diff --git a/ChangeLog b/ChangeLog index 6549b4d6..93f665f4 100644 --- a/ChangeLog +++ b/ChangeLog @@ -3,6 +3,17 @@ -Name -changes +-------------- +Sep 22, 2023 +Name: Qimen Xu, Ziao Tang, Yu Zhang +Changes: (eigenSolver.c, electronicGroundState.c, initialization.c, occupation.c, orbitalElecDensInit.c, printing.c, readfiles.c, isddft.h, readfiles.h, utils/) +1. Add band structure calculation feature. +2. Add `readDens_cube` routine for reading input density file. +3. Fix memory leak issues: +(a) when ixc[2] is nonzero, countPotentialCalculate is not initialized, +(b) EigenFilename is not initialized on processes with rank > 0. +4. Add a python script in `utils/` for processing `.eigen` files and visualizing the band structure of a given system. + -------------- Sep 18, 2023 Name: Xin Jing diff --git a/doc/.LaTeX/BandStructure.tex b/doc/.LaTeX/BandStructure.tex new file mode 100644 index 00000000..c3de73c6 --- /dev/null +++ b/doc/.LaTeX/BandStructure.tex @@ -0,0 +1,153 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[allowframebreaks,c]{} \label{BandStructure} + +\begin{center} +\Huge \textbf{Band structure} +\end{center} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[allowframebreaks]{\texttt{BAND\_STRUCTURE}} \label{BAND_STRUCTURE} +\vspace*{-12pt} +\begin{columns} +\column{0.4\linewidth} +\begin{block}{Type} +Integer +\end{block} + +\begin{block}{Default} +0 +\end{block} + +\column{0.4\linewidth} +\begin{block}{Unit} +No unit +\end{block} + +\begin{block}{Example} +\texttt{BAND\_STRUCTURE}: 1 +\end{block} +\end{columns} + +\begin{block}{Description} +Flag for calculation of the band structure. +\end{block} + +%\begin{block}{Remark} +%\end{block} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[allowframebreaks]{\texttt{KPT\_PATHS}} \label{KPT_PATHS} +\vspace*{-12pt} +\begin{columns} +\column{0.4\linewidth} +\begin{block}{Type} +Double +\end{block} + +\begin{block}{Default} +None +\end{block} + +\column{0.5\linewidth} +\begin{block}{Unit} +No unit +\end{block} + +\begin{block}{Example} +\texttt{KPT\_PATHS: 2\\} +0.0 0.0 0.0 \# Gamma\\ +0.5 0.5 0.5 \# A\\ +0.5 0.5 0.5 \# A\\ +0.5 0.5 0.0 \# M +\end{block} +\end{columns} + +\begin{block}{Description} +The k-point paths (high-symmetry lines) for band structure calculations. It starts with the total number of high-symmetry lines, followed by fractional coordinates indicating the start and end points of each line. +\end{block} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[allowframebreaks]{\texttt{KPT\_PER\_LINE}} \label{KPT_PER_LINE} +\vspace*{-12pt} +\begin{columns} +\column{0.4\linewidth} +\begin{block}{Type} +Integer +\end{block} + +\begin{block}{Default} +10 +\end{block} + +\column{0.4\linewidth} +\begin{block}{Unit} +No unit +\end{block} + +\begin{block}{Example} +\texttt{KPT\_PER\_LINE}: 15 +\end{block} +\end{columns} + +\begin{block}{Description} +The number of k-points on each high-symmetry line. +\end{block} + +\begin{block}{Remark} +This value accounts for both endpoints of the high-symmetry line. +\end{block} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[allowframebreaks]{\texttt{INPUT\_DENS\_FILE}} \label{INPUT_DENS_FILE} +\vspace*{-12pt} +\begin{columns} +\column{0.4\linewidth} +\begin{block}{Type} +String +\end{block} + +\begin{block}{Default} +None +\end{block} + +\column{0.4\linewidth} +\begin{block}{Unit} +No unit +\end{block} + +\begin{block}{Example} +\texttt{INPUT\_DENS\_FILE}: Si.dens Si.densUp Si.densDwn +\end{block} +\end{columns} + +\begin{block}{Description} +The name of the input density file(s) in cube format. +\end{block} + +\begin{block}{Remark} +For spin-unpolarized systems, only the total density file is required. For spin-polarized systems, three density files are required, which are the total electron density, spin-up density, and spin-down density, respectively. +\end{block} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/doc/.LaTeX/Introduction.tex b/doc/.LaTeX/Introduction.tex index 20e22ce3..7d860cb7 100644 --- a/doc/.LaTeX/Introduction.tex +++ b/doc/.LaTeX/Introduction.tex @@ -361,6 +361,14 @@ \hyperlink{FIRE_MAXMOV}{\texttt{FIRE\_MAXMOV}} $\vert$ \hyperlink{RESTART_FLAG}{\texttt{RESTART\_FLAG}} \end{block} + + \vspace{-2mm} + \begin{block}{Band structure} + \hyperlink{BAND_STRUCTURE}{\texttt{BAND\_STRUCTURE}} $\vert$ + \hyperlink{KPT_PATHS}{\texttt{KPT\_PATHS}} $\vert$ + \hyperlink{KPT_PER_LINE}{\texttt{KPT\_PER\_LINE}} $\vert$ + \hyperlink{INPUT_DENS_FILE}{\texttt{INPUT\_DENS\_FILE}} + \end{block} \begin{block}{Print options} \hyperlink{PRINT_ATOMS}{\texttt{PRINT\_ATOMS}} $\vert$ diff --git a/doc/.LaTeX/Manual.tex b/doc/.LaTeX/Manual.tex index 634c4b1e..53d8934d 100644 --- a/doc/.LaTeX/Manual.tex +++ b/doc/.LaTeX/Manual.tex @@ -97,6 +97,7 @@ \include{Stress} \include{MD} \include{Optimization} +\include{BandStructure} \include{Print} \include{Paral} \include{SQ} diff --git a/doc/.LaTeX/SCF.tex b/doc/.LaTeX/SCF.tex index 0ead8f67..6818c4ca 100644 --- a/doc/.LaTeX/SCF.tex +++ b/doc/.LaTeX/SCF.tex @@ -86,7 +86,7 @@ \end{block} \begin{block}{Default} -4 or 6 +4, 6, or 10 \end{block} \column{0.4\linewidth} @@ -105,7 +105,7 @@ \begin{block}{Remark} Values smaller than the default value of 4 can result in a significant increase in the number of SCF -iterations. Larger values can sometimes reduce the number of SCF iterations. For non-collinear spin calculation, default is 6 otherwise 4. +iterations. Larger values can sometimes reduce the number of SCF iterations. For non-collinear spin calculation, default is 6 otherwise 4. For band structure calculations, default is 10. \end{block} \end{frame} diff --git a/doc/Manual.pdf b/doc/Manual.pdf index fdd8e13b..a1a04250 100644 Binary files a/doc/Manual.pdf and b/doc/Manual.pdf differ diff --git a/src/eigenSolver.c b/src/eigenSolver.c index a69c17df..6624d73e 100644 --- a/src/eigenSolver.c +++ b/src/eigenSolver.c @@ -2385,4 +2385,4 @@ void Chol_orth(double *A, const int *descA, double *z, const int *descz, const i pdpotrf_("U", n, z, &ONE, &ONE, descz, &info); pdtrsm_("R", "U", "N", "N", m, n, &alpha, z, &ONE, &ONE, descz, A, &ONE, &ONE, descA); #endif //(#ifdef USE_MKL) -} \ No newline at end of file +} diff --git a/src/electronicGroundState.c b/src/electronicGroundState.c index 434ef23e..0d473f7b 100644 --- a/src/electronicGroundState.c +++ b/src/electronicGroundState.c @@ -1267,7 +1267,7 @@ void Transfer_Veff_loc(SPARC_OBJ *pSPARC, double *Veff_phi_domain, double *Veff_ if (rank == 0) printf("---Transfer Veff_loc: mpi_bcast (count = %d) to all bandcomms took %.3f ms\n",pSPARC->Nd_d_dmcomm,(t2-t1)*1e3); #endif - if ((pSPARC->countPotentialCalculate > 1) && (pSPARC->ixc[2])) + if ((pSPARC->ixc[2]) && (pSPARC->countPotentialCalculate > 1)) Transfer_vxcMGGA3_phi_psi(pSPARC, pSPARC->vxcMGGA3, pSPARC->vxcMGGA3_loc_dmcomm); // only transfer the potential they are going to use } diff --git a/src/include/isddft.h b/src/include/isddft.h index 7709c181..66cc7cb6 100644 --- a/src/include/isddft.h +++ b/src/include/isddft.h @@ -29,7 +29,8 @@ #define L_STRING 512 #define L_ATMTYPE 8 #define L_QMASS 60 - +// max length of kpoint set +#define L_kpoint 512 // TO PRINT IN COLOR #define RED "\x1B[31m" @@ -972,6 +973,18 @@ typedef struct _SPARC_OBJ{ /* EigenValue problem*/ int StandardEigenFlag; + + /* Band structure plot*/ + int n_kpt_line; + double kredx[L_kpoint],kredy[L_kpoint],kredz[L_kpoint]; + double k1_inpt_kpt[L_kpoint],k2_inpt_kpt[L_kpoint],k3_inpt_kpt[L_kpoint]; + int BandStructFlag; + int kpt_per_line; + char InDensTCubFilename[L_STRING]; + char InDensUCubFilename[L_STRING]; + char InDensDCubFilename[L_STRING]; + int densfilecount; + }SPARC_OBJ; @@ -1229,6 +1242,16 @@ typedef struct _SPARC_INPUT_OBJ{ char SPARCROOT[L_STRING]; // SPARC root directory + + /* Band structure plot*/ + int n_kpt_line; + double kredx[L_kpoint],kredy[L_kpoint],kredz[L_kpoint]; + int BandStructFlag; + int kpt_per_line; + char InDensTCubFilename[L_STRING]; + char InDensUCubFilename[L_STRING]; + char InDensDCubFilename[L_STRING]; + int densfilecount; }SPARC_INPUT_OBJ; diff --git a/src/include/readfiles.h b/src/include/readfiles.h index b1d1d53d..2b8001f5 100644 --- a/src/include/readfiles.h +++ b/src/include/readfiles.h @@ -52,6 +52,28 @@ void read_ion(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC); void read_pseudopotential_PSP(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC); +/** + * @brief Read density in cube format. + * + * @param filename Name of the density file in cube format. + * @param dens_gridsizes (OUTPUT) Grid sizes (in 3-dim) of the density read. + * @param dens_latvecs (OUTPUT) Lattice vectors (scaled) read. + * @return double* (OUTPUT) Density array. + */ +double* readDens_cube(char *filename, int dens_gridsizes[3], double dens_latvecs[9]); + + +/** + * @brief Read data from cube file and check if the lattice vectors + * and the grid sizes match with the input lattice and grid. + * + * @param pSPARC + * @param filename File name of the cube file. + * @return double* Data from file, allocated within this function. + */ +double* read_vec_cube(SPARC_OBJ *pSPARC, char *filename); + + #endif // READFILES_H diff --git a/src/include/tools.h b/src/include/tools.h index c704179c..c340ddc2 100644 --- a/src/include/tools.h +++ b/src/include/tools.h @@ -65,6 +65,31 @@ int strcmpi(const char *p1, const char *p2); void simplifyPath(char* path, char *newpath, size_t newlen); + +/** + * @brief Exact file path from a file name. + * + * @param filename File name. + * @param path (OUTPUT) Path (relative or absolute) where the file is located. + * @param maxlen Maximum length of the path. + */ +void extract_path_from_file(const char *filename, char *path, int maxlen); + + +/** + * @brief Combine a path and a file name and simplify the path. + * + * If the file name is already provided in the absolute path form, then + * path is ignored. Otherwise, the new file name would be a simplified path + * equivalent to "path/fname". + * + * @param path The path relative to which fname is given. + * @param fname The name provided relative to path. + * @param newfname (OUTPUT) The new file name. + */ +void combine_path_filename(const char *path, const char *fname, char *newfname, int maxlen); + + /** * @brief The following code for factorizing an integer is copied from Rosetta Code * https://rosettacode.org/wiki/Factors_of_an_integer#C . It is only used when diff --git a/src/initialization.c b/src/initialization.c index a4cb66c0..313f4475 100644 --- a/src/initialization.c +++ b/src/initialization.c @@ -44,7 +44,128 @@ #define min(x,y) ((x)<(y)?(x):(y)) #define max(x,y) ((x)>(y)?