! recover = .true. nq1 = 6 nq2 = 6 nq3 = 6 fildyn = 'GaAs.dyn' / Run the calculation: mpirun -np 4 ph.x -i ph.GaAs.in > ph.GaAs.out The above calculation is computationally demanding. Our example calculation took about a whole day on a 2.6 GHz quad core processor. info You can restart an interrupted ph.x calculation with recover = .true. in the INPUTPH namelist. You can cleanly exit an ongoing calculation by creating an empty file with name {prefix}.EXIT. (3) perform inverse Fourier transform of the dynamical matrix to obtain inverse Fourier components in real space using q2r.x. Below is our input file: src/GaAs-phonon/q2r.GaAs.in &INPUT fildyn = 'GaAs.dyn' zasr = 'crystal' flfrc = 'GaAs.fc' / mpirun -np 4 q2r.x -i q2r.GaAs.in > q2r.GaAs.out (4) Finally, perform Fourier transformation of the real space components to get the dynamical matrix at any q by using matdyn.x. src/GaAs-phonon/matdyn.GaAs.in &INPUT asr = 'crystal' flfrc = 'GaAs.fc' flfrq = 'GaAs.freq' flvec = 'GaAs.modes' ! loto_2d = .true. q_in_band_form = .true. q_in_cryst_coord = .true. / 5 0.500 0.500 0.500 20 ! L 0.000 0.000 0.000 20 ! G 0.500 0.000 0.500 20 ! X 0.375 0.375 0.750 20 ! K 0.000 0.000 0.000 1 ! G mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out We can now plot the phonon dispersion of GaAs: notebooks/GaAs-phonon.ipynb import numpy as np import matplotlib.pyplot as plt data = np.loadtxt(\"../src/GaAs-phonon/GaAs.freq.gp\") nbands = data.shape[1] - 1 for band in range(nbands): plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k') # High symmetry k-points (check matdyn.GaAs.in) plt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5) plt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5) plt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \\ labels=['L', '$\\Gamma$', 'X', 'U,K', '$\\Gamma$']) plt.ylabel(\"Frequency (cm$^{-1}$)\") plt.xlim(data[0, 0], data[-1, 0]) plt.ylim(0, ) plt.show() tip We may need to lower the value of conv_thr in scf calculation for more accurate result.","s":"Phonon dispersion","u":"/espresso/hands-on/phonon","h":"","p":86},{"i":89,"t":"Input file for phonon DOS calculation: src/GaAs-phonon/matdyn.dos.GaAs.in &INPUT asr = 'crystal' flfrc = 'GaAs.fc' flfrq = 'GaAs.dos.freq' flvec = 'GaAs.dos.modes' dos = .true. fldos = 'GaAs.dos' nk1 = 25 nk2 = 25 nk3 = 25 / Plot phonon DOS: notebooks/GaAs-phonon.ipynb freq, dos, pdos_Ga, pdos_As = np.loadtxt(\"../src/GaAs-phonon/GaAs.dos\", unpack=True) plt.plot(freq, dos, c='k', lw=0.5, label='Total') plt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga') plt.plot(freq, pdos_As, c='r', lw=0.5, label='As') plt.xlabel('$\\\\Omega~(cm^{-1}$)') plt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)') plt.legend(frameon=False, loc='upper left') plt.xlim(freq[0], freq[-1]) plt.show()","s":"Phonon Density of States","u":"/espresso/hands-on/phonon","h":"#phonon-density-of-states","p":86},{"i":91,"t":"School on Electron-Phonon Physics from First Principles (2018) (Video lectures on YouTube) https://github.com/nguyen-group/QE-SSP","s":"Resources","u":"/espresso/hands-on/phonon","h":"#resources","p":86},{"i":94,"t":"Perform scf calculation using Quantum Espresso pw.x QE_PATH=\"/workspaces/q-e-qe-7.2/bin\" mpirun -np 4 ${QE_PATH}/pw.x -i pw.scf.silicon.in > pw.scf.silicon.out Perform nscf calculation using pw.x. Instead of automatic k-grid, we need to provide explicit list of k-points. Such explicit list of k-points can be generated using perl script included in the Wannier package under utility. WANNIER_PATH=\"/workspaces/wannier90-3.1.0\" # directly append the k-points to the input file ${WANNIER_PATH}/utility/kmesh.pl 4 4 4 >> pw.nscf.silicon.in Run nscf calculation: mpirun -np 4 ${QE_PATH}/pw.x -i pw.nscf.silicon.in > pw.nscf.silicon.out Prepare input file for wannier90 (silicon.win). Here we need the k-points list without the weights: ${WANNIER_PATH}/utility/kmesh.pl 4 4 4 wan Generate nnkp input: # we can just provide the seedname or seedname.win ${WANNIER_PATH}/wannier90.x -pp silicon Create input file for pw2wan, and generate initial projections: mpirun -np 4 ${WANNIER_PATH}/pw2wannier90.x -i pw2wan.silicon.in > pw2 wan.silicon.out Run wannier calculation: mpirun -np 4 ${WANNIER_PATH}/wannier90.x silicon","s":"Obtain bandstructure of Silicon","u":"/espresso/hands-on/wannier","h":"#obtain-bandstructure-of-silicon","p":92},{"i":96,"t":"https://sites.google.com/view/hubbard-koopmans/program","s":"Resources","u":"/espresso/hands-on/wannier","h":"#resources","p":92},{"i":98,"t":"There are two types of structural optimization calculations in Quantum espresso: (1) relax: where only the atomic positions are allowed to vary, and (2) vc-relax: which allows to vary both the atomic positions and lattice constants. src/silicon/si_relax.in &control calculation = 'vc-relax' prefix = 'silicon' outdir = './tmp/' pseudo_dir = './pseudos/' etot_conv_thr = 1e-5 forc_conv_thr = 1e-4 / &system ibrav=2, celldm(1) =14, nat=2, ntyp=1, ecutwfc=30 / &electrons conv_thr=1e-8 / &ions / &cell cell_dofree='ibrav' / ATOMIC_SPECIES Si 28.0855 Si.pz-vbc.UPF ATOMIC_POSITIONS (alat) Si 0.00 0.00 0.00 0 0 0 Si 0.25 0.25 0.25 0 0 0 K_POINTS (automatic) 6 6 6 1 1 1 Perform the plane wave calculation: pw.x -inp si_relax.in > si_relax.out This produces following output (see the si_relax.out for more details, look for \"Final enthalpy\"): Final enthalpy = -15.8536258868 Ry Begin final coordinates new unit-cell volume = 265.89380 a.u.^3 ( 39.40140 Ang^3 ) density = 2.36728 g/cm^3 CELL_PARAMETERS (alat= 14.00000000) -0.364556379 0.000000000 0.364556379 0.000000000 0.364556379 0.364556379 -0.364556379 0.364556379 0.000000000 ATOMIC_POSITIONS (alat) Si 0.0000000000 0.0000000000 0.0000000000 0 0 0 Si 0.1822781896 0.1822781896 0.1822781896 0 0 0 End final coordinates Lattice constant = 0.364556379 * 14 / 0.5 = 10.2076 Bohr.","s":"Structure optimization","u":"/espresso/hands-on/structure-optimization","h":"","p":97},{"i":100,"t":"In order to consider spin orbit coupling effect in our electronic structure calculation in quantum espresso, we need to use a full relativistic pseudo potential. Following settings are needed in the &SYSTEM card: &SYSTEM ... noncolin = .true. lspinorb = .true. ... /","s":"Spin-Orbit Coupling","u":"/espresso/hands-on/soc","h":"","p":99},{"i":102,"t":"In simple spin polarized calculation (nspin=2), the spin quantum number (up or down) is considered in the calculation. In non-collinear case, the spin has more degrees of freedom, and can be oriented in any direction. Non-collinear magnetism is quite common in nature, where the spins are not parallel (ferromagnetic) or anti-parallel (antiferromagnetic), rather they orient in spirals, helicoids, canted or disordered. Non-collinear magnetism can occur because of geometric frustration of magnetic interaction. It can also occur due to the magnetocrystalline anisotropy which is the result of interaction between the spin and lattice interaction. This relativistic effect comes via spin-orbit coupling. We can constrain the magnetic moment: &SYSTEM ... constrained_magnetization = 'atomic direction' ... / Starting magnetization can be specified by angle1 (angle with zzz axis) and angle2 (angle of projection in xyxyxy-plane and with xxx-axis). Also check the penalty function (λ\\lambdaλ). &SYSTEM ... angle1(i) = 0.0d0 angle2(i) = 0.0d0 lambda = 0.5 ... / i is the index of the atom in ATOMIC_SPECIES card.","s":"Non collinear spin","u":"/espresso/hands-on/soc","h":"#non-collinear-spin","p":99},{"i":104,"t":"Spin-orbit coupling calculations are often hard to converge. Use a smaller mixing_beta for such calculations. First perform a collinear calculation with non-relativistic pseudopotential, and then start from the obtained charge density to perform non-colinear spin orbit calculation. &ELECTRONS ... mixing_beta = 1.0000000000d-01 startingpot = 'file' / When starting with non-collinear calculation from an existing charge density file from a collinear lsda calculation, we need to set lforcet=.true.. It assumes previous density points in z direction, and rotates in the direction specified by angle1 (initial magnetization angle with zzz-axis in degrees), and angle2 (angle in degrees for projections in xyxyxy-plane and with xxx-axis). &SYSTEM ... angle1(i) = 0.0 angle2(i) = 0.0 lforcet = .true. / Also, make sure that energy and charge density cutoffs are sufficient. Certain pseudo potentials might have issues, try with pseudo potentials from a different library. In case of metallic systems, remember to apply smearing. Common Errors S matrix not positive definite: This error might appear due to numerical instability from overlapping atoms. Check atomic positions carefully. In one my calculations, this error was resolved after setting higher ecutrho. Simplified LDA+U not implemented with noncol magnetism, use lda_plus_u_kind=1.","s":"Strategy for convergence","u":"/espresso/hands-on/soc","h":"#strategy-for-convergence","p":99},{"i":106,"t":"src/fe/pw.scf.fe_soc.in &control calculation='scf' pseudo_dir = '../pseudos/', outdir='./tmp/' prefix='fe' / &system ibrav = 3, celldm(1) = 5.39, nat= 1, ntyp= 1, noncolin=.true., lspinorb=.true., starting_magnetization(1)=0.3, ecutwfc = 70, ecutrho = 850.0, occupations='smearing', smearing='marzari-vanderbilt', degauss=0.02 / &electrons diagonalization='david' conv_thr = 1.0e-8 mixing_beta = 0.7 / ATOMIC_SPECIES Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS alat Fe 0.0 0.0 0.0 K_POINTS AUTOMATIC 14 14 14 1 1 1 Run the scf calculation: mpirun -np 8 pw.x -i pw.scf.fe_soc.in > pw.scf.fe_soc.out Prepare the input file for nscf bands calculation: src/fe/pw.bands.fe_soc.in &control calculation='bands' pseudo_dir = '../pseudos/', outdir='./tmp/' prefix='fe' / &system ibrav = 3, celldm(1) = 5.39, nat= 1, ntyp= 1, noncolin=.true., lspinorb=.true., starting_magnetization(1)=0.3, ecutwfc = 70, ecutrho = 850.0, occupations='smearing', smearing='marzari-vanderbilt', degauss=0.02 / &electrons diagonalization='david' conv_thr = 1.0e-8 mixing_beta = 0.7 / ATOMIC_SPECIES Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.1.0.0.UPF ATOMIC_POSITIONS alat Fe 0.0 0.0 0.0 K_POINTS tpiba_b 6 0.000 0.000 0.000 40 !gamma 0.000 1.000 0.000 40 !H 0.500 0.500 0.000 30 !N 0.000 0.000 0.000 30 !gamma 0.500 0.500 0.500 30 !P 0.000 1.000 0.000 1 !H Run the bands calculation: mpirun -np 8 pw.x -i pw.bands.fe_soc.in > pw.bands.fe_soc.out Finally post process the bandstructure data: src/fe/pp.bands.fe_soc.in &BANDS outdir='./tmp/', prefix='fe', filband='fe_bands_soc.dat', / In this case spin_component has been removed and we add lsigma(3)=.true. that instructs the program to compute the expectation value for the z component of the spin operator for each eigenfunction and save all values in the file fe.noncolin.data.3. All values in this case are either +1/2 or -1/2. mpirun -np 8 bands.x -i pp.bands.fe_soc.in > pp.bands.fe_soc.out","s":"Bandstructure of Fe with SOC","u":"/espresso/hands-on/soc","h":"#bandstructure-of-fe-with-soc","p":99},{"i":108,"t":"Please check the respective input files. mpirun -np 8 pw.x -i pw.scf.GaAs_soc.in > pw.scf.GaAs_soc.out mpirun -np 8 pw.x -i pw.bands.GaAs_soc.in > pw.bands.GaAs_soc.out mpirun -np 8 bands.x -i pp.bands.GaAs_soc.in > pp.bands.GaAs_soc.out","s":"SOC calculation for GaAs","u":"/espresso/hands-on/soc","h":"#soc-calculation-for-gaas","p":99},{"i":110,"t":"Quantum Espresso Tutorials ICTP Quantum Espresso workshop 2021 Ljubljana QE summer school 2019 MASTANI Summer School, IISER Pune 2014 (archive) Examples included in Quantum Espresso (qe-x.x/PW/examples/). QE mailing list archive Materials square blog Cornell PARADIM Summer School School on Electron-Phonon Physics from First Principles (2018)","s":"Resources","u":"/espresso/resources","h":"","p":109},{"i":112,"t":"QUANTUM ESPRESSO for quantum simulations of materials Advanced capabilities for materials modelling with QE Hubbard parameters from density-functional perturbation theory Self-consistent Hubbard parameters from DFPT","s":"Papers describing DFT implementations in QE","u":"/espresso/resources","h":"#papers-describing-dft-implementations-in-qe","p":109},{"i":114,"t":"A bird's–eye view of DFT Density Functional Theory: A Practical Introduction by Sholl and Steckel Materials Modelling using Density Functional Theory by Feliciano Giustino Electronic Structure: Basic Theory and Practical Method by Richard M. Martin Electronic Structure Calculations for Solids and Molecules by Jorge Kohanoff PhD Thesis of Dominik Bogdan Jochym","s":"Books","u":"/espresso/resources","h":"#books","p":109},{"i":116,"t":"This work is licensed under a Creative Commons Attribution 4.0 International License. Any third party materials in this work are not included in the article’s Creative Commons license, and users will need to obtain permission from the respective license holder to reproduce such materials. You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. Notices: No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material. To view full copy of this license, visit http://creativecommons.org/licenses/by/4.0/","s":"License","u":"/espresso/license","h":"","p":115},{"i":119,"t":"Density functional theory (DFT) calculations are ab-initio meaning the calculation is done from the scratch based on given input parameters. We need to provide the crystal structure in order to calculate DFT. Crystal structures are widely available in Crystallographic Information File (.CIF) format. There are several databases where you can look for crystal structures. http://crystallography.net/cod/ https://materialsproject.org https://mpds.io/ https://icsd.fiz-karlsruhe.de/index.xhtml http://aflowlib.org/CrystalDatabase/ http://crystdb.nims.go.jp/crystdb/search-materials In Quantum Espresso, the structure information is provided by ibrav number, and corresponding celldm values or lattice constants and cosines of angle between the axes. It is also possible to set ibrav=0 and provide lattice vectors in CELL_PARAMETERS. danger When set ibrav=0, the lattice vectors must be provided with sufficiently large number of decimal accuracy, otherwise symmetry detection may fail and strange problems may arrise. ibrav numbers for different lattice types: ibrav Lattice type 1 Simple cubic 2 Face centered cubic 3,-3 Body centered cubic 4 Hexagonal 5 Trigonal with c as 3-fold axis -5 Trigonal with <111> as 3-fold axis 6 Simple tetragonal 7 Centered tetragonal 8 Simple orthorhombic 9,-9,91 One-face centered orthorhombic 10 Face centered orthorhombic 11 Body centered orthorhombic 12 Simple monoclinic, c unique -12 Simple monoclinic, b unique 13 One base centered monoclinic, c unique -13 One base centered monoclinic, b unique 14 Triclinic","s":"Structure databases","u":"/espresso/setup/crystal-structure","h":"#structure-databases","p":117},{"i":121,"t":"Vesta - https://jp-minerals.org/vesta/en/. It helps you visualize crystal structure, create and modify supercells, crystal structures, and many other useful functionalities. We can prepare our Quantum Espresso input file using cif2cell utility. If you do not have cif2cell installed, you can use pip to install: sudo pip3 install cif2cell You may need to add it to the path in your .bashrc manually: export PATH=\"/home/pranab/.local/lib/python3.8/site-packages/:$PATH\" Running cif2cell command: cif2cell file.cif -p quantum-espresso -o inputfile.in","s":"Useful tools:","u":"/espresso/setup/crystal-structure","h":"#useful-tools","p":117},{"i":123,"t":"You can explore the crystal structure, find out k-path and many more using Xcrysdens application - http://www.xcrysden.org For certain functionality, Xcrysdens requires basic calculator program. On Ubuntu/ Debian: sudo apt update sudo apt install bc xcrysden Manual installation: # install dependencies sudo apt install --no-install-recommends bc tk libglu1-mesa libtogl2 \\ libfftw3-3 libxmu6 imagemagick openbabel libgfortran5 # download the latest version of xcrysden and extract wget http://www.xcrysden.org/download/xcrysden-1.6.2-linux_x86_64-shared.tar.gz tar -zxvf xcrysden-1.6.2-linux_x86_64-shared.tar.gz # launch (provided you extracted under your home directory) ~/xcrysden-1.6.2-bin-shared/xcrysden If you are on WSL, you need to install X-server (X-ming for Windows) on the host and set export DISPLAY=:0 in your WSL instance.","s":"Xcrysdens","u":"/espresso/setup/crystal-structure","h":"#xcrysdens","p":117},{"i":125,"t":"You can generate PWscf input files using tools in this website as well https://www.materialscloud.org/work/tools/qeinputgenerator The same website also has a tool for k-path visualization and generation https://www.materialscloud.org/work/tools/seekpath","s":"QE Input generator","u":"/espresso/setup/crystal-structure","h":"#qe-input-generator","p":117},{"i":127,"t":"Supercell construction using Vesta","s":"Resources","u":"/espresso/setup/crystal-structure","h":"#resources","p":117},{"i":129,"t":"There are several ways you can run Jupyterlab in your computer.","s":"Jupyter notebooks","u":"/espresso/setup/jupyter","h":"","p":128},{"i":131,"t":"Install Python 3 in your computer # on ubuntu / debian apt install python3 python3-pip Install the required python packages on your computer pip3 install --upgrade -r requirements.txt # or pip3 install --upgrade numpy scipy matplotlib jupyterlab Run Jupyterlab jupyter-lab # or the classic jupyter notebook jupyter-notebook","s":"1. Install on your computer","u":"/espresso/setup/jupyter","h":"#1-install-on-your-computer","p":128},{"i":133,"t":"Install Python 3 and virtualenv on your computer pip3 install --upgrade virtualenv create virtual environment in the project directory cd qe-dft virtualenv venv activate virtual env source venv/bin/activate Install required python packages under virtualenv Launch Jupyterlab Once done, deactivate virtualenv deactivate","s":"2. Install python packages via virtualenv","u":"/espresso/setup/jupyter","h":"#2-install-python-packages-via-virtualenv","p":128},{"i":135,"t":"Install Docker Create an image with Python and the required packages installed # build using the Dockerfile included in my github repo: # https://github.com/pranabdas/espresso # (adjust the Dockerfile according to your needs) docker build -t espresso . Run a container with port forwarding docker run -it --rm -p 8888:8888 -v ${PWD}:/home espresso bash Launch Jupyterlab jupyter-lab","s":"3. Run on a container","u":"/espresso/setup/jupyter","h":"#3-run-on-a-container","p":128},{"i":137,"t":"We can install Quantum Espresso on our personal laptops or desktops to run relatively less computationally intensive calculations. If we intend to perform computationally heavy tasks, we would need access to better computing resources with large number of CPU (or GPU) cores, memory, bandwidth, and disc IO. Throughout this tutorial, I will be using a Ubuntu system for smaller calculations while other computationally intensive calculations will be done in HPC clusters. Perhaps the easiest way to install Quantum Espresso is from the package manager of respective Linux distribution. This should work fine