(x):(y)) -#define N_MEMBR 164 +#define N_MEMBR 174 + + +/** + * @brief Calculate cross product of two vectors in R^3 + * + */ +void Cross_Product( + double* x,double* y,double* z, + double a1,double a2,double a3, + double b1,double b2,double b3) +{ + *x = a2*b3-a3*b2; + *y = a3*b1-a1*b3; + *z = a1*b2-a2*b1; +} + +/** + * @brief Calculate k-points for band structure calculation. + * + */ +void calculate_kpts_bandstruct(SPARC_OBJ *pSPARC) { + int rank; + MPI_Comm_rank(MPI_COMM_WORLD, &rank); + + double Lx = pSPARC->latvec_scale_x; + double Ly = pSPARC->latvec_scale_y; + double Lz = pSPARC->latvec_scale_z; + + int kppl = pSPARC->kpt_per_line; + double a1_x = pSPARC->LatVec[0]*Lx; + double a1_y = pSPARC->LatVec[1]*Lx; + double a1_z = pSPARC->LatVec[2]*Lx; + double a2_x = pSPARC->LatVec[3]*Ly; + double a2_y = pSPARC->LatVec[4]*Ly; + double a2_z = pSPARC->LatVec[5]*Ly; + double a3_x = pSPARC->LatVec[6]*Lz; + double a3_y = pSPARC->LatVec[7]*Lz; + double a3_z = pSPARC->LatVec[8]*Lz; + + double volume = 0.0; + double crossx,crossy,crossz; + Cross_Product(&crossx,&crossy,&crossz,a2_x,a2_y,a2_z,a3_x,a3_y,a3_z); + + volume = crossx*a1_x + crossy*a1_y + crossz*a1_z; + //Calculate b1 + Cross_Product(&crossx,&crossy,&crossz,a2_x,a2_y,a2_z,a3_x,a3_y,a3_z); + double b1_x = 2.0*M_PI*crossx/(volume); + double b1_y = 2.0*M_PI*crossy/(volume); + double b1_z = 2.0*M_PI*crossz/(volume); + + //Calculate b2 + Cross_Product(&crossx,&crossy,&crossz,a3_x,a3_y,a3_z,a1_x,a1_y,a1_z); + double b2_x = 2.0*M_PI*crossx/(volume); + double b2_y = 2.0*M_PI*crossy/(volume); + double b2_z = 2.0*M_PI*crossz/(volume); + + //Calculate b3 + Cross_Product(&crossx,&crossy,&crossz,a1_x,a1_y,a1_z,a2_x,a2_y,a2_z); + double b3_x = 2.0*M_PI*crossx/(volume); + double b3_y = 2.0*M_PI*crossy/(volume); + double b3_z = 2.0*M_PI*crossz/(volume); + + for (int i = 0; i < pSPARC->n_kpt_line * 2; i++) { + pSPARC->k1[i] = pSPARC->kredx[i]*b1_x + pSPARC->kredy[i]*b2_x + pSPARC->kredz[i]*b3_x; + pSPARC->k2[i] = pSPARC->kredx[i]*b1_y + pSPARC->kredy[i]*b2_y + pSPARC->kredz[i]*b3_y; + pSPARC->k3[i] = pSPARC->kredx[i]*b1_z + pSPARC->kredy[i]*b2_z + pSPARC->kredz[i]*b3_z; + pSPARC->k1_inpt_kpt[i] = pSPARC->kredx[i]; + pSPARC->k2_inpt_kpt[i] = pSPARC->kredy[i]; + pSPARC->k3_inpt_kpt[i] = pSPARC->kredz[i]; + pSPARC->kptWts[i]= 1.0; + } + + for (int i = 0; i < pSPARC->n_kpt_line; i++) { + int start_ind = i*kppl, end_ind = (i+1)*kppl-1; + pSPARC->k1[start_ind] = pSPARC->kredx[i*2]*b1_x + pSPARC->kredy[i*2]*b2_x + pSPARC->kredz[i*2]*b3_x; + pSPARC->k2[start_ind] = pSPARC->kredx[i*2]*b1_y + pSPARC->kredy[i*2]*b2_y + pSPARC->kredz[i*2]*b3_y; + pSPARC->k3[start_ind] = pSPARC->kredx[i*2]*b1_z + pSPARC->kredy[i*2]*b2_z + pSPARC->kredz[i*2]*b3_z; + pSPARC->k1_inpt_kpt[start_ind] = pSPARC->kredx[i*2]; + pSPARC->k2_inpt_kpt[start_ind] = pSPARC->kredy[i*2]; + pSPARC->k3_inpt_kpt[start_ind] = pSPARC->kredz[i*2]; + pSPARC->kptWts[start_ind]= 1.0; + pSPARC->k1[end_ind] = pSPARC->kredx[i*2+1]*b1_x + pSPARC->kredy[i*2+1]*b2_x + pSPARC->kredz[i*2+1]*b3_x; + pSPARC->k2[end_ind] = pSPARC->kredx[i*2+1]*b1_y + pSPARC->kredy[i*2+1]*b2_y + pSPARC->kredz[i*2+1]*b3_y; + pSPARC->k3[end_ind] = pSPARC->kredx[i*2+1]*b1_z + pSPARC->kredy[i*2+1]*b2_z + pSPARC->kredz[i*2+1]*b3_z; + pSPARC->k1_inpt_kpt[end_ind] = pSPARC->kredx[i*2+1]; + pSPARC->k2_inpt_kpt[end_ind] = pSPARC->kredy[i*2+1]; + pSPARC->k3_inpt_kpt[end_ind] = pSPARC->kredz[i*2+1]; + pSPARC->kptWts[end_ind]= 1.0; + double alpha = 1.0/(kppl-1.0); + double vec_x = pSPARC->kredx[i*2+1] - pSPARC->kredx[i*2]; + double vec_y = pSPARC->kredy[i*2+1] - pSPARC->kredy[i*2]; + double vec_z = pSPARC->kredz[i*2+1] - pSPARC->kredz[i*2]; + for (int j = start_ind+1; j < end_ind; j++) { + double tmpx = pSPARC->kredx[i*2] + vec_x * alpha * (j-start_ind); + double tmpy = pSPARC->kredy[i*2] + vec_y * alpha * (j-start_ind); + double tmpz = pSPARC->kredz[i*2] + vec_z * alpha * (j-start_ind); + pSPARC->k1[j] = tmpx*b1_x + tmpy*b2_x + tmpz*b3_x; + pSPARC->k2[j] = tmpx*b1_y + tmpy*b2_y + tmpz*b3_y; + pSPARC->k3[j] = tmpx*b1_z + tmpy*b2_z + tmpz*b3_z; + pSPARC->k1_inpt_kpt[j] = tmpx; + pSPARC->k2_inpt_kpt[j] = tmpy; + pSPARC->k3_inpt_kpt[j] = tmpz; + pSPARC->kptWts[j]= 1.0; + } + } + + #ifdef DEBUG + if (!rank) { + printf("Number of kpt = %d\n", pSPARC->Nkpts); + //printf("b1x: %8.4f, b1y: %8.4f, b1z: %8.4f\n",b1_x,b1_y,b1_z); + //printf("b2x: %8.4f, b2y: %8.4f, b2z: %8.4f\n",b2_x,b2_y,b2_z); + //printf("b3x: %8.4f, b3y: %8.4f, b3z: %8.4f\n",b3_x,b3_y,b3_z); + printf("Volume = %lf\n",volume); + for (int nk = 0; nk < pSPARC->Nkpts; nk++) { + printf("inpt k1[%2d]: %8.4f, k2[%2d]: %8.4f, k3[%2d]: %8.4f, kptwt[%2d]: %.3f \n", + nk,pSPARC->k1_inpt_kpt[nk],nk,pSPARC->k2_inpt_kpt[nk],nk,pSPARC->k3_inpt_kpt[nk],nk,pSPARC->kptWts[nk]); + } + } + #endif +} + /** @@ -422,7 +543,9 @@ void set_defaults(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) { memset(pSPARC_Input->MDMeth, '\0', sizeof(pSPARC_Input->MDMeth)); memset(pSPARC_Input->RelaxMeth, '\0', sizeof(pSPARC_Input->RelaxMeth)); memset(pSPARC_Input->XC, '\0', sizeof(pSPARC_Input->XC)); - + memset(pSPARC_Input->InDensTCubFilename, '\0', sizeof(pSPARC_Input->InDensTCubFilename)); + memset(pSPARC_Input->InDensUCubFilename, '\0', sizeof(pSPARC_Input->InDensUCubFilename)); + memset(pSPARC_Input->InDensDCubFilename, '\0', sizeof(pSPARC_Input->InDensDCubFilename)); /* default file names (unless otherwise supplied) */ snprintf(pSPARC_Input->filename_out, L_STRING, "%s", pSPARC_Input->filename); snprintf(pSPARC_Input->SPARCROOT, L_STRING, "%s", "UNDEFINED"); @@ -594,6 +717,10 @@ void set_defaults(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) { pSPARC_Input->max_dilatation = 1.06; // maximum lattice dilatation pSPARC_Input->TOL_RELAX_CELL = 1e-2; // in GPa (all periodic) + /* Default band structure calculation parameters */ + pSPARC_Input->BandStructFlag = 0; + pSPARC_Input->kpt_per_line = 10; // number of kpoints on each high-symmetry line + /* Default DFT-D3 correction */ pSPARC_Input->d3Flag = 0; pSPARC_Input->d3Rthr = 1600.0; @@ -1114,7 +1241,17 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { pSPARC->PrintPsiFlag[i] = pSPARC_Input->PrintPsiFlag[i]; pSPARC->PrintEnergyDensFlag = pSPARC_Input->PrintEnergyDensFlag; pSPARC->StandardEigenFlag = pSPARC_Input->StandardEigenFlag; - + pSPARC->BandStructFlag = pSPARC_Input->BandStructFlag; + pSPARC->n_kpt_line = pSPARC_Input->n_kpt_line; + pSPARC->kpt_per_line = pSPARC_Input->kpt_per_line; + if (pSPARC->BandStructFlag == 1) { + for (int i = 0; i < pSPARC->n_kpt_line*2; i++) { + pSPARC->kredx[i] = pSPARC_Input->kredx[i]; + pSPARC->kredy[i] = pSPARC_Input->kredy[i]; + pSPARC->kredz[i] = pSPARC_Input->kredz[i]; + } + } + pSPARC->densfilecount = pSPARC_Input->densfilecount; // double type values pSPARC->range_x = pSPARC_Input->range_x; pSPARC->range_y = pSPARC_Input->range_y; @@ -1201,7 +1338,19 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { strncpy(pSPARC->filename , pSPARC_Input->filename,sizeof(pSPARC->filename)); strncpy(pSPARC->filename_out , pSPARC_Input->filename_out,sizeof(pSPARC->filename_out)); strncpy(pSPARC->SPARCROOT , pSPARC_Input->SPARCROOT,sizeof(pSPARC->SPARCROOT)); + strncpy(pSPARC->InDensTCubFilename, pSPARC_Input->InDensTCubFilename,sizeof(pSPARC->InDensTCubFilename)); + strncpy(pSPARC->InDensUCubFilename, pSPARC_Input->InDensUCubFilename,sizeof(pSPARC->InDensUCubFilename)); + strncpy(pSPARC->InDensDCubFilename, pSPARC_Input->InDensDCubFilename,sizeof(pSPARC->InDensDCubFilename)); + if (pSPARC->BandStructFlag == 1) { + if (pSPARC->densfilecount != 3 && pSPARC->spin_typ == 1) { + printf("Please provide 3 files for band structure with spin polarization!\n"); + exit(EXIT_FAILURE); + } else if(pSPARC->densfilecount != 1 && pSPARC->spin_typ == 0) { + printf("Please provide 1 density file for band structure without spin polarization!\n"); + exit(EXIT_FAILURE); + } + } // find exchange correltaion decomposition xc_decomposition(pSPARC); @@ -1249,8 +1398,8 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { pSPARC->Exc = 0.0; pSPARC->Eband = 0.0; pSPARC->Entropy = 0.0; - pSPARC->Etot = 0.0; pSPARC->Escc = 0.0; + pSPARC->Etot = 0.0; // 3 different spin options if(pSPARC->spin_typ == 0) { @@ -1294,6 +1443,13 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { } #endif + if (pSPARC->BandStructFlag == 1) { + pSPARC->MAXIT_SCF = 1; + pSPARC->MINIT_SCF = 1; + pSPARC->PrintElecDensFlag = 0; + pSPARC->PrintEigenFlag = 1; + } + // estimate Nstates if not provided if (pSPARC->Nstates < 0) { // estimate Nstates using the linear function y = 1.2 * x + 5 @@ -1829,6 +1985,8 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { if (pSPARC->rhoTrigger < 0) { pSPARC->rhoTrigger = (pSPARC->spin_typ == 2 ? 6 : 4); + if (pSPARC->BandStructFlag == 1) + pSPARC->rhoTrigger = 10; } // set default simple (linear) mixing parameter to be the same as for pulay mixing @@ -2195,21 +2353,30 @@ void SPARC_copy_input(SPARC_OBJ *pSPARC, SPARC_INPUT_OBJ *pSPARC_Input) { exit(EXIT_FAILURE); } - // number of k-points after symmetry reduction (currently only - // takes into account the time reversal symmetry) - // WARNING: Time-reversal symmetry only if there is no magnetic field applied - // this won't work with kpt shift - // pSPARC->Nkpts_sym = ceil(pSPARC->Kx*pSPARC->Ky*pSPARC->Kz/2.0); - pSPARC->Nkpts_sym = pSPARC->Nkpts; // will be updated after actual symmetry reduction - - // at this point symmetry reduction is not done yet - pSPARC->kptWts = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); - pSPARC->k1 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); - pSPARC->k2 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); - pSPARC->k3 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); - // calculate the k point and weights (shift in kpt may apply) - Calculate_kpoints(pSPARC); - + if (pSPARC->BandStructFlag == 1) { + pSPARC->Nkpts = pSPARC->kpt_per_line * pSPARC->n_kpt_line; + pSPARC->Nkpts_sym = pSPARC->Nkpts; + pSPARC->kptWts = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k1 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k2 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k3 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + calculate_kpts_bandstruct(pSPARC); + } else { + // number of k-points after symmetry reduction (currently only + // takes into account the time reversal symmetry) + // WARNING: Time-reversal symmetry only if there is no magnetic field applied + // this won't work with kpt shift + // pSPARC->Nkpts_sym = ceil(pSPARC->Kx*pSPARC->Ky*pSPARC->Kz/2.0); + pSPARC->Nkpts_sym = pSPARC->Nkpts; // will be updated after actual symmetry reduction + + // at this point symmetry reduction is not done yet + pSPARC->kptWts = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k1 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k2 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + pSPARC->k3 = (double *)malloc(pSPARC->Nkpts_sym * sizeof(double)); + // calculate the k point and weights (shift in kpt may apply) + Calculate_kpoints(pSPARC); + } // flag to indicate if it is a gamma-point calculation pSPARC->isGammaPoint = (int)(pSPARC->Nkpts_sym == 1 && fabs(pSPARC->k1[0]) < TEMP_TOL @@ -3171,7 +3338,7 @@ void write_output_init(SPARC_OBJ *pSPARC) { } fprintf(output_fp,"***************************************************************************\n"); - fprintf(output_fp,"* SPARC (version Sept 20, 2023) *\n"); + fprintf(output_fp,"* SPARC (version Sept 22, 2023) *\n"); fprintf(output_fp,"* Copyright (c) 2020 Material Physics & Mechanics Group, Georgia Tech *\n"); fprintf(output_fp,"* Distributed under GNU General Public License 3 (GPL) *\n"); fprintf(output_fp,"* Start time: %s *\n",c_time_str); @@ -3497,6 +3664,21 @@ void write_output_init(SPARC_OBJ *pSPARC) { fprintf(output_fp,"D3_RTHR: %.15G\n",pSPARC->d3Rthr); fprintf(output_fp,"D3_CN_THR: %.15G\n",pSPARC->d3Cn_thr); } + if (pSPARC->BandStructFlag) { + fprintf(output_fp,"BAND_STRUCTURE: %d\n",pSPARC->BandStructFlag); + fprintf(output_fp, "INPUT_DENS_FILE: "); + fprintf(output_fp, "%s ", pSPARC->InDensTCubFilename); + if (pSPARC->densfilecount > 1) { + fprintf(output_fp, "%s ", pSPARC->InDensUCubFilename); + fprintf(output_fp, "%s ", pSPARC->InDensDCubFilename); + } + fprintf(output_fp, "\n"); + fprintf(output_fp,"KPT_PER_LINE: %d\n",pSPARC->kpt_per_line); + fprintf(output_fp,"KPT_PATHS: %d\n",pSPARC->n_kpt_line); + for (int i = 0; i < 2*pSPARC->n_kpt_line; i++) { + fprintf(output_fp, "%lf %lf %lf\n", pSPARC->kredx[i], pSPARC->kredy[i], pSPARC->kredz[i]); + } + } fprintf(output_fp,"OUTPUT_FILE: %s\n",pSPARC->filename_out); fprintf(output_fp,"***************************************************************************\n"); @@ -3666,8 +3848,10 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, - MPI_INT, MPI_INT, MPI_INT, MPI_INT, - MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, + MPI_INT, MPI_INT, MPI_INT, MPI_INT, MPI_INT, + MPI_INT, MPI_INT, MPI_INT, + MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, + MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, @@ -3681,7 +3865,7 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_DOUBLE, MPI_CHAR, MPI_CHAR, MPI_CHAR, MPI_CHAR, MPI_CHAR, - MPI_CHAR}; + MPI_CHAR, MPI_CHAR, MPI_CHAR, MPI_CHAR}; int blens[N_MEMBR] = {3, 3, 7, /* int array */ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, @@ -3701,8 +3885,9 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, /* int */ - 9, 3, L_QMASS, /* double array */ + 1, 1, 1, 1, 1, 1, 1, 1, /* int */ + 9, 3, L_QMASS, L_kpoint, L_kpoint, + L_kpoint, /* double array */ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, @@ -3716,7 +3901,7 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { 1, 1, 1, 1, 1, 1, 1, 1, /* double */ 32, 32, 32, L_STRING, L_STRING, /* char */ - L_STRING}; + L_STRING, L_STRING, L_STRING, L_STRING}; // calculating offsets in an architecture independent manner MPI_Aint addr[N_MEMBR],disps[N_MEMBR], base; @@ -3821,10 +4006,17 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { MPI_Get_address(&sparc_input_tmp.PrintEnergyDensFlag, addr + i++); MPI_Get_address(&sparc_input_tmp.eig_paral_maxnp, addr + i++); MPI_Get_address(&sparc_input_tmp.StandardEigenFlag, addr + i++); + MPI_Get_address(&sparc_input_tmp.n_kpt_line, addr + i++); + MPI_Get_address(&sparc_input_tmp.BandStructFlag, addr + i++); + MPI_Get_address(&sparc_input_tmp.kpt_per_line, addr + i++); + MPI_Get_address(&sparc_input_tmp.densfilecount, addr + i++); // double array type MPI_Get_address(&sparc_input_tmp.LatVec, addr + i++); MPI_Get_address(&sparc_input_tmp.kptshift, addr + i++); MPI_Get_address(&sparc_input_tmp.NPT_NHqmass, addr + i++); + MPI_Get_address(&sparc_input_tmp.kredx, addr + i++); + MPI_Get_address(&sparc_input_tmp.kredy, addr + i++); + MPI_Get_address(&sparc_input_tmp.kredz, addr + i++); // double type MPI_Get_address(&sparc_input_tmp.range_x, addr + i++); MPI_Get_address(&sparc_input_tmp.range_y, addr + i++); @@ -3891,7 +4083,9 @@ void SPARC_Input_MPI_create(MPI_Datatype *pSPARC_INPUT_MPI) { MPI_Get_address(&sparc_input_tmp.filename, addr + i++); MPI_Get_address(&sparc_input_tmp.filename_out, addr + i++); MPI_Get_address(&sparc_input_tmp.SPARCROOT, addr + i++); - + MPI_Get_address(&sparc_input_tmp.InDensTCubFilename, addr + i++); + MPI_Get_address(&sparc_input_tmp.InDensUCubFilename, addr + i++); + MPI_Get_address(&sparc_input_tmp.InDensDCubFilename, addr + i++); for (i = 0; i < N_MEMBR; i++) { disps[i] = addr[i] - base; } diff --git a/src/occupation.c b/src/occupation.c index 50e04533..c110c963 100644 --- a/src/occupation.c +++ b/src/occupation.c @@ -42,6 +42,12 @@ double smearing_function(double beta, double lambda, double lambda_f, int type) */ double Calculate_occupation(SPARC_OBJ *pSPARC, double x1, double x2, double tol, int max_iter) { + #ifdef DEBUG + int rank; + MPI_Comm_rank(MPI_COMM_WORLD, &rank); + double t1, t2; + #endif + double Efermi, g_nk; int n, Ns, k, Nk, spn_i; @@ -52,10 +58,30 @@ double Calculate_occupation(SPARC_OBJ *pSPARC, double x1, double x2, double tol, // Efermi = Calculate_FermiLevel(pSPARC, x1, x2, tol, max_iter, occ_constraint); int totalLambdaNumber = pSPARC->Nspin * pSPARC->Nkpts_sym * Ns; double *totalLambdaArray = (double *)calloc(totalLambdaNumber, sizeof(double)); + + #ifdef DEBUG + t1 = MPI_Wtime(); + #endif + collect_all_lambda(pSPARC, totalLambdaArray); + + #ifdef DEBUG + t2 = MPI_Wtime(); + if (rank == 0) + printf("collect_all_lambda took: %.3f ms\n",(t2-t1)*1000); + t1 = MPI_Wtime(); + #endif + Efermi = local_Calculate_FermiLevel(pSPARC, x1, x2, totalLambdaArray, tol, max_iter, local_occ_constraint); free(totalLambdaArray); - + + #ifdef DEBUG + t2 = MPI_Wtime(); + if (rank == 0) + printf("Calculate Efermi locally took: %.3f ms\n",(t2-t1)*1000); + t1 = MPI_Wtime(); + #endif + // find occupations for (spn_i = 0; spn_i < pSPARC->Nspin_spincomm; spn_i++) { for (k = 0; k < Nk; k++) { @@ -67,6 +93,13 @@ double Calculate_occupation(SPARC_OBJ *pSPARC, double x1, double x2, double tol, } } } + + #ifdef DEBUG + t2 = MPI_Wtime(); + if (rank == 0) + printf("Calculate occ from eigvals locally took: %.3f ms\n",(t2-t1)*1000); + #endif + return Efermi; } @@ -429,4 +462,4 @@ double local_occ_constraint(SPARC_OBJ *pSPARC, double lambda_f, double *totalLam } g *= 1.0 / pSPARC->Nkpts; // find average return g + Ne; -} \ No newline at end of file +} diff --git a/src/orbitalElecDensInit.c b/src/orbitalElecDensInit.c index e712b5a9..e1a731ce 100644 --- a/src/orbitalElecDensInit.c +++ b/src/orbitalElecDensInit.c @@ -11,6 +11,7 @@ #include #include +#include #include #include #include @@ -25,10 +26,80 @@ #include "isddft.h" #include "tools.h" #include "electronDensity.h" - +#include "parallelization.h" +#include "readfiles.h" #define max(x,y) ((x)>(y)?(x):(y)) +/** + * @brief Read vector(s) from Cube file(s) and distribute in comm. + * + * @param pSPARC + * @param filenames An array of n file names. + * @param data_dist The pointer to the final distributed vector. + * @param n Number of files (also number of columns of data_dist). + * @param DMverts Domain vertices of the local distributed domain. + * @param comm Communicator with a Cartesian topology. + */ +void read_cube_and_dist_vec( + SPARC_OBJ *pSPARC, char filenames[3][L_STRING+L_PSD], double *data_dist, int n, + int DMverts[6], MPI_Comm comm) +{ + if (comm == MPI_COMM_NULL) return; + int rank; + MPI_Comm_rank(comm, &rank); + + // initialize D2D for distributing the vectors from root to comm + MPI_Comm send_comm; + if (rank != 0) { + send_comm = MPI_COMM_NULL; + } else { + int dims[3] = {1,1,1}, periods[3] = {1,1,1}; + // create a cartesian topology on one process (rank 0) + MPI_Cart_create(MPI_COMM_SELF, 3, dims, periods, 0, &send_comm); + } + int gridsizes[3]; + gridsizes[0] = pSPARC->Nx; + gridsizes[1] = pSPARC->Ny; + gridsizes[2] = pSPARC->Nz; + int sdims[3], sVert[6], rdims[3], periods[3], coords[3]; + sdims[0] = sdims[1] = sdims[2] = 1; + sVert[0] = 0; sVert[1] = gridsizes[0] - 1; + sVert[2] = 0; sVert[3] = gridsizes[1] - 1; + sVert[4] = 0; sVert[5] = gridsizes[2] - 1; + + MPI_Cart_get(comm, 3, rdims, periods, coords); + D2D_OBJ d2d_sender, d2d_recvr; + Set_D2D_Target(&d2d_sender, &d2d_recvr, gridsizes, sVert, DMverts, send_comm, sdims, comm, rdims, comm); + + int DMnx = DMverts[1] - DMverts[0] + 1; + int DMny = DMverts[3] - DMverts[2] + 1; + int DMnz = DMverts[5] - DMverts[4] + 1; + int DMnd = DMnx * DMny * DMnz; + + double *vec_in = NULL; + // loop over the n filenames + for (int i = 0; i < n; i++) { + // let root process read the density from file + if (rank == 0) { + vec_in = read_vec_cube(pSPARC, filenames[i]); + } + + // distribute the density from root to comm + D2D(&d2d_sender, &d2d_recvr, gridsizes, sVert, vec_in, DMverts, data_dist+i*DMnd, send_comm, sdims, comm, rdims, comm, sizeof(double)); + + if (rank == 0) free(vec_in); + } + + Free_D2D_Target(&d2d_sender, &d2d_recvr, send_comm, comm); + + if (rank == 0) { + MPI_Comm_free(&send_comm); + } +} + + + /** * @brief Initialze electron density. */ @@ -41,24 +112,43 @@ void Init_electronDensity(SPARC_OBJ *pSPARC) { if (pSPARC->dmcomm_phi != MPI_COMM_NULL) { int DMnd = pSPARC->Nd_d; - // for 1st Relax step/ MDstep, set electron density to be sum of atomic potentials + // for 1st Relax step/ MDstep, set initial electron density if( (pSPARC->elecgs_Count - pSPARC->StressCount) == 0){ - // TODO: implement restart based on previous MD electron density. Things to consider: - // 1) Each processor stores the density in its memory in a separate file at the end of MD (same frequency as the main restart file). - // 2) After all processors have printed their density, a counter in main restart file will be updated. - // 3) If the counter says "success" then use the density from previous step as guess otherwise start from a guess based on electronDens_at. - // 4) Change (pSPARC->elecgs_Count + !pSPARC->RestartFlag) > 3 condition to pSPARC->elecgs_Count >= 3, below - - // copy initial electron density - memcpy(pSPARC->electronDens, pSPARC->electronDens_at, DMnd * sizeof(double)); - // get intial magnetization - if (pSPARC->spin_typ == 1) { - memcpy(pSPARC->mag, pSPARC->mag_at, DMnd * sizeof(double)); - Calculate_diagonal_Density(pSPARC, DMnd, pSPARC->mag, pSPARC->electronDens, pSPARC->electronDens+DMnd, pSPARC->electronDens+2*DMnd); - } else if (pSPARC->spin_typ == 2) { - memcpy(pSPARC->mag+DMnd, pSPARC->mag_at, DMnd * 3 * sizeof(double)); - Calculate_Magnorm(pSPARC, DMnd, pSPARC->mag+DMnd*1, pSPARC->mag+DMnd*2, pSPARC->mag+DMnd*3, pSPARC->mag); - Calculate_diagonal_Density(pSPARC, DMnd, pSPARC->mag, pSPARC->electronDens, pSPARC->electronDens+DMnd, pSPARC->electronDens+2*DMnd); + // read initial density from file + if (pSPARC->BandStructFlag == 1) { + char inputDensFnames[3][L_STRING+L_PSD]; + // set up input density filename + if (rank == 0) { + char INPUT_DIR[L_PSD]; + extract_path_from_file(pSPARC->filename, INPUT_DIR, L_PSD); + combine_path_filename(INPUT_DIR, pSPARC->InDensTCubFilename, inputDensFnames[0], L_STRING+L_PSD); + combine_path_filename(INPUT_DIR, pSPARC->InDensUCubFilename, inputDensFnames[1], L_STRING+L_PSD); + combine_path_filename(INPUT_DIR, pSPARC->InDensDCubFilename, inputDensFnames[2], L_STRING+L_PSD); + } + + int nFileToRead = pSPARC->densfilecount; + read_cube_and_dist_vec( + pSPARC, inputDensFnames, pSPARC->electronDens, nFileToRead, + pSPARC->DMVertices, pSPARC->dmcomm_phi + ); + } else { + // TODO: implement restart based on previous MD electron density. Things to consider: + // 1) Each processor stores the density in its memory in a separate file at the end of MD (same frequency as the main restart file). + // 2) After all processors have printed their density, a counter in main restart file will be updated. + // 3) If the counter says "success" then use the density from previous step as guess otherwise start from a guess based on electronDens_at. + // 4) Change (pSPARC->elecgs_Count + !pSPARC->RestartFlag) > 3 condition to pSPARC->elecgs_Count >= 3, below + + // copy initial electron density + memcpy(pSPARC->electronDens, pSPARC->electronDens_at, DMnd * sizeof(double)); + // get intial magnetization + if (pSPARC->spin_typ == 1) { + memcpy(pSPARC->mag, pSPARC->mag_at, DMnd * sizeof(double)); + Calculate_diagonal_Density(pSPARC, DMnd, pSPARC->mag, pSPARC->electronDens, pSPARC->electronDens+DMnd, pSPARC->electronDens+2*DMnd); + } else if (pSPARC->spin_typ == 2) { + memcpy(pSPARC->mag+DMnd, pSPARC->mag_at, DMnd * 3 * sizeof(double)); + Calculate_Magnorm(pSPARC, DMnd, pSPARC->mag+DMnd*1, pSPARC->mag+DMnd*2, pSPARC->mag+DMnd*3, pSPARC->mag); + Calculate_diagonal_Density(pSPARC, DMnd, pSPARC->mag, pSPARC->electronDens, pSPARC->electronDens+DMnd, pSPARC->electronDens+2*DMnd); + } } // Storing atom position needed for charge extrapolation in future Relax/MD steps diff --git a/src/printing.c b/src/printing.c index dc77241b..4882d78e 100644 --- a/src/printing.c +++ b/src/printing.c @@ -219,7 +219,7 @@ void printEigen(SPARC_OBJ *pSPARC) { int *kpt_displs= (int *)malloc((pSPARC->npkpt+1) * sizeof(int)); char EigenFilename[L_STRING]; - snprintf(EigenFilename, L_STRING, "%s", pSPARC->EigenFilename); + if (rank == 0) snprintf(EigenFilename, L_STRING, "%s", pSPARC->EigenFilename); FILE *output_fp; // first create an empty file @@ -299,11 +299,19 @@ void printEigen(SPARC_OBJ *pSPARC) { double *kpt_sendbuf = (double *)malloc(Nk * 3 * sizeof(double)); int *kpt_recvcounts = (int *)malloc(pSPARC->npkpt * sizeof(int)); // int *kpt_displs = (int *)malloc((pSPARC->npkpt+1) * sizeof(int)); - for (i = 0; i < Nk; i++) { - kpt_sendbuf[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); - kpt_sendbuf[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); - kpt_sendbuf[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); - } + if (pSPARC->BandStructFlag == 1) { + for (i = 0; i < Nk; i++) { + kpt_sendbuf[3*i ] = pSPARC->k1_inpt_kpt[i]; + kpt_sendbuf[3*i+1] = pSPARC->k2_inpt_kpt[i]; + kpt_sendbuf[3*i+2] = pSPARC->k3_inpt_kpt[i]; + } + } else { + for (i = 0; i < Nk; i++) { + kpt_sendbuf[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); + kpt_sendbuf[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); + kpt_sendbuf[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); + } + } kpt_displs[0] = 0; for (i = 0; i < pSPARC->npkpt; i++) { kpt_recvcounts[i] = Nk_i[i] * 3; @@ -322,10 +330,18 @@ void printEigen(SPARC_OBJ *pSPARC) { // collect all the kpoints assigend to each kptcomm double *kpt_sendbuf = (double *)malloc(Nk * 3 * sizeof(double)); int kpt_recvcounts[1]={0}, i; - for (i = 0; i < Nk; i++) { - kpt_sendbuf[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); - kpt_sendbuf[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); - kpt_sendbuf[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); + if (pSPARC->BandStructFlag == 1) { + for (i = 0; i < Nk; i++){ + kpt_sendbuf[3*i ] = pSPARC->k1_inpt_kpt[i]; + kpt_sendbuf[3*i+1] = pSPARC->k2_inpt_kpt[i]; + kpt_sendbuf[3*i+2] = pSPARC->k3_inpt_kpt[i]; + } + } else { + for (i = 0; i < Nk; i++) { + kpt_sendbuf[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); + kpt_sendbuf[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); + kpt_sendbuf[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); + } } // collect reduced kpoints from all kptcomms MPI_Gatherv(kpt_sendbuf, Nk*3, MPI_DOUBLE, @@ -351,10 +367,18 @@ void printEigen(SPARC_OBJ *pSPARC) { kpt_displs[0] = 0; displs_all[0] = 0; if (pSPARC->BC != 1) { - for (i = 0; i < Nk; i++) { - kred_i[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); - kred_i[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); - kred_i[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); + if(pSPARC->BandStructFlag == 1) { + for (i = 0; i < Nk; i++) { + kred_i[3*i ] = pSPARC->k1_inpt_kpt[i]; + kred_i[3*i+1] = pSPARC->k2_inpt_kpt[i]; + kred_i[3*i+2] = pSPARC->k3_inpt_kpt[i]; + } + } else { + for (i = 0; i < Nk; i++) { + kred_i[3*i ] = pSPARC->k1_loc[i]*pSPARC->range_x/(2.0*M_PI); + kred_i[3*i+1] = pSPARC->k2_loc[i]*pSPARC->range_y/(2.0*M_PI); + kred_i[3*i+2] = pSPARC->k3_loc[i]*pSPARC->range_z/(2.0*M_PI); + } } } else { kred_i[0] = kred_i[1] = kred_i[2] = 0.0; @@ -378,7 +402,17 @@ void printEigen(SPARC_OBJ *pSPARC) { int Nk_Kcomm_indx = Nk_i[Kcomm_indx]; for (k = 0; k < Nk_Kcomm_indx; k++) { int kred_index = kpt_displs[Kcomm_indx]/3+k+1; - fprintf(output_fp, + if (pSPARC->BandStructFlag == 1) { + fprintf(output_fp, + "\n" + "kred #%d = (%f,%f,%f)\n" + "n eigval occ\n", + kred_index, + pSPARC->k1_inpt_kpt[kred_index-1], + pSPARC->k2_inpt_kpt[kred_index-1], + pSPARC->k3_inpt_kpt[kred_index-1]); + } else { + fprintf(output_fp, "\n" "kred #%d = (%f,%f,%f)\n" "weight = %f\n" @@ -388,6 +422,7 @@ void printEigen(SPARC_OBJ *pSPARC) { kred_i[kpt_displs[Kcomm_indx]+3*k+1], kred_i[kpt_displs[Kcomm_indx]+3*k+2], (pSPARC->kptWts[kred_index-1]+0.0)/pSPARC->Nkpts); + } for (i = 0; i < pSPARC->Nstates; i++) { fprintf(output_fp, "%-7d%20.12E %18.12f\n", i+1, @@ -401,7 +436,18 @@ void printEigen(SPARC_OBJ *pSPARC) { int Nk_Kcomm_indx = Nk_i[Kcomm_indx]; for (k = 0; k < Nk_Kcomm_indx; k++) { int kred_index = kpt_displs[Kcomm_indx]/3+k+1; - fprintf(output_fp, + if (pSPARC->BandStructFlag == 1) { + fprintf(output_fp, + "\n" + "kred #%d = (%f,%f,%f)\n" + " Spin-up Spin-down\n" + "n eigval occ eigval occ\n", + kred_index, + pSPARC->k1_inpt_kpt[kred_index-1], + pSPARC->k2_inpt_kpt[kred_index-1], + pSPARC->k3_inpt_kpt[kred_index-1]); + } else { + fprintf(output_fp, "\n" "kred #%d = (%f,%f,%f)\n" "weight = %f\n" @@ -412,6 +458,7 @@ void printEigen(SPARC_OBJ *pSPARC) { kred_i[kpt_displs[Kcomm_indx]+3*k+1], kred_i[kpt_displs[Kcomm_indx]+3*k+2], (pSPARC->kptWts[kred_index-1]+0.0)/pSPARC->Nkpts); + } for (i = 0; i < pSPARC->Nstates; i++) { fprintf(output_fp, "%-7d%20.12E %18.12f %20.12E %18.12f\n", i+1, @@ -982,4 +1029,4 @@ void GatherEnergyDensity_dmcomm_phi(SPARC_OBJ *pSPARC, double *rho_send, double rho_recv[i] = rho_send[i]; } } -} \ No newline at end of file +} diff --git a/src/readfiles.c b/src/readfiles.c index a1537fae..ba6ea92e 100644 --- a/src/readfiles.c +++ b/src/readfiles.c @@ -55,14 +55,82 @@ void find_element(char element[8], char *atom_type) } +/** + * @brief Read strings from a given line, with comments removed. + * This function takes in a string and reads all the strings deliminated by + * spaces into a list of strings until it reaches the `#` character or the end + * of the line, or until it reaches the maximum number of input strings allowed. + * + * @param input_fp File pointer that points to the line to be read. + * @param max_nstr Maximum number of input strings allowed. + * @param inputArgv (OUTPUT) The input arguments. + * @return int Count of input arguments. + */ +int readStringInputsFromLine(char *line, const int max_nstr, char inputArgv[][L_STRING]) { + char *token; + + int inputArgc = 0; // Initialize the count of input args + + // Read the entire line from the file + token = strtok(line, " "); + + while (token != NULL) { + // Remove newline characters if present + token[strcspn(token, "\n")] = '\0'; + + // Ignore comments indicated by '#' and exit the loop + if (token[0] == '#' || token[0] == '\0') { + break; + } + #ifdef DEBUG + printf("count = %d, token = `%s`\n", inputArgc, token); + #endif + // if count exceeds max number, exit + if (inputArgc >= max_nstr) { + printf("Error: Exceeded the maximum number of inputs (%d).\n", max_nstr); + return -1; + } + + // Copy the file name into the array + strncpy(inputArgv[inputArgc], token, L_STRING); + inputArgc++; // Increment the count + token = strtok(NULL, " "); + } + + return inputArgc; // Success +} + + +/** + * @brief Read strings from a line in a file, with comments removed. + * This function takes in a file pointer and starts to read from the inital + * position of the file pointer. It reads all the strings deliminated by spaces + * into a list of strings until it reaches the `#` character or the end + * of the line, or until it reaches the maximum number of input strings allowed. + * + * @param input_fp File pointer that points to the line to be read. + * @param max_nstr Maximum number of input strings allowed. + * @param inputArgv (OUTPUT) The input arguments. + * @return int Count of input arguments. + */ +int readStringInputsFromFile(FILE *input_fp, const int max_nstr, char inputArgv[][L_STRING]) { + char line[L_STRING*3+20]; // Assuming a maximum length for the line + // Read the entire line from the file + if (fgets(line, sizeof(line), input_fp) == NULL) { + fprintf(stderr, "Error reading line from file.\n"); + return -1; + } + + int inputArgc = readStringInputsFromLine(line, max_nstr, inputArgv); + return inputArgc; +} + /** * @brief Read input file. */ void read_input(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) { - char *input_filename = malloc(L_STRING * sizeof(char)); - char *str = malloc(L_STRING * sizeof(char)); - char *temp = malloc(L_STRING * sizeof(char)); + char input_filename[L_STRING], str[L_STRING], temp[L_STRING]; int i, Flag_smear_typ = 0, Flag_Temp = 0, Flag_elecT = 0, Flag_ionT = 0, Flag_ionT_end = 0; // Flag_eqT = 0, int Flag_cell = 0; int Flag_latvec_scale = 0; @@ -735,6 +803,77 @@ void read_input(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) { fscanf(input_fp,"%d", &pSPARC_Input->npNdy_SQ); fscanf(input_fp,"%d", &pSPARC_Input->npNdz_SQ); fscanf(input_fp, "%*[^\n]\n"); + } else if (strcmpi(str,"BAND_STRUCTURE:") == 0) { + fscanf(input_fp, "%d", &pSPARC_Input->BandStructFlag); + fscanf(input_fp, "%*[^\n]\n"); + } else if (strcmpi(str,"KPT_PER_LINE:") == 0) { + fscanf(input_fp, "%d", &pSPARC_Input->kpt_per_line); + fscanf(input_fp, "%*[^\n]\n"); + } else if (strcmpi(str,"KPT_PATHS:") == 0) { + fscanf(input_fp, "%d", &pSPARC_Input->n_kpt_line); + fscanf(input_fp, "%*[^\n]\n"); + char tmpstr[L_STRING]; + double kpt_x, kpt_y, kpt_z; + for (int line = 0; line < 2 * pSPARC_Input->n_kpt_line; line++) { + // read x coords + fscanf(input_fp, "%s", tmpstr); + // if this line is a comment, skip it + if (tmpstr[0]== '#') { + fscanf(input_fp, "%*[^\n]\n"); + line--; + continue; + } + kpt_x = strtod(tmpstr, NULL); + // read y coords + fscanf(input_fp, "%s", tmpstr); + kpt_y = strtod(tmpstr, NULL); + // read z coords + fscanf(input_fp, "%s", tmpstr); + kpt_z = strtod(tmpstr, NULL); + fscanf(input_fp, "%*[^\n]\n"); + pSPARC_Input->kredx[line] = kpt_x; + pSPARC_Input->kredy[line] = kpt_y; + pSPARC_Input->kredz[line] = kpt_z; + } + + #ifdef DEBUG + for (int line = 0; line < pSPARC_Input->n_kpt_line; line++) { + int k_ind = 2 * line; + printf(" Starting coordinates of k-point line %d: (%lf, %lf, %lf)\n", line+1, + pSPARC_Input->kredx[k_ind], pSPARC_Input->kredy[k_ind], pSPARC_Input->kredz[k_ind]); + k_ind++; + printf(" Ending coordinates of k-point line %d: (%lf, %lf, %lf)\n", line+1, + pSPARC_Input->kredx[k_ind], pSPARC_Input->kredy[k_ind], pSPARC_Input->kredz[k_ind]); + } + #endif + } else if (strcmpi(str,"INPUT_DENS_FILE:") == 0) { + char inputDensFnames[3][L_STRING]; // at