for us and this is recommended option. Following commands are for Ubuntu/Debian. First make sure your system is up-to-date. sudo apt update && sudo apt upgrade Install Quantum Espresso from apt repository: sudo apt install --no-install-recommends \\ libfftw3-dev \\ quantum-espresso tip Pre-built binaries of Quantum ESPRESSO for Ubuntu is included in my GitHub repository releases for easy installation. Please refer to the release notes for more details on how to install. If you want to compile from the source yourself, here are the installation steps for the Quantum Espresso version 7.2 in a Ubuntu (LTS 22.04) system. I will be compiling for single processor. First install the recommended libraries and dependencies: sudo apt install --no-install-recommends \\ autoconf \\ build-essential \\ ca-certificates \\ gfortran \\ libblas3 \\ libc6 \\ libfftw3-dev \\ libgcc-s1 \\ liblapack-dev \\ wget If you want to compile for parallel processing, you also need to install: sudo apt install --no-install-recommends \\ libopenmpi-dev \\ libscalapack-openmpi-dev \\ libelpa17 # use libelpa4 on Ubuntu 20.04 Download Quantum Espresso (latest version 7.2 at the time of writing): wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz Un-tar the source files: tar -zxvf q-e-qe-7.2.tar.gz Go to the qe directory and issue configure: cd q-e-qe-7.2 ./configure Here we can provide various configuration options. Read the manual in oder to properly understand. But in most cases we will be just fine with the defaults, it should detect the system configuration automatically, in case you don't get what you want, try the various configuration flags with configure. caution Note that certain programs/utilities bundled with Quantum Espresso might not work correctly in parallel compilation, so we may need serial compilation for those by ./configure --disable-parallel option in case parallel option is automatically detected. Finally, compile the source files and create the binary executables: # compile individual packages make pw # or compile everything make all # we can parallelize e.g., below command uses 4 CPUs make -j4 all Now, the binary files or their symbolic links (shortcuts) would be placed in the bin directory. It would be good idea to include the executable path to your .bashrc (or .zshrc or whatever shell you use) file: # use the correct path if it differs from mine echo 'export PATH=\"/root/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc Finally, you may need to restart your terminal or source .bashrc. source ~/.bashrc You can compile the documentation by going to particular directory (e.g., PW or PP) and execute (you need to have LaTeX installed in your system): make doc If you want docs in PDF format, you can use latex commands to create them as well: pdflatex filename.tex We are now ready to run Quantum Espresso pw.x (or any other program) using mpirun by following command: pw.x -inp inputfile > outputfile # For parallel version mpirun -np 12 pw.x -inp inputfile > outputfile Where -np 12 specifies the number of processors. -inp stands for input file. Alternatively, we can use -i, or -in, or -input, or even standard input redirect <. But beware some systems may not interpret all the different options, I think safe option is to use -i. Once installation is completed, optionally we can run tests if everything went OK. Go to the test-suite directory and run make run-tests If all is well, we will see Passed messages and we are good to go. caution Note that the above installation steps may not be the most optimal way to run Quantum Espresso in your computer. There are multiple implementations of same library. For example, you can replace openmpi libraries with Intel MKL or MPICH implementations. Please do research yourself or ask help from someone who has knowledge about high performance computing.","s":"Quantum Espresso installation","u":"/espresso/setup/install","h":"","p":136},{"i":139,"t":"We will install a very hand scripting package PWscf Toolkit (PWTK). First we need to install following dependencies: sudo apt install tcl tcllib Download the file from - http://pwtk.ijs.si/download/pwtk-2.0.tar.gz wget \"http://pwtk.ijs.si/download/pwtk-2.0.tar.gz\" Above command will download and save the file to your current directory. Next we need to just un-tar (no need to compile): tar -zxvf pwtk-2.0.tar.gz Add the path (modify below as appropriate) to .bashrc: echo 'export PATH=\"/root/pwtk-2.0:$PATH\"' >> ~/.bashrc source ~/.bashrc","s":"Installing PWTK","u":"/espresso/setup/install","h":"#installing-pwtk","p":136},{"i":141,"t":"In order to perform computationally heavy calculations, we would require access to high performance computing facilities.","s":"High Performance Computing","u":"/espresso/setup/hpc","h":"","p":140},{"i":143,"t":"Connect to a login node via ssh: ssh {username}@atlas9.nus.edu.sg Secure copy files between local and remote machines: scp {username}@10.10.0.2:/remote/file.txt /local/directory scp local/file.txt {username}@10.10.0.2:/remote/directory Check disk usage: du -hs . du -hs /path/ Rsync to synchronize two folders: rsync -azhv --delete /source/my_project/ /destination/my_project","s":"Useful UNIX commands","u":"/espresso/setup/hpc","h":"#useful-unix-commands","p":140},{"i":145,"t":"Check your storage quota: hpc s PBS commands: hpc pbs summary Example scrips for job submissions: hpc pbs script parallel20 hpc pbs vasp List available modules: module avail Load a module: module load {module-name} Purge loaded modules: module purge Quantum Espresso is already installed in NUS HPC clusters. Here is a sample job script for NUS HPC clusters: scripts/pbs_job.sh #!/bin/bash #PBS -q parallel24 #PBS -l select=2:ncpus=24:mpiprocs=24:mem=96GB #PBS -j eo #PBS -N qe-project-xx source /etc/profile.d/rec_modules.sh module load espresso6.5-intel_18 ## module load espresso6.5-Centos6_Intel cd $PBS_O_WORKDIR; np=$( cat ${PBS_NODEFILE} | wc -l ); mpirun -np $np -f ${PBS_NODEFILE} pw.x -inp qe-scf.in > qe-scf.out info Notice that the lines beginning with #PBS are actually PBS commands, not comments. For comments, I am using ##. Query about a queue system: qstat -q Check status of a particular queue system: qstat -Qx parallel24 Submitting a job: qsub pbs_job.sh Check running jobs: qstat Details about a job: qstat -f {job-id} Stopping a job: qdel {job-id}","s":"Running jobs at NUS HPC","u":"/espresso/setup/hpc","h":"#running-jobs-at-nus-hpc","p":140},{"i":147,"t":"If you need to modify certain parameters while the program is running, e.g., you want to change the mixing_beta value because SCF accuracy is oscillation without any sign of convergence. Create an empty file named {prefix}.EXIT in the directory where you have the input file or in the outdir as set in the &CONTROL card of input file. touch {prefix}.EXIT That will stop the program on the next iteration, and save the state. In order to restart, set the restart_mode in &CONTROL card to 'restart' and re-run after necessary changes. You must re-submit the job with the same number of processors. &CONTROL ... restart_mode = 'restart' ... /","s":"Abort and restart a calculation","u":"/espresso/setup/hpc","h":"#abort-and-restart-a-calculation","p":140},{"i":149,"t":"If you need a newer or specific version of Quantum Espresso that is not installed in the NUS clusters or you have modified the source codes yourself, here are the steps that I followed to successfully compile. info Quantum Espresso project is primarily hosted on GitLab, and its mirror is maintained at GitHub. You may check their repository at GitLab for more up to date information. The releases via GitLab can be found under: https://gitlab.com/QEF/q-e/-/releases Download and decompress the source files. wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz tar -zxvf q-e-qe-7.2.tar.gz Load the necessary modules (applicable for NUS clusters, last checked in Jun 2022): module load xe_2018 module load fftw/3.3.7 Go to QE directory and run configure: cd q-e-qe-7.2 ./configure You will see output something like: ... BLAS_LIBS= -lmkl_intel_lp64 -lmkl_sequential -lmkl_core LAPACK_LIBS= FFT_LIBS= ... For me, the LAPACK_LIBS and FFT_LIBS libs were not automatically detected. We need to specify them manually. First, get the link libraries line specific to your version of MKL and other configurations from the Intel link advisor. For my case, the link line was: -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl We need to insert the link for BLAS_LIBS, LAPACK_LIBS, and SCALAPACK_LIBS. We also need to find out where is the FFTW lib located. In NUS HPC, we can use module avail command to see where a particular module is located, usually under /app1/modules/. Open make.inc and make the following changes: make.inc # ... CFLAGS = -O2 $(DFLAGS) $(IFLAGS) CFLAGS = -O3 $(DFLAGS) $(IFLAGS) F90FLAGS = $(FFLAGS) -nomodule -fpp $(FDFLAGS) $(CUDA_F90FLAGS) $(IFLAGS) $(MODFLAGS) # compiler flags with and without optimization for fortran-77 # the latter is NEEDED to properly compile dlamch.f, used by lapack - FFLAGS = -O2 -assume byterecl -g -traceback + FFLAGS = -O3 -assume byterecl -g -traceback FFLAGS_NOOPT = -O0 -assume byterecl -g -traceback # ... # If you have nothing better, use the local copy # BLAS_LIBS = $(TOPDIR)/LAPACK/libblas.a - BLAS_LIBS = -lmkl_intel_lp64 -lmkl_sequential -lmkl_core + BLAS_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl # If you have nothing better, use the local copy # LAPACK = liblapack # LAPACK_LIBS = $(TOPDIR)/external/lapack/liblapack.a - LAPACK = + LAPACK = liblapack - LAPACK_LIBS = + LAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl - SCALAPACK_LIBS = + SCALAPACK_LIBS = -L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl # nothing is needed here if the internal copy of FFTW is compiled # (needs -D__FFTW in DFLAGS) - FFT_LIBS = + FFT_LIBS = -L/app1/centos6.3/gnu/fftw/3.3.7/lib/ -lmpi # ... Now we are ready to compile: make -j8 all I am parallelizing with 8 processors to speed things up. You may add the q-e-qe-7.2/bin path to your .bashrc: echo 'export PATH=\"/home/svu/{username}/q-e-qe-7.2/bin:$PATH\"' >> ~/.bashrc And don't forget to load dependencies before calling QE executables. module load xe_2018 module load fftw/3.3.7 note If you are submitting job via PBS queue, you need to provide full path of the QE executables, e.g., /home/svu/{username}/q-e-qe-7.2/bin/pw.x. PBS system won't read your bash settings, neither the relative paths of your login node would apply.","s":"Compiling Quantum Espresso using Intel® Math Kernel Library (MKL)","u":"/espresso/setup/hpc","h":"#compiling-quantum-espresso-using-intel-math-kernel-library-mkl","p":140},{"i":151,"t":"If you need to install Intel oneAPI libraries yourself, following instructions might be useful. Please refer to Intel website for up to date information. Intel oneAPI Base Toolkit:​ wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/992857b9-624c-45de-9701-f6445d845359/l_BaseKit_p_2023.2.0.49397_offline.sh # requires gnu-awk sudo apt update && sudo apt install -y --no-install-recommends gawk gcc g++ # interactive cli installation sudo apt install -y --no-install-recommends ncurses-term sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --cli # list components included in oneAPI Base Toolkit sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --list-components # install a subset of components with silent/unattended option sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --silent --eula accept --components intel.oneapi.lin.dpcpp-cpp-compiler:intel.oneapi.lin.mkl.devel note If you install oneAPI without sudo privilege, it will be installed under the user directory: /home/{username}/intel/oneapi/. After installation is completed, the setup script will print the installation location. HPC Toolkit​ wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/0722521a-34b5-4c41-af3f-d5d14e88248d/l_HPCKit_p_2023.2.0.49440_offline.sh sudo sh ./l_HPCKit_p_2023.2.0.49440_offline.sh -a --silent --eula accept Intel MKL library​ Installing individual components: wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/adb8a02c-4ee7-4882-97d6-a524150da358/l_onemkl_p_2023.2.0.49497_offline.sh sudo sh ./l_onemkl_p_2023.2.0.49497_offline.sh -a --silent --eula accept After installation, do not forget to source the environment variables before using: source /opt/intel/oneapi/setvars.sh Compile quantum espresso: wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz tar -zxvf q-e-qe-7.2.tar.gz rm q-e-qe-7.2.tar.gz cd q-e-qe-7.2 ./configure \\ F90=mpiifort \\ MPIF90=mpiifort \\ CC=mpicc CXX=icc \\ F77=mpiifort \\ FFLAGS=\"-O3 -assume byterecl -g -traceback\" \\ LAPACK_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" \\ BLAS_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" \\ SCALAPACK_LIBS=\"-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl\" make -j4 all","s":"Installing Intel oneAPI libraries","u":"/espresso/setup/hpc","h":"#installing-intel-oneapi-libraries","p":140},{"i":153,"t":"Please check out the official documentation for more details. It requires cmake version 3.14 or later. apt update && apt install autoconf cmake gawk gcc g++ make I used following steps to successfully compile Quantum Espresso using 2023 versions of Intel libraries in Ubuntu 22.04 system: cd q-e-qe-7.2 mkdir build && cd build cmake -DCMAKE_C_COMPILER=mpiicc -DCMAKE_Fortran_COMPILER=mpiifort -DQE_ENABLE_SCALAPACK=ON .. make -j4 mv bin .. cd .. rm -rf build","s":"Compiling Quantum Espresso with CMake","u":"/espresso/setup/hpc","h":"#compiling-quantum-espresso-with-cmake","p":140},{"i":155,"t":"https://nusit.nus.edu.sg/services/getting-started/introductory-guide-for-new-hpc-users/ https://help.nscc.sg/pbspro-quickstartguide/ https://www.youtube.com/watch?v=doudMLEaq3w","s":"Resources","u":"/espresso/setup/hpc","h":"#resources","p":140},{"i":157,"t":"In Quantum Espresso, pseudopotential replaces the actual electron-ion interaction. The pseudopotential describes the atomic nucleus and all the electrons except the outermost valence shell. The rapidly changing potential field near the atomic core is replaced by a smoother function that simulates the potential field far from the core very well. By doing so, it requires less number plane wave basis for wavefunction expansion. tip You may try my Pseudos Web-App, where you can look for pseudopotentials by element name, and download them. Currently, Standard Solid State Pseudopotentials (SSSP) and GBRV pseudopotentials are included. We can choose form various pseudopotential libraries. Choice of pseudopotential depends on the problem we are investigating, e.g., if there is a heavy element present in our system and we are interested in the spin-orbit coupling effects, we should choose a full relativistic pseudopotential. We need to be careful whether our chosen pseudopotential correctly reproduces physical properties. Various pseudopotential libraries: https://www.quantum-espresso.org/pseudopotentials https://www.materialscloud.org/discover/sssp/table/efficiency http://www.pseudo-dojo.org https://www.physics.rutgers.edu/gbrv/ https://nninc.cnf.cornell.edu http://www.quantum-simulation.org/potentials/ BLYP pseudopotentials SCAN pseudopotentials Pseudopotential naming conventions in PSLibrary: an example pseudopotential filename is O.rel-pbe-n-rrkjus_psl.1.0.0.UPF. O → denotes the atomic species rel → full relativistic (optional) pbe → exchange correlation functional n → non-linear core correction (optional) rrkjus → pseudopotential type Exchange correlation functionals: Identifier Functional pz Perdew-Zunger (LDA) pbe Perdew-Burke-Ernzerhof (GGA) pw91 Perdew-Wang 91 (GGA) blyp Becke-Lee-Yang-Parr (GGA) Pseudopotential types: Identifier PP types ae all-electron rrkj Rappe-Rabe-Kaxiras-Joannopoulos (Norm conserving) rrkjus Rappe-Rabe-Kaxiras-Joannopoulos (Ultrasoft) kjpaw Kresse-Joubert (PAW) Ultra soft pseudopotentials are computationally efficient than the norm conserving pseudopotentials. You will find the recommended ecutwfc in the header of each pseudopotential file. If you choose an ultra-soft pseudopotential, you will need ecutrho about 8 times the value of ecutwfc. The default ecutrho is 4 times ecutwfc in Quantum Espresso code, which is a good choice for norm conserving pseudopotentials. You should check energy convergence against ecutwfc for your system. By using pseudopotential, we want to get rid of the core electrons that do not participate in the chemical properties of material. This is known also as rigid core approximation. Instead of accounting the nucleus and core electrons separately, we want to have a pseudopotential that interacts in a similar way with the valence electrons. info We can mix different types of pseudo potentials (e.g., norm conserving, ultra-soft, or PAW), but we cannot mix different exchange correlation functional (e.g., PBE and LDA). Exchange correlation functional can be read from the pseudopotential file or be provided via input_dft parameter in Quantum Espresso. \"sol\" in PBE-sol stands for solid. For bulk systems PBE-sol should be used, while PBE is appropriate for molecules. In case of 2D materials generally PBE is chosen, but one can check PBE-sol. Common error If you mix PBE with PBE-sol type, it results in Error: conflicting values for igcx. However, it is allowed to mix those two types of pseudo. We can set desired exchange correlation functional via input_dft instead of reading from the pseudopotential file.","s":"Pseudo potentials","u":"/espresso/setup/pseudo-potential","h":"","p":156},{"i":159,"t":"Naming convention for PP files","s":"Resources","u":"/espresso/setup/pseudo-potential","h":"#resources","p":156},{"i":161,"t":"Hatree-Fock theory is foundational to many subsequent electronic structure theories. It is an independent particle model or mean filed theory. Consider we have two non-interacting electrons. In that case, the Hamiltonian would be separable, and the total wavefunction Ψ(r1,r2)\\Psi(\\textbf{r}_1, \\textbf{r}_2)Ψ(r1​,r2​) would be product of the individual wave function. Now if we consider two electrons are forming a single system, then there are two issues. (1) We can no longer ignore the electron-electron interaction. (2) The wavefunction describing fermions must be antisymmetric with respect to the interchange of any set of space-spin coordinates. A simple Hartree product fails to satisfy that condition: ΨHP(r1,r2,⋯ ,rN)=ϕ1(r1)ϕ2(r2)⋯ϕN(rN)\\Psi_{HP}(\\textbf{r}_1, \\textbf{r}_2, \\cdots, \\textbf{r}_N) = \\phi_1(\\textbf{r}_1) \\phi_2(\\textbf{r}_2) \\cdots \\phi_N(\\textbf{r}_N)ΨHP​(r1​,r2​,⋯,rN​)=ϕ1​(r1​)ϕ2​(r2​)⋯ϕN​(rN​) In order to satisfy the antisymmetry condition, for our two electron system we can formulate a total wavefunction of the form: Ψ(r1,r2)=12[χ1(r1)χ2(r2)−χ1(r2)χ2(r1)]\\Psi(\\textbf{r}_1, \\textbf{r}_2) = \\frac{1}{\\sqrt{2}} [\\chi_1(\\textbf{r}_1) \\chi_2(\\textbf{r}_2) - \\chi_1(\\textbf{r}_2)\\chi_2(\\textbf{r}_1)]Ψ(r1​,r2​)=2​1​[χ1​(r1​)χ2​(r2​)−χ1​(r2​)χ2​(r1​)]","s":"Hartree-Fock Theory","u":"/espresso/theory/hartree-fock","h":"","p":160},{"i":163,"t":"The above equation can be written as: Ψ(r1,r2)=12∣χ1(r1)χ2(r1)χ1(r2)χ2(r2)∣\\Psi(\\textbf{r}_1, \\textbf{r}_2) = \\frac{1}{\\sqrt{2}} \\begin{vmatrix} \\chi_1(\\textbf{r}_1) & \\chi_2(\\textbf{r}_1) \\\\ \\chi_1(\\textbf{r}_2) & \\chi_2(\\textbf{r}_2) \\end{vmatrix}Ψ(r1​,r2​)=2​1​​χ1​(r1​)χ1​(r2​)​χ2​(r1​)χ2​(r2​)​​ Now what happens if we have more than two electrons? We can generalize the above determinant form to NNN electrons: Ψ=1N!