most 3 file names + int nInputDensFname = readStringInputsFromFile(input_fp, 3, inputDensFnames); + pSPARC_Input->densfilecount = nInputDensFname; + if (nInputDensFname == 1) { + strncpy(pSPARC_Input->InDensTCubFilename, inputDensFnames[0], L_STRING); + } else if (nInputDensFname == 3) { + strncpy(pSPARC_Input->InDensTCubFilename, inputDensFnames[0], L_STRING); + strncpy(pSPARC_Input->InDensUCubFilename, inputDensFnames[1], L_STRING); + strncpy(pSPARC_Input->InDensDCubFilename, inputDensFnames[2], L_STRING); + } else { + printf(RED "[FATAL] Density file names not provided properly! (Provide 1 file w/o spin or 3 files with spin)\n" RESET); + exit(EXIT_FAILURE); + } + + #ifdef DEBUG + if (nInputDensFname >= 0) { + printf("Density file names read = (["); + for (int i = 0; i < nInputDensFname; i++) { + if (i == 0) printf("%s", inputDensFnames[i]); + else printf(", %s", inputDensFnames[i]); + } + printf("], %d)\n", nInputDensFname); + } + printf("Total Dens file name: %s\n", pSPARC_Input->InDensTCubFilename); + printf("Dens_up file name: %s\n", pSPARC_Input->InDensUCubFilename); + printf("Dens_dw file name: %s\n", pSPARC_Input->InDensDCubFilename); + #endif } else { printf("\nCannot recognize input variable identifier: \"%s\"\n",str); exit(EXIT_FAILURE); @@ -953,13 +1092,185 @@ void read_input(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) { pSPARC_Input->kptshift[2] = 0.5; } } - free(input_filename); - free(str); - free(temp); fclose(input_fp); } +/** + * @brief Read density in cube format. + * + * @param filename Name of the density file in cube format. + * @param dens_gridsizes (OUTPUT) Grid sizes (in 3-dim) of the density read. + * @param dens_latvecs (OUTPUT) Lattice vectors (scaled) read. + * @return double* (OUTPUT) Density array. + */ +double* readDens_cube(char *filename, int dens_gridsizes[3], double dens_latvecs[9]) { +#ifdef DEBUG + printf("Reading CUBE file: %s ...\n", filename); +#endif + + FILE *dens_fp = fopen(filename, "r"); + if (dens_fp == NULL) { + printf("Cannot open file \"%s\"\n", filename); + exit(EXIT_FAILURE); + } + + int n_atom,cube_size_x,cube_size_y,cube_size_z; + double x1,x2,x3; + double y1,y2,y3; + double z1,z2,z3; + char tempchar[L_STRING]; + double tempval; + + fscanf(dens_fp, "%*[^\n]\n"); + fscanf(dens_fp,"%s", tempchar); + fscanf(dens_fp,"%s", tempchar); + + fscanf(dens_fp, "%lf", &tempval); + fscanf(dens_fp, "%*[^\n]\n"); + fscanf(dens_fp, "%d", &n_atom); + // printf("n_atom = %d\n", n_atom); + + fscanf(dens_fp, "%*[^\n]\n"); + fscanf(dens_fp, "%d", &cube_size_x); + fscanf(dens_fp, "%lf", &x1); + fscanf(dens_fp, "%lf", &x2); + fscanf(dens_fp, "%lf", &x3); + fscanf(dens_fp, "%d", &cube_size_y); + fscanf(dens_fp, "%lf", &y1); + fscanf(dens_fp, "%lf", &y2); + fscanf(dens_fp, "%lf", &y3); + fscanf(dens_fp, "%d", &cube_size_z); + fscanf(dens_fp, "%lf", &z1); + fscanf(dens_fp, "%lf", &z2); + fscanf(dens_fp, "%lf", &z3); + + dens_latvecs[0] = cube_size_x * x1; + dens_latvecs[1] = cube_size_x * x2; + dens_latvecs[2] = cube_size_x * x3; + dens_latvecs[3] = cube_size_y * y1; + dens_latvecs[4] = cube_size_y * y2; + dens_latvecs[5] = cube_size_y * y3; + dens_latvecs[6] = cube_size_z * z1; + dens_latvecs[7] = cube_size_z * z2; + dens_latvecs[8] = cube_size_z * z3; + dens_gridsizes[0] = cube_size_x; + dens_gridsizes[1] = cube_size_y; + dens_gridsizes[2] = cube_size_z; + + int len = cube_size_x * cube_size_y * cube_size_z; + double *dens = malloc(len * sizeof(double)); + assert(dens != NULL); + + // read density data and save it in dens + for(int i = 0; i < n_atom; i++) { + fscanf(dens_fp, "%lf",&tempval); + fscanf(dens_fp, "%lf",&tempval); + fscanf(dens_fp, "%lf",&tempval); + fscanf(dens_fp, "%lf",&tempval); + fscanf(dens_fp, "%lf",&tempval); + } + + for (int i = 0; i < cube_size_x; i++) + { + for (int j = 0; j < cube_size_y; j++) + { + for (int k = 0; k < cube_size_z; k++) + { + fscanf(dens_fp, "%lf", &dens[(i)+(j)*cube_size_x+(k)*cube_size_x*cube_size_y]); + } + } + } + + return dens; +} + + +/** + * @brief Double-check if the given scaled latvecs are equiv. to the + * latvecs and the given scale factors. + * + * @param latvecs_scaled The scaled lattice vectors. + * @param latvec Lattice vectors to be scaled. + * @param scalex Scale factor in the 1st dim. + * @param scaley Scale factor in the 2nd dim. + * @param scalez Scale factor in the 3rd dim. + * @return int 0 - success, 1 - fail. + */ +int check_lattice( + const double latvecs_scaled[9], const double latvec[9], + const double scalex, const double scaley, const double scalez, + double tol) +{ + // check lattice vectors + double diffx = (latvecs_scaled[0] - scalex * latvec[0]) + * (latvecs_scaled[0] - scalex * latvec[0]) + + (latvecs_scaled[1] - scalex * latvec[1]) + * (latvecs_scaled[1] - scalex * latvec[1]) + + (latvecs_scaled[2] - scalex * latvec[2]) + * (latvecs_scaled[2] - scalex * latvec[2]); + diffx = sqrt(diffx); + + double diffy = (latvecs_scaled[3] - scaley * latvec[3]) + * (latvecs_scaled[3] - scaley * latvec[3]) + + (latvecs_scaled[4] - scaley * latvec[4]) + * (latvecs_scaled[4] - scaley * latvec[4]) + + (latvecs_scaled[5] - scaley * latvec[5]) + * (latvecs_scaled[5] - scaley * latvec[5]); + diffy = sqrt(diffy); + + double diffz = (latvecs_scaled[6] - scalez * latvec[6]) + * (latvecs_scaled[6] - scalez * latvec[6]) + + (latvecs_scaled[7] - scalez * latvec[7]) + * (latvecs_scaled[7] - scalez * latvec[7]) + + (latvecs_scaled[8] - scalez * latvec[8]) + * (latvecs_scaled[8] - scalez * latvec[8]); + diffz = sqrt(diffz); + + if (diffx > tol || diffy > tol || diffz > tol) { + return 1; + } + return 0; +} + +/** + * @brief Read data from cube file and check if the lattice vectors + * and the grid sizes match with the input lattice and grid. + * + * @param pSPARC + * @param filename File name of the cube file. + * @return double* Data from file, allocated within this function. + */ +double* read_vec_cube(SPARC_OBJ *pSPARC, char *filename) { + int dens_gridsizes[3]; + double dens_latvecs[9]; + // read_dens2(filename, dens, gridsizes, dens_latvecs); + double *dens = readDens_cube(filename, dens_gridsizes, dens_latvecs); + + // check lattice vectors + if (check_lattice(dens_latvecs, pSPARC->LatVec, + pSPARC->latvec_scale_x, pSPARC->latvec_scale_y, + pSPARC->latvec_scale_z, 1e-4) == 1) + { + printf("\n[FATAL] Incorrect CUBE file (%s): inconsistent lattice vectors!\n", filename); + free(dens); + MPI_Abort(MPI_COMM_WORLD,1); + } + + // check gridsizes + int gridsizes[3]; + gridsizes[0] = pSPARC->Nx; + gridsizes[1] = pSPARC->Ny; + gridsizes[2] = pSPARC->Nz; + if (gridsizes[0] != dens_gridsizes[0] || gridsizes[1] != dens_gridsizes[1] || gridsizes[2] != dens_gridsizes[2]) { + printf("\n[FATAL] Incorrect CUBE file (%s): inconsistent grid sizes!\n", filename); + free(dens); + MPI_Abort(MPI_COMM_WORLD,1); + } + + return dens; +} + /** * @brief Read ion file. @@ -1647,3 +1958,5 @@ void read_pseudopotential_PSP(SPARC_INPUT_OBJ *pSPARC_Input, SPARC_OBJ *pSPARC) exit(EXIT_FAILURE); } } + + diff --git a/src/tools.c b/src/tools.c index cc8a8172..35aa7ae9 100644 --- a/src/tools.c +++ b/src/tools.c @@ -239,6 +239,47 @@ char* goUpper(char* head, char* tail, char* prefix) } +/** + * @brief Exact file path from a file name. + * + * @param filename File name. + * @param path (OUTPUT) Path (relative or absolute) where the file is located. + * @param maxlen Maximum length of the path. + */ +void extract_path_from_file(const char *filename, char *path, int maxlen) { + const char *inpt_path = filename; + char *pch = strrchr(inpt_path,'/'); // find last occurrence of '/' + if (pch == NULL) { // in case '/' is not found + snprintf(path, maxlen, "%s", "."); + } else { + memcpy(path, inpt_path, pch-inpt_path); + path[(int)(pch-inpt_path)] = '\0'; + } +} + + +/** + * @brief Combine a path and a file name and simplify the path. + * + * If the file name is already provided in the absolute path form, then + * path is ignored. Otherwise, the new file name would be a simplified path + * equivalent to "path/fname". + * + * @param path The path relative to which fname is given. + * @param fname The name provided relative to path. + * @param newfname (OUTPUT) The new file name. + */ +void combine_path_filename(const char *path, const char *fname, char *newfname, int maxlen) +{ + if (fname[0] == '/') { // absolute path + snprintf(newfname, maxlen, "%s", fname); + } else { // relative path to where the .ion file is located + snprintf(newfname, maxlen, "%s/%s", path, fname); + } + // simplify the final path + simplifyPath(newfname, newfname, maxlen); +} + /** * @brief The following code for factorizing an integer is copied from Rosetta Code diff --git a/tests/CdS_bandstruct/densfiles/CdS_high_accuracy.indens b/tests/CdS_bandstruct/densfiles/CdS_high_accuracy.indens new file mode 100644 index 00000000..78b33729 --- /dev/null +++ b/tests/CdS_bandstruct/densfiles/CdS_high_accuracy.indens @@ -0,0 +1,5408 @@ +Electron density in Cube format printed by SPARC-X (Print time: Wed Sep 20 17:58:33 2023) +Cell length: 5.885907 5.885907 5.885907, boundary condition: P P P. + 2 0.000000 0.000000 0.000000 + 30 0.196197 0.000000 0.000000 + 30 0.000000 0.196197 0.000000 + 30 0.000000 0.000000 0.196197 + 48 20.000000 0.000000 0.000000 0.000000 + 16 6.000000 4.414430 1.471477 4.414430 + 1.074046E+00 1.224221E+00 1.593968E+00 1.885541E+00 1.840052E+00 1.449317E+00 + 9.286507E-01 5.019613E-01 2.471043E-01 1.251633E-01 7.384413E-02 5.281188E-02 + 4.409072E-02 4.140544E-02 4.247557E-02 4.637144E-02 5.275738E-02 6.168622E-02 + 7.371062E-02 9.048695E-02 1.174743E-01 1.719930E-01 2.936880E-01 5.445187E-01 + 9.648874E-01 1.481223E+00 1.874193E+00 1.928239E+00 1.641799E+00 1.258481E+00 + + 1.258481E+00 1.390828E+00 1.697107E+00 1.910884E+00 1.808903E+00 1.399275E+00 + 8.879633E-01 4.789248E-01 2.372927E-01 1.221681E-01 7.379307E-02 5.413107E-02 + 4.633855E-02 4.456428E-02 4.668931E-02 5.184941E-02 5.971287E-02 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1.494451E-01 2.185219E-01 4.103320E-01 8.761642E-01 1.539205E+00 + 1.910559E+00 1.796986E+00 + 1.936577E+00 1.932680E+00 1.695803E+00 1.133217E+00 5.478150E-01 2.145947E-01 + 9.344822E-02 5.985451E-02 5.402834E-02 6.107993E-02 7.776115E-02 1.029348E-01 + 1.353912E-01 1.754355E-01 2.368405E-01 3.846347E-01 7.362517E-01 1.287571E+00 + 1.748204E+00 1.910559E+00 + 1.609968E+00 1.485582E+00 1.140820E+00 6.830768E-01 3.213802E-01 1.390127E-01 + 7.349839E-02 5.486022E-02 5.441071E-02 6.539181E-02 8.641247E-02 1.163814E-01 + 1.525825E-01 1.917456E-01 2.394580E-01 3.329644E-01 5.445053E-01 9.023265E-01 + 1.287571E+00 1.539205E+00 + 9.016795E-01 7.856857E-01 5.615784E-01 3.263737E-01 1.653255E-01 8.710322E-02 + 5.716697E-02 4.878259E-02 5.258195E-02 6.650694E-02 9.040873E-02 1.230919E-01 + 1.600806E-01 1.949225E-01 2.285578E-01 2.786407E-01 3.785834E-01 5.445053E-01 + 7.362517E-01 8.761642E-01 + 3.926595E-01 3.268767E-01 2.330347E-01 1.462750E-01 8.850265E-02 5.811918E-02 + 4.483302E-02 4.235467E-02 4.871612E-02 6.398600E-02 8.866335E-02 1.215236E-01 + 1.572174E-01 1.878376E-01 2.120415E-01 2.385959E-01 2.786407E-01 3.329644E-01 + 3.846347E-01 4.103320E-01 + 