∣χ1(r1)χ2(r1)⋯χN(r1)χ1(r2)χ2(r2)⋯χN(r2)⋮⋮⋱⋮χ1(rN)χ2(rN)⋯χN(rN)∣\\Psi = \\frac{1}{\\sqrt{N!}} \\begin{vmatrix} \\chi_1(\\textbf{r}_1) & \\chi_2(\\textbf{r}_1) & \\cdots & \\chi_N(\\textbf{r}_1) \\\\ \\chi_1(\\textbf{r}_2) & \\chi_2(\\textbf{r}_2) & \\cdots & \\chi_N(\\textbf{r}_2) \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\chi_1(\\textbf{r}_N) & \\chi_2(\\textbf{r}_N) & \\cdots & \\chi_N(\\textbf{r}_N) \\end{vmatrix}Ψ=N!​1​​χ1​(r1​)χ1​(r2​)⋮χ1​(rN​)​χ2​(r1​)χ2​(r2​)⋮χ2​(rN​)​⋯⋯⋱⋯​χN​(r1​)χN​(r2​)⋮χN​(rN​)​​ The above antisymmetrized product can describe electrons that move independently of each other while they experience an average (mean-field) Coulomb force.","s":"Slater determinant","u":"/espresso/theory/hartree-fock","h":"#slater-determinant","p":160},{"i":165,"t":"http://vergil.chemistry.gatech.edu/notes/hf-intro/hf-intro.html","s":"Resources","u":"/espresso/theory/hartree-fock","h":"#resources","p":160},{"i":167,"t":"This tutorial is result of my personal notes while trying (which I still do) to learn Density Functional Theory calculations myself. I am no expert in this subject. I am sharing this notes here, just in case it helps you getting started. I will cite numerous other resources that I am following. Hope you will find this tutorial helpful. The quantum espresso input files, jupyter notebooks (containing python code for visualizations), and other source files related to this tutorial can be found on GitHub: pranabdas/espresso. You may clone the repository to your local machine: git clone https://github.com/pranabdas/espresso.git Or, if you do not have git installed, download zipped copy of the repository here.","s":"Density Functional Theory using Quantum Espresso","u":"/espresso/","h":"","p":166},{"i":169,"t":"Lately, I decided to follow specific pattern for the filenames, but you can choose whatever works best for you. Note that all example files in this tutorial does not follow this convention yet. {program}.{calculation}.{system}.{in, out} {program}.{calculation}.{system_description}.{in, out} {pw, pp, ...}.{scf, bands, ...}.{silicon, al_slab}.{in, out} Example: pw.bands.silicon.in → input file for the bands calculation using PWscf program for silicon. For PWTK scripts, we will use .pwtk extension (e.g., silicon_vc_relax.pwtk).","s":"Filename conventions","u":"/espresso/","h":"#filename-conventions","p":166},{"i":171,"t":"1 Bohr = 0.529177249 Å 1 Rydberg (Ry) = 13.6056981 eV. Angstrom to Bohr converter: lattice constants are often provided in angstrom, you can use following utility to convert to Bohr. Å = 1.8897259886 Bohr. Copy","s":"Unit conversions","u":"/espresso/","h":"#unit-conversions","p":166},{"i":174,"t":"Wannier functions are an alternative representation of Bloch states in terms of a localized basis set. Suppose we have NNN atoms each separated by lattice constant aaa in one dimension. Bloch states are indexed by the wave vector kkk. H∣k⟩=ϵk∣k⟩\\mathcal{H}\\ket{k} = \\epsilon_k \\ket{k}H∣k⟩=ϵk​∣k⟩⟨x∣k⟩=ψk(x)\\braket{x | k} = \\psi_k(x)⟨x∣k⟩=ψk​(x) From the Bloch theorem, we have ψk(x+a)=eikaψk(x)\\psi_k(x + a) = e^{ika}\\psi_k(x)ψk​(x+a)=eikaψk​(x) Now, we want to find an alternative representation in terms of Wannier basis ∣n⟩\\ket{n}∣n⟩, where the states are labeled using site index (n = 1, 2, ..., N) instead of quantum number kkk. Wannier basis set is complete and orthonormal. ∣k⟩=∑n=1Nank∣n⟩\\ket{k} = \\sum_{n=1}^N a_{nk} \\ket{n}∣k⟩=n=1∑N​ank​∣n⟩⟨x∣k⟩=∑nank⟨x∣n⟩\\braket{x | k} = \\sum_n a_{nk} \\braket{x | n}⟨x∣k⟩=n∑​ank​⟨x∣n⟩⇒ψk(x)=∑nankw(x−na)\\Rightarrow \\psi_k(x) = \\sum_n a_{nk} w(x - na)⇒ψk​(x)=n∑​ank​w(x−na) where www represents Wannier function. Apply translation operator on both sides: Taψk(x)=∑nankTaw(x−na)⇒ ψk(x+a)=∑nankw(x−(n−1)a)⇒ eikaψk(x)=∑na(n+1)kw(x+na)⇒ eika∑nankw(x−na)=∑na(n+1)kw(x+na)⇒ eika∑nankw(x−na)=∑na(n+1)kw(x+na)\\begin{aligned} &T_a \\psi_k(x) = \\sum_n a_{nk} T_a w(x - na) \\\\ \\Rightarrow~ & \\psi_k(x + a) = \\sum_n a_{nk} w\\bigl(x - (n-1)a\\bigr) \\\\ \\Rightarrow~ & e^{ika} \\psi_k(x) = \\sum_n a_{(n+1)k} w(x + na) \\\\ \\Rightarrow~ & e^{ika} \\sum_n a_{nk} w(x - na) = \\sum_n a_{(n+1)k} w(x + na) \\\\ \\Rightarrow~ & e^{ika} \\sum_n a_{nk} w(x - na) = \\sum_n a_{(n+1)k} w(x + na) \\\\ \\end{aligned}⇒ ⇒ ⇒ ⇒ ​Ta​ψk​(x)=n∑​ank​Ta​w(x−na)ψk​(x+a)=n∑​ank​w(x−(n−1)a)eikaψk​(x)=n∑​a(n+1)k​w(x+na)eikan∑​ank​w(x−na)=n∑​a(n+1)k​w(x+na)eikan∑​ank​w(x−na)=n∑​a(n+1)k​w(x+na)​∴ a(n+1)k=ankeika=a(n−1)kei2ka⋯=a0kei(n+1)ka\\begin{aligned} \\therefore ~ a_{(n+1)k} &= a_{nk} e^{ika} \\\\ &= a_{(n-1)k}e^{i2ka} \\\\ &\\qquad\\cdots \\\\ &= a_{0 k}e^{i(n+1)ka} \\end{aligned}∴ a(n+1)k​​=ank​eika=a(n−1)k​ei2ka⋯=a0k​ei(n+1)ka​ Since Bloch states are orthonormal: ⟨k∣k⟩=⟨k∣∑nank∣n⟩=∑mn⟨m∣amk∗ank∣n⟩=∑n∣ank∣2=Na0k2=1\\begin{aligned} \\braket{k | k} &= \\braket{k | \\sum_n a_{nk} | n} \\\\ &= \\sum_{mn} \\braket{m | a_{mk}^* a_{nk} | n} \\\\ &= \\sum_{n} | a_{nk} |^2 \\\\ &= N a_{0k}^2 \\\\ &= 1 \\end{aligned}⟨k∣k⟩​=⟨k∣n∑​ank​∣n⟩=mn∑​⟨m∣amk∗​ank​∣n⟩=n∑​∣ank​∣2=Na0k2​=1​⇒a0k=1N(up to a phase factor)\\Rightarrow a_{0k} = \\frac{1}{\\sqrt{N}} \\qquad\\text{(up to a phase factor)}⇒a0k​=N​1​(up to a phase factor)∣k⟩=1N∑neikna∣n⟩\\ket{k} = \\frac{1}{\\sqrt{N}} \\sum_n e^{ikna} \\ket{n}∣k⟩=N​1​n∑​eikna∣n⟩ While Bloch states represent the eigenstates of the single-particle Hamiltonian, WF (in general) cannot be assigned a single eigen-value, instead WFs are obtained as liner combination of Bloch states corresponding to different energies. The Hamiltonian can now be written as: H=∑m∑n∣m⟩⟨m∣H∣n⟩⟨n∣=∑nϵn∣n⟩⟨n∣+∑m≠n(−tmn)∣m⟩⟨n∣\\begin{aligned} \\mathcal{H} &= \\sum_m \\sum_n \\ket{m} \\braket{m | \\mathcal{H} | n} \\bra{n} \\\\ &= \\sum_n \\epsilon_n \\ket{n} \\bra{n} + \\sum_{m\\neq n} (-t_{mn}) \\ket{m} \\bra{n} \\end{aligned}H​=m∑​n∑​∣m⟩⟨m∣H∣n⟩⟨n∣=n∑​ϵn​∣n⟩⟨n∣+m=n∑​(−tmn​)∣m⟩⟨n∣​ where ϵn\\epsilon_nϵn​ is onsite or diagonal term and tmnt_{mn}tmn​ (> 0) is hopping or off-diagonal term.","s":"Introduction","u":"/espresso/theory/wannier","h":"#introduction","p":172},{"i":176,"t":"The choice of Wannier function is not unique. One such option could be the set that maximizes localization. Two different sets of Wannier basis are connected via unitary transformation. MLWFs can be considered as a generalization of localized molecular orbitals (LMOs) to periodic systems.","s":"Maximally Localized Wannier Function","u":"/espresso/theory/wannier","h":"#maximally-localized-wannier-function","p":172},{"i":178,"t":"Introduction to Wannier Basis lecture by Vijay A. Singh Maximally localized generalized Wannier functions for composite energy bands, Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997) Maximally localized Wannier functions for entangled energy bands, Souza, Marzari and Vanderbilt, Phys. Rev. B 65, 035109 (2001) Maximally localized Wannier functions: Theory and applications, Marzari et. al., Rev. Mod. Phys. 84, 1419 (2012) Introduction to Maximally Localized Wannier Functions, Ambrosetti and Silvestrelli, Reviews in Computational Chemistry, Ch. 6, pp. 327 (2016)","s":"Resources","u":"/espresso/theory/wannier","h":"#resources","p":172},{"i":180,"t":"We want to calculate the electronic structure of real materials and their physical properties by ab-initio method. Electrons are microscopic particle, hence their dynamics is governed by the laws of quantum mechanics. Quantum particles are described by the wave function. λ⋅p=h\\lambda \\cdot p = hλ⋅p=h where hhh is the Plank constant. The Wavefunction of an electron in a potential filed (V)(V)(V) is calculated by solving the Schrödinger equation: −ℏ22m∇2Ψ(r,t)+V(r,t)=iℏ∂Ψ(r,t)∂t-\\frac{\\hbar^2}{2m} \\nabla^2 \\Psi(\\textbf{r}, t) + V(\\textbf{r}, t) = i\\hbar \\frac{\\partial\\Psi(\\textbf{r}, t)}{\\partial t}−2mℏ2​∇2Ψ(r,t)+V(r,t)=iℏ∂t∂Ψ(r,t)​ Fortunately, in most practical purposes, the potential field is not a function of time (t)(t)(t), or even if it is a function of time, they changes relatively slowly compared to the dynamics we are interested in. For example, the electrons inside a material are subjected to the Coulomb field of the nucleus. The nucleus is heavy and their motion is much slower than the motion of the electrons. In such situation, we can separate out the spatial and temporal parts of the wave function: Ψ(r,t)=ψ(r)f(t)\\Psi(\\textbf{r}, t) = \\psi(\\textbf{r}) f(t)Ψ(r,t)=ψ(r)f(t) That reduces our task to solving only time independent Schrödinger equation: [−ℏ2∇22m+v(r)]ψ(r)=ϵψ(r)\\left[-\\frac{\\hbar^2 \\nabla^2}{2m} + v(\\textbf{r})\\right] \\psi(\\textbf{r}) = \\epsilon \\psi(\\textbf{r})[−2mℏ2∇2​+v(r)]ψ(r)=ϵψ(r) Once we have the wavefunction, we can calculate the observables by taking the expectation values. ⟨ψi∣ψj⟩=δij\\braket{\\psi_i | \\psi_j} = \\delta_{ij}⟨ψi​∣ψj​⟩=δij​⟨ψi∣H^∣ψi⟩=ϵi\\braket{\\psi_i | \\hat{H} | \\psi_i} = \\epsilon_i⟨ψi​∣H^∣ψi​⟩=ϵi​ However, the challenge is to solve the Schrödinger equation as a real physical system is consists of a large number of atoms. The Schrödinger equation becomes coupled many-body equation. [−ℏ2m∑i=1N∇i2+∑i=1NV(ri)+∑i=1N∑j - -Search the documentation - - + +Search the documentation + + -

Search the documentation

Copyright © 2024 Pranab Das. All rights reserved.
+

Search the documentation

Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/setup/crystal-structure/index.html b/setup/crystal-structure/index.html index 2b98a2b9..5084533a 100644 --- a/setup/crystal-structure/index.html +++ b/setup/crystal-structure/index.html @@ -2,13 +2,13 @@ - -Crystal structure • Quantum Espresso Tutorial - - + +Crystal structure • Quantum Espresso Tutorial + + -

Crystal structure

Structure databases​

+

Crystal structure

Structure databases​

Density functional theory (DFT) calculations are ab-initio meaning the calculation is done from the scratch based on given input parameters. We need to provide the crystal structure in order to calculate DFT. Crystal structures are @@ -31,7 +31,7 @@ problems may arrise.

ibrav numbers for different lattice types:

ibravLattice type
1Simple cubic
2Face centered cubic
3,-3Body centered cubic
4Hexagonal
5Trigonal with c as 3-fold axis
-5Trigonal with <111> as 3-fold axis
6Simple tetragonal
7Centered tetragonal
8Simple orthorhombic
9,-9,91One-face centered orthorhombic
10Face centered orthorhombic
11Body centered orthorhombic
12Simple monoclinic, c unique
-12Simple monoclinic, b unique
13One base centered monoclinic, c unique
-13One base centered monoclinic, b unique
14Triclinic
-

Useful tools:​

+

Useful tools:​

Vesta - https://jp-minerals.org/vesta/en/. It helps you visualize crystal structure, create and modify supercells, crystal structures, and many other useful functionalities.

@@ -42,7 +42,7 @@

Useful to 
export PATH="/home/pranab/.local/lib/python3.8/site-packages/:$PATH"

Running cif2cell command:

cif2cell file.cif -p quantum-espresso -o inputfile.in
-

Xcrysdens​

+

Xcrysdens​

You can explore the crystal structure, find out k-path and many more using Xcrysdens application - http://www.xcrysden.org

For certain functionality, Xcrysdens requires basic calculator program. On @@ -52,14 +52,14 @@

Xcrysdens
# install dependencies
sudo apt install --no-install-recommends bc tk libglu1-mesa libtogl2 \
      libfftw3-3 libxmu6 imagemagick openbabel libgfortran5

# download the latest version of xcrysden and extract
wget http://www.xcrysden.org/download/xcrysden-1.6.2-linux_x86_64-shared.tar.gz
tar -zxvf xcrysden-1.6.2-linux_x86_64-shared.tar.gz

# launch (provided you extracted under your home directory)
~/xcrysden-1.6.2-bin-shared/xcrysden

If you are on WSL, you need to install X-server (X-ming for Windows) on the host and set export DISPLAY=:0 in your WSL instance.

-

QE Input generator​

+

QE Input generator​

You can generate PWscf input files using tools in this website as well https://www.materialscloud.org/work/tools/qeinputgenerator

The same website also has a tool for k-path visualization and generation https://www.materialscloud.org/work/tools/seekpath

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/setup/hpc/index.html b/setup/hpc/index.html index 56421190..4009c840 100644 --- a/setup/hpc/index.html +++ b/setup/hpc/index.html @@ -2,15 +2,15 @@ - -High Performance Computing • Quantum Espresso Tutorial - - + +High Performance Computing • Quantum Espresso Tutorial + + -

High Performance Computing

In order to perform computationally heavy calculations, we would require access +

High Performance Computing

In order to perform computationally heavy calculations, we would require access to high performance computing facilities.

-

Useful UNIX commands​

+

Useful UNIX commands​

Connect to a login node via ssh:

ssh {username}@atlas9.nus.edu.sg

Secure copy files between local and remote machines:

@@ -19,7 +19,7 @@

U 
du -hs .
du -hs /path/

Rsync to synchronize two folders:

rsync -azhv --delete /source/my_project/ /destination/my_project
-

Running jobs at NUS HPC​

+

Running jobs at NUS HPC​

Check your storage quota:

hpc s

PBS commands:

@@ -50,7 +50,7 @@ 

qstat -f {job-id}

Stopping a job:

qdel {job-id}
-

Abort and restart a calculation​

+

Abort and restart a calculation​

If you need to modify certain parameters while the program is running, e.g., you want to change the mixing_beta value because SCF accuracy is oscillation without any sign of convergence. Create an empty file named {prefix}.EXIT in @@ -62,7 +62,7 @@ 

&CONTROL
  ...
  restart_mode = 'restart'
  ...
/

-

Compiling Quantum Espresso using Intel® Math Kernel Library (MKL)​

+

Compiling Quantum Espresso using Intel® Math Kernel Library (MKL)​

If you need a newer or specific version of Quantum Espresso that is not installed in the NUS clusters or you have modified the source codes yourself, here are the steps that I followed to successfully compile.

@@ -103,18 +103,18 @@

Installing Intel oneAPI libraries​

+

Installing Intel oneAPI libraries​

If you need to install Intel oneAPI libraries yourself, following instructions might be useful. Please refer to Intel website for up to date information.

-

Intel oneAPI Base Toolkit:​

+

Intel oneAPI Base Toolkit:​

wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/992857b9-624c-45de-9701-f6445d845359/l_BaseKit_p_2023.2.0.49397_offline.sh

# requires gnu-awk
sudo apt update && sudo apt install -y --no-install-recommends gawk gcc g++

# interactive cli installation
sudo apt install -y --no-install-recommends ncurses-term
sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --cli

# list components included in oneAPI Base Toolkit
sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --list-components

# install a subset of components with silent/unattended option
sudo sh ./l_BaseKit_p_2023.2.0.49397_offline.sh -a --silent --eula accept --components intel.oneapi.lin.dpcpp-cpp-compiler:intel.oneapi.lin.mkl.devel
note

If you install oneAPI without sudo privilege, it will be installed under the user directory: /home/{username}/intel/oneapi/. After installation is completed, the setup script will print the installation location.