1.881167E-01 1.501189E-01 1.111911E-01 7.853312E-02 5.559535E-02 4.171798E-02 + 3.545988E-02 3.597141E-02 4.326612E-02 5.817974E-02 8.146509E-02 1.121535E-01 + 1.455082E-01 1.740488E-01 1.948534E-01 2.120415E-01 2.285578E-01 2.394580E-01 + 2.368405E-01 2.185219E-01 + 1.205112E-01 9.338256E-02 7.038356E-02 5.233385E-02 3.937225E-02 3.143203E-02 + 2.830234E-02 2.997354E-02 3.694048E-02 5.013633E-02 7.031167E-02 9.689782E-02 + 1.266121E-01 1.536629E-01 1.740488E-01 1.878376E-01 1.949225E-01 1.917456E-01 + 1.754355E-01 1.494451E-01 + 8.914055E-02 6.836398E-02 5.156951E-02 3.885599E-02 2.996898E-02 2.468961E-02 + 2.288852E-02 2.467451E-02 3.053860E-02 4.123092E-02 5.734357E-02 7.859741E-02 + 1.029657E-01 1.266121E-01 1.455082E-01 1.572174E-01 1.600806E-01 1.525825E-01 + 1.353912E-01 1.125964E-01 + 6.852154E-02 5.307605E-02 4.050067E-02 3.094887E-02 2.427504E-02 2.031188E-02 + 1.896677E-02 2.033020E-02 2.475609E-02 3.274442E-02 4.466928E-02 6.036470E-02 + 7.859741E-02 9.689782E-02 1.121535E-01 1.215236E-01 1.230919E-01 1.163814E-01 + 1.029348E-01 8.588206E-02 + 5.450867E-02 4.343772E-02 3.402181E-02 2.657258E-02 2.116552E-02 1.779120E-02 + 1.642396E-02 1.711491E-02 2.007199E-02 2.558159E-02 3.382792E-02 4.466928E-02 + 5.734357E-02 7.031167E-02 8.146509E-02 8.866335E-02 9.040873E-02 8.641247E-02 + 7.776115E-02 6.644300E-02 + 4.686719E-02 3.900013E-02 3.165254E-02 2.533569E-02 2.038933E-02 1.700293E-02 + 1.524510E-02 1.513443E-02 1.674482E-02 2.020573E-02 2.558159E-02 3.274442E-02 + 4.123092E-02 5.013633E-02 5.817974E-02 6.398600E-02 6.650694E-02 6.539181E-02 + 6.107993E-02 5.454066E-02 + 4.706758E-02 4.117159E-02 3.452934E-02 2.801169E-02 2.239572E-02 1.818062E-02 + 1.554431E-02 1.446505E-02 1.487228E-02 1.674482E-02 2.007199E-02 2.475608E-02 + 3.053860E-02 3.694048E-02 4.326612E-02 4.871612E-02 5.258195E-02 5.441071E-02 + 5.402834E-02 5.150089E-02 + 6.137963E-02 5.579978E-02 4.704365E-02 3.738321E-02 2.873044E-02 2.210106E-02 + 1.766942E-02 1.522926E-02 1.446505E-02 1.513443E-02 1.711491E-02 2.033020E-02 + 2.467451E-02 2.997354E-02 3.597141E-02 4.235467E-02 4.878259E-02 5.486021E-02 + 5.985451E-02 6.253379E-02 + 1.177120E-01 1.072596E-01 8.518872E-02 6.168769E-02 4.315269E-02 3.039244E-02 + 2.228999E-02 1.766942E-02 1.554431E-02 1.524510E-02 1.642395E-02 1.896677E-02 + 2.288852E-02 2.830234E-02 3.545988E-02 4.483302E-02 5.716697E-02 7.349839E-02 + 9.344822E-02 1.113965E-01 + 3.192275E-01 2.859624E-01 2.090929E-01 1.303683E-01 7.606079E-02 4.612643E-02 + 3.039244E-02 2.210106E-02 1.818062E-02 1.700293E-02 1.779120E-02 2.031188E-02 + 2.468961E-02 3.143203E-02 4.171798E-02 5.811918E-02 8.710322E-02 1.390127E-01 + 2.145947E-01 2.884614E-01 + 8.383941E-01 7.521601E-01 5.415658E-01 3.130392E-01 1.545991E-01 7.606079E-02 + 4.315269E-02 2.873044E-02 2.239572E-02 2.038932E-02 2.116552E-02 2.427504E-02 + 2.996898E-02 3.937225E-02 5.559535E-02 8.850265E-02 1.653255E-01 3.213802E-01 + 5.478150E-01 7.558781E-01 + 1.572762E+00 1.452388E+00 1.116039E+00 6.696599E-01 3.130392E-01 1.303683E-01 + 6.168769E-02 3.738321E-02 2.801169E-02 2.533569E-02 2.657258E-02 3.094887E-02 + 3.885599E-02 5.233385E-02 7.853312E-02 1.462750E-01 3.263737E-01 6.830768E-01 + 1.133217E+00 1.467033E+00 + 1.923894E+00 1.884206E+00 1.655590E+00 1.116039E+00 5.415658E-01 2.090929E-01 + 8.518872E-02 4.704365E-02 3.452934E-02 3.165254E-02 3.402181E-02 4.050067E-02 + 5.156951E-02 7.038356E-02 1.111911E-01 2.330347E-01 5.615784E-01 1.140820E+00 + 1.695803E+00 1.922389E+00 + 1.669845E+00 1.796620E+00 1.884206E+00 1.452388E+00 7.521601E-01 2.859624E-01 + 1.072596E-01 5.579978E-02 4.117159E-02 3.900013E-02 4.343772E-02 5.307605E-02 + 6.836398E-02 9.338256E-02 1.501189E-01 3.268767E-01 7.856857E-01 1.485582E+00 + 1.932680E+00 1.844630E+00 diff --git a/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.inpt b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.inpt new file mode 100644 index 00000000..548caecf --- /dev/null +++ b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.inpt @@ -0,0 +1,58 @@ +# Test: CdS band structure calculation +LATVEC: +5.8859069297953903 0.0 0.0 +0.0 5.8859069297953903 0.0 +0.0 0.0 5.8859069297953903 +LATVEC_SCALE: 1.0 1.0 1.0 +MESH_SPACING: 0.20 +FD_ORDER: 12 +BC: P P P +KPOINT_GRID: 7 7 7 +EXCHANGE_CORRELATION: GGA_PBE +ELEC_TEMP_TYPE: fermi-dirac +ELEC_TEMP: 315.775131 +TOL_SCF: 1e-6 +MAXIT_SCF: 50 +PRINT_EIGEN: 1 +PRINT_DENSITY: 1 +MIXING_VARIABLE: density +MIXING_PRECOND: none + +# RHO_TRIGGER: 40 + +# Band sturcture calculation +# First do a ground-state calculation with `BAND_STRUCTURE: 0` and `PRINT_DENSITY: 1`, +# then run a band structure calculation with `BAND_STRUCTURE: 1` and provide the k-path +# using the `KPT_PATHS` keyword. +BAND_STRUCTURE: 1 +INPUT_DENS_FILE: ../densfiles/CdS_high_accuracy.indens +KPT_PER_LINE: 10 # number of k-points on each high-symmetry line +KPT_PATHS: 9 +0.0 0.0 0.0 +0.0 0.5 0.5 + +0.0 0.5 0.5 +0.25 0.5 0.75 + +0.25 0.5 0.75 +0.375 0.375 0.75 + +0.375 0.375 0.75 +0.0 0.0 0.0 + +0.0 0.0 0.0 +0.5 0.5 0.5 + +0.5 0.5 0.5 +0.25 0.625 0.625 + +0.25 0.625 0.625 +0.25 0.5 0.75 + +0.25 0.5 0.75 +0.5 0.5 0.5 + +0.5 0.5 0.5 +0.375 0.375 0.75 + + diff --git a/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.ion b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.ion new file mode 100644 index 00000000..54da4349 --- /dev/null +++ b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.ion @@ -0,0 +1,13 @@ +ATOM_TYPE: Cd +N_TYPE_ATOM: 1 +PSEUDO_POT: ../../../psps/48_Cd_20_2.2_2.3_pbe_n_v1.0.psp8 +COORD_FRAC: + 0.0000000000000000 0.0000000000000000 0.0000000000000000 + +ATOM_TYPE: S +N_TYPE_ATOM: 1 +PSEUDO_POT: ../../../psps/16_S_6_1.8_1.9_pbe_n_v1.0.psp8 +COORD_FRAC: + 0.7500000000000000 0.2500000000000000 0.7500000000000000 + + diff --git a/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refeigen b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refeigen new file mode 100644 index 00000000..84248420 --- /dev/null +++ b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refeigen @@ -0,0 +1,2071 @@ +Final eigenvalues (Ha) and occupation numbers + +kred #1 = (0.000000,0.000000,0.000000) +n eigval occ +1 -3.561476003093E+00 2.000000000000 +2 -2.219812084542E+00 2.000000000000 +3 -2.106237522187E+00 2.000000000000 +4 -2.106237520717E+00 2.000000000000 +5 -3.027360871984E-01 2.000000000000 +6 -2.192318788470E-01 2.000000000000 +7 -2.192318765608E-01 2.000000000000 +8 -1.431727756797E-01 2.000000000000 +9 -5.993191544691E-02 2.000000000000 +10 -5.993191416516E-02 2.000000000000 +11 3.807899182337E-01 2.000000000000 +12 4.067832297411E-01 1.999999999607 +13 4.067832314840E-01 1.999999999607 +14 4.773218598352E-01 0.000000000000 +15 5.342862499759E-01 0.000000000000 +16 5.342862516601E-01 0.000000000000 +17 8.889368231549E-01 0.000000000000 +18 8.889411903954E-01 0.000000000000 +19 9.482452710204E-01 0.000000000000 +20 9.482466680966E-01 0.000000000000 + +kred #2 = (0.000000,0.055556,0.055556) +n eigval occ +1 -3.561473782195E+00 2.000000000000 +2 -2.219824014584E+00 2.000000000000 +3 -2.106259921473E+00 2.000000000000 +4 -2.106242735754E+00 2.000000000000 +5 -3.026640782908E-01 2.000000000000 +6 -2.190160957548E-01 2.000000000000 +7 -2.184114047020E-01 2.000000000000 +8 -1.408326618221E-01 2.000000000000 +9 -6.015702730641E-02 2.000000000000 +10 -5.955959781330E-02 2.000000000000 +11 3.538574373051E-01 2.000000000000 +12 3.999015077048E-01 2.000000000000 +13 4.204153184997E-01 1.999672898252 +14 4.702441707657E-01 0.000000000000 +15 5.432933180744E-01 0.000000000000 +16 5.601495413428E-01 0.000000000000 +17 8.661136777707E-01 0.000000000000 +18 8.702823812088E-01 0.000000000000 +19 9.528852692202E-01 0.000000000000 +20 9.592015483980E-01 0.000000000000 + +kred #3 = (0.000000,0.111111,0.111111) +n eigval occ +1 -3.561467388679E+00 2.000000000000 +2 -2.219858377696E+00 2.000000000000 +3 -2.106324279678E+00 2.000000000000 +4 -2.106257743278E+00 2.000000000000 +5 -3.025096076782E-01 2.000000000000 +6 -2.184246179739E-01 2.000000000000 +7 -2.160226608076E-01 2.000000000000 +8 -1.340015731529E-01 2.000000000000 +9 -6.078404536061E-02 2.000000000000 +10 -5.820847821725E-02 2.000000000000 +11 3.151086771367E-01 2.000000000000 +12 3.742356814491E-01 2.000000000000 +13 4.232633544618E-01 1.994371200423 +14 4.836908350837E-01 0.000000000000 +15 5.667804048936E-01 0.000000000000 +16 6.041167248990E-01 0.000000000000 +17 8.224603429926E-01 0.000000000000 +18 8.365032267377E-01 0.000000000000 +19 9.586635218001E-01 0.000000000000 +20 9.927393498483E-01 0.000000000000 + +kred #4 = (0.000000,0.166667,0.166667) +n eigval occ +1 -3.561457596993E+00 2.000000000000 +2 -2.219911059344E+00 2.000000000000 +3 -2.106422482979E+00 2.000000000000 +4 -2.106280713727E+00 2.000000000000 +5 -3.024126638626E-01 2.000000000000 +6 -2.176016760616E-01 2.000000000000 +7 -2.122929825325E-01 2.000000000000 +8 -1.234178055203E-01 2.000000000000 +9 -6.162391321101E-02 2.000000000000 +10 -5.515510135526E-02 2.000000000000 +11 2.770675448453E-01 2.000000000000 +12 3.398876844697E-01 2.000000000000 +13 4.242743115924E-01 1.984606507738 +14 5.063880903589E-01 0.000000000000 +15 5.903045366950E-01 0.000000000000 +16 6.473387366595E-01 0.000000000000 +17 7.861946098410E-01 0.000000000000 +18 8.017900256005E-01 0.000000000000 +19 9.439042453055E-01 0.000000000000 +20 9.720632940056E-01 0.000000000000 + +kred #5 = (0.000000,0.222222,0.222222) +n eigval occ +1 -3.561445591911E+00 2.000000000000 +2 -2.219975739566E+00 2.000000000000 +3 -2.106542288224E+00 2.000000000000 +4 -2.106308854201E+00 2.000000000000 +5 -3.024968643601E-01 2.000000000000 +6 -2.167256539782E-01 2.000000000000 +7 -2.076153570612E-01 2.000000000000 +8 -1.108351302531E-01 2.000000000000 +9 -6.222782641309E-02 2.000000000000 +10 -4.913376999479E-02 2.000000000000 +11 2.421467682833E-01 2.000000000000 +12 3.071370549277E-01 2.000000000000 +13 4.262461748142E-01 1.894436949752 +14 5.235224830711E-01 0.000000000000 +15 5.948251307885E-01 0.000000000000 +16 6.886806191310E-01 0.000000000000 +17 7.714212496825E-01 0.000000000000 +18 7.767916860524E-01 0.000000000000 +19 9.337184246244E-01 0.000000000000 +20 9.601544039592E-01 0.000000000000 + +kred #6 = (0.000000,0.277778,0.277778) +n eigval occ +1 -3.561432823870E+00 2.000000000000 +2 -2.220044639208E+00 2.000000000000 +3 -2.106668986081E+00 2.000000000000 +4 -2.106338756077E+00 2.000000000000 +5 -3.027980697061E-01 2.000000000000 +6 -2.159527880815E-01 2.000000000000 +7 -2.025320230859E-01 2.000000000000 +8 -9.930763018795E-02 2.000000000000 +9 -6.175997587512E-02 2.000000000000 +10 -3.864513116127E-02 2.000000000000 +11 2.119176104823E-01 2.000000000000 +12 2.790227904670E-01 2.000000000000 +13 4.281659341542E-01 1.449285667021 +14 5.093795844015E-01 0.000000000000 +15 6.047379856470E-01 0.000000000000 +16 7.250976716975E-01 0.000000000000 +17 7.525268924918E-01 0.000000000000 +18 7.844203125944E-01 0.000000000000 +19 9.202218636110E-01 0.000000000000 +20 9.564436446412E-01 0.000000000000 + +kred #7 = (0.000000,0.333333,0.333333) +n eigval occ +1 -3.561420832886E+00 2.000000000000 +2 -2.220109447833E+00 2.000000000000 +3 -2.106787296091E+00 2.000000000000 +4 -2.106366812875E+00 2.000000000000 +5 -3.032526374275E-01 2.000000000000 +6 -2.153774000023E-01 2.000000000000 +7 -1.976765997075E-01 2.000000000000 +8 -9.175398866760E-02 2.000000000000 +9 -5.926527787426E-02 2.000000000000 +10 -2.378662352290E-02 2.000000000000 +11 1.882953077360E-01 2.000000000000 +12 2.562192512994E-01 2.000000000000 +13 4.268723031046E-01 1.811231428084 +14 4.707928549739E-01 0.000000000000 +15 6.357189886312E-01 0.000000000000 +16 7.256733505094E-01 0.000000000000 +17 7.698555090068E-01 0.000000000000 +18 7.889786691654E-01 0.000000000000 +19 9.062848431098E-01 0.000000000000 +20 9.547077724917E-01 0.000000000000 + +kred #8 = (0.000000,0.388889,0.388889) +n eigval occ +1 -3.561411062802E+00 2.000000000000 +2 -2.220162326206E+00 2.000000000000 +3 -2.106883208545E+00 2.000000000000 +4 -2.106389655126E+00 2.000000000000 +5 -3.037316176403E-01 2.000000000000 +6 -2.150187308811E-01 2.000000000000 +7 -1.936789848863E-01 2.000000000000 +8 -8.835379430019E-02 2.000000000000 +9 -5.491961221553E-02 2.000000000000 +10 -8.238612176770E-03 2.000000000000 +11 1.737196100055E-01 2.000000000000 +12 2.384391193158E-01 2.000000000000 +13 4.082082712260E-01 1.999999998366 +14 4.475283664535E-01 0.000000020524 +15 6.726100683006E-01 0.000000000000 +16 7.181540139985E-01 0.000000000000 +17 7.857187975243E-01 0.000000000000 +18 7.913696823793E-01 0.000000000000 +19 8.935530273664E-01 0.000000000000 +20 9.556953818075E-01 0.000000000000 + +kred #9 = (0.000000,0.444444,0.444444) +n eigval occ +1 -3.561404688282E+00 2.000000000000 +2 -2.220196862316E+00 2.000000000000 +3 -2.106945552198E+00 2.000000000000 +4 -2.106404549915E+00 2.000000000000 +5 -3.040921276887E-01 2.000000000000 +6 -2.148393368685E-01 2.000000000000 +7 -1.910588932511E-01 2.000000000000 +8 -8.726885792743E-02 2.000000000000 +9 -5.063642540928E-02 2.000000000000 +10 2.748028233795E-03 2.000000000000 +11 1.691018758627E-01 2.000000000000 +12 2.255602837936E-01 2.000000000000 +13 3.802326342343E-01 2.000000000000 +14 4.443120515558E-01 0.000000511788 +15 7.049346415920E-01 0.000000000000 +16 7.151143689295E-01 0.000000000000 +17 7.819703424627E-01 0.000000000000 +18 8.022720339829E-01 0.000000000000 +19 8.837532077012E-01 0.000000000000 +20 9.256299750897E-01 0.000000000000 + +kred #10 = (0.000000,0.500000,0.500000) +n eigval occ +1 -3.561402474887E+00 2.000000000000 +2 -2.220208860679E+00 2.000000000000 +3 -2.106967156143E+00 2.000000000000 +4 -2.106409720158E+00 2.000000000000 +5 -3.042257028832E-01 2.000000000000 +6 -2.147873133570E-01 2.000000000000 +7 -1.901481086547E-01 2.000000000000 +8 -8.705711753251E-02 2.000000000000 +9 -4.882549327524E-02 2.000000000000 +10 6.464471045854E-03 2.000000000000 +11 1.694148655186E-01 2.000000000000 +12 2.201799327567E-01 2.000000000000 +13 3.687876566971E-01 2.000000000000 +14 4.440780918726E-01 0.000000646692 +15 7.144760587103E-01 0.000000000000 +16 7.189405457540E-01 0.000000000000 +17 7.801933793751E-01 0.000000000000 +18 8.063911621596E-01 0.000000000000 +19 8.794583118779E-01 0.000000000000 +20 9.103435204619E-01 0.000000000000 + +kred #11 = (0.000000,0.500000,0.500000) +n eigval occ +1 -3.561402474887E+00 2.000000000000 +2 -2.220208860679E+00 2.000000000000 +3 -2.106967156143E+00 2.000000000000 +4 -2.106409720158E+00 2.000000000000 +5 -3.042257028832E-01 2.000000000000 +6 -2.147873133570E-01 2.000000000000 +7 -1.901481086547E-01 2.000000000000 +8 -8.705711753251E-02 2.000000000000 +9 -4.882549327524E-02 2.000000000000 +10 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0.000002059771 +15 7.095901505747E-01 0.000000000000 +16 7.169353319223E-01 0.000000000000 +17 7.774490957413E-01 0.000000000000 +18 8.098825629827E-01 0.000000000000 +19 8.737478875794E-01 0.000000000000 +20 9.176646641887E-01 0.000000000000 + +kred #13 = (0.055556,0.500000,0.555556) +n eigval occ +1 -3.561402481236E+00 2.000000000000 +2 -2.220208546037E+00 2.000000000000 +3 -2.106954621316E+00 2.000000000000 +4 -2.106422325530E+00 2.000000000000 +5 -3.042640146791E-01 2.000000000000 +6 -2.142443920725E-01 2.000000000000 +7 -1.909167052652E-01 2.000000000000 +8 -8.677314699121E-02 2.000000000000 +9 -4.971284078554E-02 2.000000000000 +10 5.455883812915E-03 2.000000000000 +11 1.719157766446E-01 2.000000000000 +12 2.224290054232E-01 2.000000000000 +13 3.753619142813E-01 2.000000000000 +14 4.395644234867E-01 0.000059012694 +15 6.959599610523E-01 0.000000000000 +16 7.118949706878E-01 0.000000000000 +17 7.707766169112E-01 0.000000000000 +18 8.182052874475E-01 0.000000000000 +19 8.642129882283E-01 0.000000000000 +20 9.336428695624E-01 0.000000000000 + +kred #14 = (0.083333,0.500000,0.583333) +n eigval occ +1 -3.561402488455E+00 2.000000000000 +2 -2.220208188239E+00 2.000000000000 +3 -2.106939603579E+00 2.000000000000 +4 -2.106437423487E+00 2.000000000000 +5 -3.043083137114E-01 2.000000000000 +6 -2.135801872518E-01 2.000000000000 +7 -1.918359820731E-01 2.000000000000 +8 -8.642571351050E-02 2.000000000000 +9 -5.075197573326E-02 2.000000000000 +10 4.385362615122E-03 2.000000000000 +11 1.739722417329E-01 2.000000000000 +12 2.262640544052E-01 2.000000000000 +13 3.825115855192E-01 2.000000000000 +14 4.345854230260E-01 0.008539876225 +15 6.776330380871E-01 0.000000000000 +16 7.023449274261E-01 0.000000000000 +17 7.652335463599E-01 0.000000000000 +18 8.273480529787E-01 0.000000000000 +19 8.555406654571E-01 0.000000000000 +20 9.497190651636E-01 0.000000000000 + +kred #15 = (0.111111,0.500000,0.611111) +n eigval occ +1 -3.561402497312E+00 2.000000000000 +2 -2.220207749335E+00 2.000000000000 +3 -2.106919846343E+00 2.000000000000 +4 -2.106457279127E+00 2.000000000000 +5 -3.043637195886E-01 2.000000000000 +6 -2.126804174580E-01 2.000000000000 +7 -1.930464120713E-01 2.000000000000 +8 -8.595938087494E-02 2.000000000000 +9 -5.207379616675E-02 2.000000000000 +10 3.172059525878E-03 2.000000000000 +11 1.754270653610E-01 2.000000000000 +12 2.328983452995E-01 2.000000000000 +13 3.896089278644E-01 2.000000000000 +14 4.299931546735E-01 0.594841644721 +15 6.563975835696E-01 0.000000000000 +16 6.894921755137E-01 0.000000000000 +17 7.641845713309E-01 0.000000000000 +18 8.350838361669E-01 0.000000000000 +19 8.477562991052E-01 0.000000000000 +20 9.657269863499E-01 0.000000000000 + +kred #16 = (0.138889,0.500000,0.638889) +n eigval occ +1 -3.561402506736E+00 2.000000000000 +2 -2.220207282262E+00 2.000000000000 +3 -2.106896760988E+00 2.000000000000 +4 -2.106480469200E+00 2.000000000000 +5 -3.044239707397E-01 2.000000000000 +6 -2.115836831596E-01 2.000000000000 +7 -1.944710845116E-01 2.000000000000 +8 -8.540674578800E-02 2.000000000000 +9 -5.354380534576E-02 2.000000000000 +10 1.988617490505E-03 2.000000000000 +11 1.759343499678E-01 2.000000000000 +12 2.423772926746E-01 2.000000000000 +13 3.912484596992E-01 2.000000000000 +14 4.310202560504E-01 0.263239848060 +15 6.329497454664E-01 0.000000000000 +16 6.769759879021E-01 0.000000000000 +17 7.671928684043E-01 0.000000000000 +18 8.388757671792E-01 0.000000000000 +19 8.421163226776E-01 0.000000000000 +20 9.749672339221E-01 0.000000000000 + +kred #17 = (0.166667,0.500000,0.666667) +n eigval occ +1 -3.561402515592E+00 2.000000000000 +2 -2.220206843357E+00 2.000000000000 +3 -2.106872431445E+00 2.000000000000 +4 -2.106504897146E+00 2.000000000000 +5 -3.044818003755E-01 2.000000000000 +6 -2.103567963617E-01 2.000000000000 +7 -1.960036742497E-01 2.000000000000 +8 -8.482425055740E-02 2.000000000000 +9 -5.499349048924E-02 2.000000000000 +10 9.665349901729E-04 2.000000000000 +11 1.757174695834E-01 2.000000000000 +12 2.538888176415E-01 2.000000000000 +13 3.844691728258E-01 2.000000000000 +14 4.406692660582E-01 0.000019549117 +15 6.086708341472E-01 0.000000000000 +16 6.670105823454E-01 0.000000000000 +17 7.729160293217E-01 0.000000000000 +18 8.314130752662E-01 0.000000000000 +19 8.455998787932E-01 0.000000000000 +20 9.783438520042E-01 0.000000000000 + +kred #18 = (0.194444,0.500000,0.694444) +n eigval occ +1 -3.561402522811E+00 2.000000000000 +2 -2.220206485559E+00 2.000000000000 +3 -2.106849892185E+00 2.000000000000 +4 -2.106527516623E+00 2.000000000000 +5 -3.045298125832E-01 2.000000000000 +6 -2.091218057567E-01 2.000000000000 +7 -1.974861414125E-01 2.000000000000 +8 -8.429481476965E-02 2.000000000000 +9 -5.623263815973E-02 2.000000000000 +10 1.913044762741E-04 2.000000000000 +11 1.752036671715E-01 2.000000000000 +12 2.658727206721E-01 2.000000000000 +13 3.738660431449E-01 2.000000000000 +14 4.544951022347E-01 0.000000000019 +15 5.857665039213E-01 0.000000000000 +16 6.600765896257E-01 0.000000000000 +17 7.802784418976E-01 0.000000000000 +18 8.228249475541E-01 0.000000000000 +19 8.482921556424E-01 0.000000000000 +20 9.786769838343E-01 0.000000000000 + +kred #19 = (0.222222,0.500000,0.722222) +n eigval occ +1 -3.561402527524E+00 2.000000000000 +2 -2.220206252023E+00 2.000000000000 +3 -2.106833290726E+00 2.000000000000 +4 -2.106544170440E+00 2.000000000000 +5 -3.045615713625E-01 2.000000000000 +6 -2.081110145404E-01 2.000000000000 +7 -1.986576317921E-01 2.000000000000 +8 -8.391789731883E-02 2.000000000000 +9 -5.707378731013E-02 2.000000000000 +10 -2.888829333671E-04 2.000000000000 +11 1.747525491576E-01 2.000000000000 +12 2.757710088956E-01 2.000000000000 +13 3.643034500733E-01 2.000000000000 +14 4.674083853362E-01 0.000000000000 +15 5.676508100502E-01 0.000000000000 +16 6.560438090424E-01 0.000000000000 +17 7.880359323375E-01 0.000000000000 +18 8.144534048172E-01 0.000000000000 +19 8.498060849106E-01 0.000000000000 +20 9.783250601077E-01 0.000000000000 + +kred #20 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561402529160E+00 2.000000000000 +2 -2.220206170917E+00 2.000000000000 +3 -2.106827058194E+00 2.000000000000 +4 -2.106550421155E+00 2.000000000000 +5 -3.045726788826E-01 2.000000000000 +6 -2.076957347165E-01 2.000000000000 +7 -1.991285697593E-01 2.000000000000 +8 -8.378045057392E-02 2.000000000000 +9 -5.737260521222E-02 2.000000000000 +10 -4.511327149629E-04 2.000000000000 +11 1.745789258102E-01 2.000000000000 +12 2.798386287307E-01 2.000000000000 +13 3.602879870853E-01 2.000000000000 +14 4.731601440066E-01 0.000000000000 +15 5.601839608277E-01 0.000000000000 +16 6.547245673049E-01 0.000000000000 +17 7.924739311539E-01 0.000000000000 +18 8.098269556341E-01 0.000000000000 +19 8.502905316328E-01 0.000000000000 +20 9.781492668686E-01 0.000000000000 + +kred #21 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561402529160E+00 2.000000000000 +2 -2.220206170917E+00 2.000000000000 +3 -2.106827058194E+00 2.000000000000 +4 -2.106550421155E+00 2.000000000000 +5 -3.045726788826E-01 2.000000000000 +6 -2.076957347165E-01 2.000000000000 +7 -1.991285697593E-01 2.000000000000 +8 -8.378045057392E-02 2.000000000000 +9 -5.737260521222E-02 2.000000000000 +10 -4.511327149627E-04 2.000000000000 +11 1.745789258102E-01 2.000000000000 +12 2.798386287307E-01 2.000000000000 +13 3.602879870853E-01 2.000000000000 +14 4.731601440066E-01 0.000000000000 +15 5.601839608277E-01 0.000000000000 +16 6.547245673051E-01 0.000000000000 +17 7.924739311587E-01 0.000000000000 +18 8.098269557786E-01 0.000000000000 +19 8.502905322879E-01 0.000000000000 +20 9.781844246897E-01 