-

HPC Toolkit​

+

HPC Toolkit​

wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/0722521a-34b5-4c41-af3f-d5d14e88248d/l_HPCKit_p_2023.2.0.49440_offline.sh
sudo sh ./l_HPCKit_p_2023.2.0.49440_offline.sh -a --silent --eula accept
-

Intel MKL library​

+

Intel MKL library​

Installing individual components:

wget https://registrationcenter-download.intel.com/akdlm/IRC_NAS/adb8a02c-4ee7-4882-97d6-a524150da358/l_onemkl_p_2023.2.0.49497_offline.sh
sudo sh ./l_onemkl_p_2023.2.0.49497_offline.sh -a --silent --eula accept

After installation, do not forget to source the environment variables before @@ -122,18 +122,18 @@

Inte 
source /opt/intel/oneapi/setvars.sh

Compile quantum espresso:

wget https://gitlab.com/QEF/q-e/-/archive/qe-7.2/q-e-qe-7.2.tar.gz
tar -zxvf q-e-qe-7.2.tar.gz
rm q-e-qe-7.2.tar.gz
cd q-e-qe-7.2
./configure \
  F90=mpiifort \
  MPIF90=mpiifort \
  CC=mpicc CXX=icc \
  F77=mpiifort \
  FFLAGS="-O3 -assume byterecl -g -traceback" \
  LAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \
  BLAS_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl" \
  SCALAPACK_LIBS="-L${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lmkl_blacs_intelmpi_lp64 -lpthread -lm -ldl"
make -j4 all
-

Compiling Quantum Espresso with CMake​

+

Compiling Quantum Espresso with CMake​

Please check out the official documentation for more details. It requires cmake version 3.14 or later.

apt update && apt install autoconf cmake gawk gcc g++ make

I used following steps to successfully compile Quantum Espresso using 2023 versions of Intel libraries in Ubuntu 22.04 system:

cd q-e-qe-7.2
mkdir build && cd build
cmake -DCMAKE_C_COMPILER=mpiicc -DCMAKE_Fortran_COMPILER=mpiifort -DQE_ENABLE_SCALAPACK=ON ..
make -j4
mv bin ..
cd ..
rm -rf build
-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/setup/install/index.html b/setup/install/index.html index 0950d838..ed625810 100644 --- a/setup/install/index.html +++ b/setup/install/index.html @@ -2,13 +2,13 @@ - -Quantum Espresso installation • Quantum Espresso Tutorial - - + +Quantum Espresso installation • Quantum Espresso Tutorial + + -

Quantum Espresso installation

We can install Quantum Espresso on our personal laptops or desktops to run +

Quantum Espresso installation

We can install Quantum Espresso on our personal laptops or desktops to run relatively less computationally intensive calculations. If we intend to perform computationally heavy tasks, we would need access to better computing resources with large number of CPU (or GPU) cores, memory, bandwidth, and disc IO.

@@ -78,7 +78,7 @@ library. For example, you can replace openmpi libraries with Intel MKL or MPICH implementations. Please do research yourself or ask help from someone who has knowledge about high performance computing.

-

Installing PWTK​

+

Installing PWTK​

We will install a very hand scripting package PWscf Toolkit (PWTK). First we need to install following dependencies:

sudo apt install tcl tcllib
@@ -88,6 +88,6 @@

Instal need to just un-tar (no need to compile):

tar -zxvf pwtk-2.0.tar.gz

Add the path (modify below as appropriate) to .bashrc:

-
echo 'export PATH="/root/pwtk-2.0:$PATH"' >> ~/.bashrc
source ~/.bashrc

Copyright © 2024 Pranab Das. All rights reserved.
+
echo 'export PATH="/root/pwtk-2.0:$PATH"' >> ~/.bashrc
source ~/.bashrc
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/setup/jupyter/index.html b/setup/jupyter/index.html index 88840255..c5fff1d7 100644 --- a/setup/jupyter/index.html +++ b/setup/jupyter/index.html @@ -2,14 +2,14 @@ - -Jupyter notebooks • Quantum Espresso Tutorial - - + +Jupyter notebooks • Quantum Espresso Tutorial + + -

Jupyter notebooks

There are several ways you can run Jupyterlab in your computer.

-

1. Install on your computer​

+

Jupyter notebooks

There are several ways you can run Jupyterlab in your computer.

+

1. Install on your computer​

  • Install Python 3 in your computer 
    # on ubuntu / debian
    apt install python3 python3-pip
    @@ -21,7 +21,7 @@ 

    jupyter-lab
    # or the classic jupyter notebook
    jupyter-notebook

-

2. Install python packages via virtualenv​

+

2. Install python packages via virtualenv​

  • Install Python 3 and virtualenv on your computer 
    pip3 install --upgrade virtualenv
    @@ -38,7 +38,7 @@ 

    deactivate

-

3. Run on a container​

+

3. Run on a container​

  • Install Docker
  • Create an image with Python and the required packages installed @@ -50,6 +50,6 @@

    3
  • Launch Jupyterlab 
    jupyter-lab
    • -

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/setup/pseudo-potential/index.html b/setup/pseudo-potential/index.html index bd9cf1e4..56891756 100644 --- a/setup/pseudo-potential/index.html +++ b/setup/pseudo-potential/index.html @@ -2,13 +2,13 @@ - -Pseudo potentials • Quantum Espresso Tutorial - - + +Pseudo potentials • Quantum Espresso Tutorial + + -

Pseudo potentials

In Quantum Espresso, pseudopotential replaces the actual electron-ion +

Pseudo potentials

In Quantum Espresso, pseudopotential replaces the actual electron-ion interaction. The pseudopotential describes the atomic nucleus and all the electrons except the outermost valence shell. The rapidly changing potential field near the atomic core is replaced by a smoother function that simulates the @@ -75,9 +75,9 @@ igcx. However, it is allowed to mix those two types of pseudo. We can set desired exchange correlation functional via input_dft instead of reading from the pseudopotential file.

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/sitemap.xml b/sitemap.xml index 5566539d..ff3c49b0 100644 --- a/sitemap.xml +++ b/sitemap.xml @@ -1 +1 @@ -https://pranabdas.github.io/espresso/searchweekly0.5https://pranabdas.github.io/espresso/weekly0.5https://pranabdas.github.io/espresso/category/hands-onweekly0.5https://pranabdas.github.io/espresso/category/setupweekly0.5https://pranabdas.github.io/espresso/category/theoryweekly0.5https://pranabdas.github.io/espresso/hands-on/aluminumweekly0.5https://pranabdas.github.io/espresso/hands-on/bandsweekly0.5https://pranabdas.github.io/espresso/hands-on/Bi2Se3weekly0.5https://pranabdas.github.io/espresso/hands-on/convergenceweekly0.5https://pranabdas.github.io/espresso/hands-on/dft-uweekly0.5https://pranabdas.github.io/espresso/hands-on/dosweekly0.5https://pranabdas.github.io/espresso/hands-on/epsilonweekly0.5https://pranabdas.github.io/espresso/hands-on/feweekly0.5https://pranabdas.github.io/espresso/hands-on/fermi-surfaceweekly0.5https://pranabdas.github.io/espresso/hands-on/GaAsweekly0.5https://pranabdas.github.io/espresso/hands-on/grapheneweekly0.5https://pranabdas.github.io/espresso/hands-on/kpdosweekly0.5https://pranabdas.github.io/espresso/hands-on/molecular-dynamics-pwweekly0.5https://pranabdas.github.io/espresso/hands-on/niweekly0.5https://pranabdas.github.io/espresso/hands-on/pdosweekly0.5https://pranabdas.github.io/espresso/hands-on/phononweekly0.5https://pranabdas.github.io/espresso/hands-on/scfweekly0.5https://pranabdas.github.io/espresso/hands-on/socweekly0.5https://pranabdas.github.io/espresso/hands-on/structure-optimizationweekly0.5https://pranabdas.github.io/espresso/hands-on/wannierweekly0.5https://pranabdas.github.io/espresso/licenseweekly0.5https://pranabdas.github.io/espresso/resourcesweekly0.5https://pranabdas.github.io/espresso/setup/crystal-structureweekly0.5https://pranabdas.github.io/espresso/setup/hpcweekly0.5https://pranabdas.github.io/espresso/setup/installweekly0.5https://pranabdas.github.io/espresso/setup/jupyterweekly0.5https://pranabdas.github.io/espresso/setup/pseudo-potentialweekly0.5https://pranabdas.github.io/espresso/theory/dftweekly0.5https://pranabdas.github.io/espresso/theory/hartree-fockweekly0.5https://pranabdas.github.io/espresso/theory/problem-statementweekly0.5https://pranabdas.github.io/espresso/theory/wannierweekly0.5 \ No newline at end of file +https://pranabdas.github.io/espresso/searchweekly0.5https://pranabdas.github.io/espresso/category/hands-onweekly0.5https://pranabdas.github.io/espresso/category/setupweekly0.5https://pranabdas.github.io/espresso/category/theoryweekly0.5https://pranabdas.github.io/espresso/hands-on/aluminumweekly0.5https://pranabdas.github.io/espresso/hands-on/bandsweekly0.5https://pranabdas.github.io/espresso/hands-on/Bi2Se3weekly0.5https://pranabdas.github.io/espresso/hands-on/convergenceweekly0.5https://pranabdas.github.io/espresso/hands-on/dft-uweekly0.5https://pranabdas.github.io/espresso/hands-on/dosweekly0.5https://pranabdas.github.io/espresso/hands-on/epsilonweekly0.5https://pranabdas.github.io/espresso/hands-on/feweekly0.5https://pranabdas.github.io/espresso/hands-on/fermi-surfaceweekly0.5https://pranabdas.github.io/espresso/hands-on/GaAsweekly0.5https://pranabdas.github.io/espresso/hands-on/grapheneweekly0.5https://pranabdas.github.io/espresso/hands-on/kpdosweekly0.5https://pranabdas.github.io/espresso/hands-on/molecular-dynamics-pwweekly0.5https://pranabdas.github.io/espresso/hands-on/niweekly0.5https://pranabdas.github.io/espresso/hands-on/pdosweekly0.5https://pranabdas.github.io/espresso/hands-on/phononweekly0.5https://pranabdas.github.io/espresso/hands-on/scfweekly0.5https://pranabdas.github.io/espresso/hands-on/socweekly0.5https://pranabdas.github.io/espresso/hands-on/structure-optimizationweekly0.5https://pranabdas.github.io/espresso/hands-on/wannierweekly0.5https://pranabdas.github.io/espresso/licenseweekly0.5https://pranabdas.github.io/espresso/resourcesweekly0.5https://pranabdas.github.io/espresso/setup/crystal-structureweekly0.5https://pranabdas.github.io/espresso/setup/hpcweekly0.5https://pranabdas.github.io/espresso/setup/installweekly0.5https://pranabdas.github.io/espresso/setup/jupyterweekly0.5https://pranabdas.github.io/espresso/setup/pseudo-potentialweekly0.5https://pranabdas.github.io/espresso/theory/dftweekly0.5https://pranabdas.github.io/espresso/theory/hartree-fockweekly0.5https://pranabdas.github.io/espresso/theory/problem-statementweekly0.5https://pranabdas.github.io/espresso/theory/wannierweekly0.5https://pranabdas.github.io/espresso/weekly0.5 \ No newline at end of file diff --git a/theory/dft/index.html b/theory/dft/index.html index ff5b3c8a..8f322f3b 100644 --- a/theory/dft/index.html +++ b/theory/dft/index.html @@ -2,13 +2,13 @@ - -Introduction to Density Functional Theory • Quantum Espresso Tutorial - - + +Introduction to Density Functional Theory • Quantum Espresso Tutorial + + -

Introduction to Density Functional Theory

Density functional theory (DFT) approaches the many-body problem by focusing on +

Introduction to Density Functional Theory

Density functional theory (DFT) approaches the many-body problem by focusing on the electronic density which is a function of three spatial coordinates instead of finding the wave functions. DFT tries to minimize the energy of a system (ground state) in a self consistent way, and it is very successful in @@ -17,7 +17,7 @@ function of the variable xx while F[f]F[f] is a functional of the function ff.

y=f(x)y = f(x)

ff is a function, it takes a number xx as input and output yy is also a number.

y=F[f(x)]y = F[f(x)]

FF is a functional it takes function f(x)f(x) as input and output yy is a number.

-

Hohenberg-Kohn Theorem 1​

+

Hohenberg-Kohn Theorem 1​

The ground state density n(r)n(\textbf{r}) determines the external potential energy v(r)v(\textbf{r}) to within a trivial additive constant.

@@ -30,7 +30,7 @@

Hohenberg-Kohn Theorem 2​

+

Hohenberg-Kohn Theorem 2​

Total energy of the system E(n)E(n) is minimal when n(r)n(\textbf{r}) is the actual ground-state density, among all possible electron densities.

@@ -43,7 +43,7 @@

Ψ0(r1,r2,…,rN)=Ψ[n0(r)]\Psi_0(\textbf{r}_1, \textbf{r}_2, \dots, \textbf{r}_N) = \Psi[n_0(\textbf{r})] -

Kohn-Sham hypothesis​

+

Kohn-Sham hypothesis​

For any system of NN interacting electrons in a given external potential vext(r)v_{ext} (\textbf{r}), there is a virtual system of NN non-interacting @@ -72,16 +72,16 @@

K solving a non-interacting Hamiltonian.

info

vext(r)v_{ext}(\textbf{r}) includes the potential energy due to nuclear field, and external electric and magnetic fields if present.

-

Exchange-correlation functional​

-

Local Density Approximation (LDA)​

+

Exchange-correlation functional​

+

Local Density Approximation (LDA)​

Energy functional is a function of the local charge density:

Exc=∫n(r)ϵxc(n(r))drE_{xc} = \int n(\textbf{r}) \epsilon_{xc}(n(\textbf{r})) d\textbf{r} -vxc(r)=ϵxc(n(r))+n(r)dϵxc(n)dn∣n=n(r)v_{xc}(\textbf{r}) = \epsilon_{xc}(n(\textbf{r})) + n(\textbf{r})\frac{d\epsilon_{xc}(n)}{dn}\bigg\rvert_{n=n(\textbf{r})}
-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/theory/hartree-fock/index.html b/theory/hartree-fock/index.html index 2566336a..a39153a3 100644 --- a/theory/hartree-fock/index.html +++ b/theory/hartree-fock/index.html @@ -2,13 +2,13 @@ - -Hartree-Fock Theory • Quantum Espresso Tutorial - - + +Hartree-Fock Theory • Quantum Espresso Tutorial + + -

Hartree-Fock Theory

Hatree-Fock theory is foundational to many subsequent electronic structure +

Hartree-Fock Theory

Hatree-Fock theory is foundational to many subsequent electronic structure theories. It is an independent particle model or mean filed theory. Consider we have two non-interacting electrons. In that case, the Hamiltonian would be separable, and the total wavefunction Ψ(r1,r2)\Psi(\textbf{r}_1, \textbf{r}_2) would @@ -34,7 +34,7 @@ s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">​1​[χ1​(r1​)χ2​(r2​)−χ1​(r2​)χ2​(r1​)] -

Slater determinant​

+

Slater determinant​

The above equation can be written as:

Ψ(r1,r2)=12∣χ1(r1)χ2(r1)χ1(r2)χ2(r2)∣\Psi(\textbf{r}_1, \textbf{r}_2) = \frac{1}{\sqrt{2}} \begin{vmatrix} @@ -77,14 +77,14 @@

Sla c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">​1​​χ1​(r1​)χ1​(r2​)⋮χ1​(rN​)​χ2​(r1​)χ2​(r2​)⋮χ2​(rN​)​⋯⋯⋱⋯​χN​(r1​)χN​(r2​)⋮χN​(rN​)​​χ1​(r1​)χ1​(r2​)⋮χ1​(rN​)​χ2​(r1​)χ2​(r2​)⋮χ2​(rN​)​⋯⋯⋱⋯​χN​(r1​)χN​(r2​)⋮χN​(rN​)​​

The above antisymmetrized product can describe electrons that move independently of each other while they experience an average (mean-field) Coulomb force.

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
Copyright © 2024 Pranab Das. All rights reserved.
\ No newline at end of file diff --git a/theory/problem-statement/index.html b/theory/problem-statement/index.html index ac3f2db4..106e2bd1 100644 --- a/theory/problem-statement/index.html +++ b/theory/problem-statement/index.html @@ -2,13 +2,13 @@ - -What problem are we trying to solve? • Quantum Espresso Tutorial - - + +What problem are we trying to solve? • Quantum Espresso Tutorial + + -

What problem are we trying to solve?

We want to calculate the electronic structure of real materials and their +

What problem are we trying to solve?

We want to calculate the electronic structure of real materials and their physical properties by ab-initio method. Electrons are microscopic particle, hence their dynamics is governed by the laws of quantum mechanics. Quantum particles are described by the wave function.

@@ -35,7 +35,7 @@

However, the challenge is to solve the Schrödinger equation as a real physical system is consists of a large number of atoms. The Schrödinger equation becomes coupled many-body equation.

-[−ℏ2m∑i=1N∇i2+∑i=1NV(ri)+∑i=1N∑j<iU(ri,rj)]ψ(r1,r2,...,rN)=Eψ(r1,r2,...,rN)\left[-\frac{\hbar}{2m} \sum_{i=1}^N \nabla_i^2 + \sum_{i=1}^NV(\textbf{r}_i) +[−ℏ2m∑i=1N∇i2+∑i=1NV(ri)+∑i=1N∑j<iU(ri,rj)]ψ(r1,r2,...,rN)=Eψ(r1,r2,...,rN)\left[-\frac{\hbar}{2m} \sum_{i=1}^N \nabla_i^2 + \sum_{i=1}^NV(\textbf{r}_i) + \sum_{i=1}^N \sum_{j<i}U(\textbf{r}_i, \textbf{r}_j)\right]\psi(\textbf{r}_1, \textbf{r}_2, ..., \textbf{r}_N) = E\psi(\textbf{r}_1, \textbf{r}_2, ..., \textbf{r}_N) diff --git a/theory/wannier/index.html b/theory/wannier/index.html index 3f93da9d..c2968527 100644 --- a/theory/wannier/index.html +++ b/theory/wannier/index.html @@ -2,13 +2,13 @@ - -Wannier basis • Quantum Espresso Tutorial - - + +Wannier basis • Quantum Espresso Tutorial + + -

Wannier basis

Introduction​

+

Wannier basis

Introduction​

Wannier functions are an alternative representation of Bloch states in terms of a localized basis set. Suppose we have NN atoms each separated by lattice constant aa in one dimension. Bloch states are indexed by the wave vector kk.

@@ -84,18 +84,18 @@ \end{aligned}

where ϵn\epsilon_n is onsite or diagonal term and tmnt_{mn} (> 0) is hopping or off-diagonal term.

-

Maximally Localized Wannier Function​

+

Maximally Localized Wannier Function​

The choice of Wannier function is not unique. One such option could be the set that maximizes localization. Two different sets of Wannier basis are connected via unitary transformation. MLWFs can be considered as a generalization of localized molecular orbitals (LMOs) to periodic systems.

-

Resources​

+

Resources​

Copyright © 2024 Pranab Das. All rights reserved.
+
\ No newline at end of file