0.000000000000 + +kred #22 = (0.263889,0.486111,0.750000) +n eigval occ +1 -3.561401004414E+00 2.000000000000 +2 -2.220214228648E+00 2.000000000000 +3 -2.106830140055E+00 2.000000000000 +4 -2.106565878115E+00 2.000000000000 +5 -3.047498211818E-01 2.000000000000 +6 -2.072495278147E-01 2.000000000000 +7 -1.989620608688E-01 2.000000000000 +8 -8.307333174150E-02 2.000000000000 +9 -5.731088891425E-02 2.000000000000 +10 1.284558235777E-03 2.000000000000 +11 1.774707993091E-01 2.000000000000 +12 2.764980342350E-01 2.000000000000 +13 3.569189348110E-01 2.000000000000 +14 4.709187366440E-01 0.000000000000 +15 5.575703867452E-01 0.000000000000 +16 6.492047630792E-01 0.000000000000 +17 7.900618505421E-01 0.000000000000 +18 8.127922195477E-01 0.000000000000 +19 8.516619763748E-01 0.000000000000 +20 9.839678466710E-01 0.000000000000 + +kred #23 = (0.277778,0.472222,0.750000) +n eigval occ +1 -3.561399630669E+00 2.000000000000 +2 -2.220221490909E+00 2.000000000000 +3 -2.106832241989E+00 2.000000000000 +4 -2.106580462574E+00 2.000000000000 +5 -3.049190045609E-01 2.000000000000 +6 -2.068591628441E-01 2.000000000000 +7 -1.987770584097E-01 2.000000000000 +8 -8.237790238605E-02 2.000000000000 +9 -5.732658383656E-02 2.000000000000 +10 2.700195720126E-03 2.000000000000 +11 1.810368902119E-01 2.000000000000 +12 2.727899548846E-01 2.000000000000 +13 3.535376727520E-01 2.000000000000 +14 4.687190418655E-01 0.000000000000 +15 5.564244277677E-01 0.000000000000 +16 6.435382343743E-01 0.000000000000 +17 7.861375999511E-01 0.000000000000 +18 8.166030533343E-01 0.000000000000 +19 8.542623876257E-01 0.000000000000 +20 9.888781150811E-01 0.000000000000 + +kred #24 = (0.291667,0.458333,0.750000) +n eigval occ +1 -3.561398418277E+00 2.000000000000 +2 -2.220227906990E+00 2.000000000000 +3 -2.106833493789E+00 2.000000000000 +4 -2.106593918446E+00 2.000000000000 +5 -3.050764518752E-01 2.000000000000 +6 -2.065273200231E-01 2.000000000000 +7 -1.985731685929E-01 2.000000000000 +8 -8.169145603439E-02 2.000000000000 +9 -5.742904783202E-02 2.000000000000 +10 3.808572752102E-03 2.000000000000 +11 1.851348863195E-01 2.000000000000 +12 2.688360018871E-01 2.000000000000 +13 3.501661229549E-01 2.000000000000 +14 4.666632975585E-01 0.000000000000 +15 5.565812678682E-01 0.000000000000 +16 6.378424357935E-01 0.000000000000 +17 7.820290386709E-01 0.000000000000 +18 8.201630275795E-01 0.000000000000 +19 8.579051921607E-01 0.000000000000 +20 9.925107765121E-01 0.000000000000 + +kred #25 = (0.305556,0.444444,0.750000) +n eigval occ +1 -3.561397376366E+00 2.000000000000 +2 -2.220233432381E+00 2.000000000000 +3 -2.106834058663E+00 2.000000000000 +4 -2.106605971225E+00 2.000000000000 +5 -3.052184382427E-01 2.000000000000 +6 -2.062542758695E-01 2.000000000000 +7 -1.983526886216E-01 2.000000000000 +8 -8.101219507689E-02 2.000000000000 +9 -5.762674971019E-02 2.000000000000 +10 4.631882774672E-03 2.000000000000 +11 1.895520258077E-01 2.000000000000 +12 2.648218400864E-01 2.000000000000 +13 3.468517903533E-01 2.000000000000 +14 4.648622134937E-01 0.000000000000 +15 5.577704775557E-01 0.000000000000 +16 6.323032052059E-01 0.000000000000 +17 7.783005617101E-01 0.000000000000 +18 8.230940728950E-01 0.000000000000 +19 8.624035367020E-01 0.000000000000 +20 9.945432498178E-01 0.000000000000 + +kred #26 = 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2.792566554941E-01 2.000000000000 +13 3.233408980526E-01 2.000000000000 +14 5.029248443157E-01 0.000000000000 +15 5.971490969058E-01 0.000000000000 +16 6.415212699377E-01 0.000000000000 +17 7.940869451140E-01 0.000000000000 +18 8.039973198605E-01 0.000000000000 +19 8.601261334523E-01 0.000000000000 +20 9.405666053849E-01 0.000000000000 + +kred #47 = (0.333333,0.333333,0.333333) +n eigval occ +1 -3.561393390659E+00 2.000000000000 +2 -2.220254384197E+00 2.000000000000 +3 -2.106745732329E+00 2.000000000000 +4 -2.106742521088E+00 2.000000000000 +5 -3.058027937601E-01 2.000000000000 +6 -2.019739622052E-01 2.000000000000 +7 -2.007781857763E-01 2.000000000000 +8 -7.637476813828E-02 2.000000000000 +9 -6.079550079376E-02 2.000000000000 +10 4.776166857032E-03 2.000000000000 +11 2.187432795348E-01 2.000000000000 +12 2.627103122887E-01 2.000000000000 +13 3.099807576779E-01 2.000000000000 +14 4.784032364829E-01 0.000000000000 +15 5.546455177591E-01 0.000000000000 +16 5.872840068452E-01 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(0.444444,0.444444,0.444444) +n eigval occ +1 -3.561369275367E+00 2.000000000000 +2 -2.220382348701E+00 2.000000000000 +3 -2.106889941913E+00 2.000000000000 +4 -2.106889444863E+00 2.000000000000 +5 -3.085675918819E-01 2.000000000000 +6 -1.974375580526E-01 2.000000000000 +7 -1.972719810926E-01 2.000000000000 +8 -6.201120557554E-02 2.000000000000 +9 -5.990055777907E-02 2.000000000000 +10 4.385694456878E-02 2.000000000000 +11 2.333737852384E-01 2.000000000000 +12 2.452460359562E-01 2.000000000000 +13 2.845308495717E-01 2.000000000000 +14 4.681768626034E-01 0.000000000000 +15 4.998627992888E-01 0.000000000000 +16 5.084807452424E-01 0.000000000000 +17 6.092408800921E-01 0.000000000000 +18 9.733607564391E-01 0.000000000000 +19 9.912876348192E-01 0.000000000000 +20 1.066942788340E+00 0.000000000000 + +kred #50 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561365971302E+00 2.000000000000 +2 -2.220399840750E+00 2.000000000000 +3 -2.106909558866E+00 2.000000000000 +4 -2.106909557387E+00 2.000000000000 +5 -3.089922604032E-01 2.000000000000 +6 -1.968562815600E-01 2.000000000000 +7 -1.968562806426E-01 2.000000000000 +8 -5.969162889398E-02 2.000000000000 +9 -5.969162787100E-02 2.000000000000 +10 4.854064954445E-02 2.000000000000 +11 2.432089087714E-01 2.000000000000 +12 2.432089126609E-01 2.000000000000 +13 2.760871374498E-01 2.000000000000 +14 4.782428122533E-01 0.000000000000 +15 4.926016304942E-01 0.000000000000 +16 4.926016348502E-01 0.000000000000 +17 5.809338513742E-01 0.000000000000 +18 1.011984712156E+00 0.000000000000 +19 1.012165853936E+00 0.000000000000 +20 1.074946742320E+00 0.000000000000 + +kred #51 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561365971302E+00 2.000000000000 +2 -2.220399840750E+00 2.000000000000 +3 -2.106909558866E+00 2.000000000000 +4 -2.106909557387E+00 2.000000000000 +5 -3.089922604032E-01 2.000000000000 +6 -1.968562815600E-01 2.000000000000 +7 -1.968562806426E-01 2.000000000000 +8 -5.969162889398E-02 2.000000000000 +9 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2.000000000000 +14 4.760644245590E-01 0.000000000000 +15 4.934943603077E-01 0.000000000000 +16 4.953787497550E-01 0.000000000000 +17 5.847512632697E-01 0.000000000000 +18 1.005300474377E+00 0.000000000000 +19 1.010592078977E+00 0.000000000000 +20 1.078862703022E+00 0.000000000000 + +kred #53 = (0.444444,0.527778,0.527778) +n eigval occ +1 -3.561367627126E+00 2.000000000000 +2 -2.220391105714E+00 2.000000000000 +3 -2.106905888214E+00 2.000000000000 +4 -2.106893288046E+00 2.000000000000 +5 -3.087750850341E-01 2.000000000000 +6 -1.973513282696E-01 2.000000000000 +7 -1.968165258924E-01 2.000000000000 +8 -6.090157098978E-02 2.000000000000 +9 -5.972408737490E-02 2.000000000000 +10 4.596603380824E-02 2.000000000000 +11 2.375592219288E-01 2.000000000000 +12 2.447478900241E-01 2.000000000000 +13 2.804030312626E-01 2.000000000000 +14 4.715337596630E-01 0.000000000000 +15 4.962172730587E-01 0.000000000000 +16 5.021974172590E-01 0.000000000000 +17 5.955319234095E-01 0.000000000000 +18 9.875061483190E-01 0.000000000000 +19 1.005734895153E+00 0.000000000000 +20 1.070560204384E+00 0.000000000000 + +kred #54 = (0.416667,0.541667,0.541667) +n eigval occ +1 -3.561369661835E+00 2.000000000000 +2 -2.220380368897E+00 2.000000000000 +3 -2.106901284468E+00 2.000000000000 +4 -2.106873378550E+00 2.000000000000 +5 -3.085115690027E-01 2.000000000000 +6 -1.979623821334E-01 2.000000000000 +7 -1.967762744573E-01 2.000000000000 +8 -6.235091452199E-02 2.000000000000 +9 -5.976209168845E-02 2.000000000000 +10 4.281210548757E-02 2.000000000000 +11 2.320110410013E-01 2.000000000000 +12 2.464745343151E-01 2.000000000000 +13 2.847735644303E-01 2.000000000000 +14 4.666985174088E-01 0.000000000000 +15 5.008207995036E-01 0.000000000000 +16 5.119943235109E-01 0.000000000000 +17 6.118559333352E-01 0.000000000000 +18 9.667119907661E-01 0.000000000000 +19 9.970800299685E-01 0.000000000000 +20 1.059690280187E+00 0.000000000000 + +kred #55 = (0.388889,0.555556,0.555556) +n eigval occ +1 -3.561372445919E+00 2.000000000000 +2 -2.220365672143E+00 2.000000000000 +3 -2.106894811288E+00 2.000000000000 +4 -2.106846291417E+00 2.000000000000 +5 -3.081571340681E-01 2.000000000000 +6 -1.988028522711E-01 2.000000000000 +7 -1.967371300551E-01 2.000000000000 +8 -6.427072819130E-02 2.000000000000 +9 -5.981118436346E-02 2.000000000000 +10 3.851779961725E-02 2.000000000000 +11 2.258546485041E-01 2.000000000000 +12 2.485572282628E-01 2.000000000000 +13 2.900968883021E-01 2.000000000000 +14 4.625476856996E-01 0.000000000000 +15 5.072840374791E-01 0.000000000000 +16 5.245392001292E-01 0.000000000000 +17 6.324002676783E-01 0.000000000000 +18 9.443543067973E-01 0.000000000000 +19 9.849964747032E-01 0.000000000000 +20 1.050628445687E+00 0.000000000000 + +kred #56 = (0.361111,0.569444,0.569444) +n eigval occ +1 -3.561375916998E+00 2.000000000000 +2 -2.220347339370E+00 2.000000000000 +3 -2.106886444126E+00 2.000000000000 +4 -2.106812786284E+00 2.000000000000 +5 -3.077254740783E-01 2.000000000000 +6 -1.998566543021E-01 2.000000000000 +7 -1.967153317854E-01 2.000000000000 +8 -6.656895144507E-02 2.000000000000 +9 -5.986868262721E-02 2.000000000000 +10 3.320528166230E-02 2.000000000000 +11 2.196729916754E-01 2.000000000000 +12 2.507469866554E-01 2.000000000000 +13 2.964017951666E-01 2.000000000000 +14 4.595982424196E-01 0.000000000000 +15 5.155260665593E-01 0.000000000000 +16 5.396341911109E-01 0.000000000000 +17 6.561983710261E-01 0.000000000000 +18 9.212634000306E-01 0.000000000000 +19 9.695069059530E-01 0.000000000000 +20 1.037769604355E+00 0.000000000000 + +kred #57 = (0.333333,0.583333,0.583333) +n eigval occ +1 -3.561379997839E+00 2.000000000000 +2 -2.220325771885E+00 2.000000000000 +3 -2.106876156103E+00 2.000000000000 +4 -2.106773802642E+00 2.000000000000 +5 -3.072330936082E-01 2.000000000000 +6 -2.011018366372E-01 2.000000000000 +7 -1.967303179087E-01 2.000000000000 +8 -6.914780399660E-02 2.000000000000 +9 -5.993292727543E-02 2.000000000000 +10 2.703012982393E-02 2.000000000000 +11 2.138798434631E-01 2.000000000000 +12 2.528475716807E-01 2.000000000000 +13 3.038182242265E-01 2.000000000000 +14 4.580884000376E-01 0.000000000001 +15 5.254240965168E-01 0.000000000000 +16 5.570247513873E-01 0.000000000000 +17 6.825592631293E-01 0.000000000000 +18 8.978417658227E-01 0.000000000000 +19 9.512924932030E-01 0.000000000000 +20 1.025103078195E+00 0.000000000000 + +kred #58 = (0.305556,0.597222,0.597222) +n eigval occ +1 -3.561384598466E+00 2.000000000000 +2 -2.220301437655E+00 2.000000000000 +3 -2.106863921259E+00 2.000000000000 +4 -2.106730433170E+00 2.000000000000 +5 -3.066985369471E-01 2.000000000000 +6 -2.025100756567E-01 2.000000000000 +7 -1.968035666492E-01 2.000000000000 +8 -7.191384670677E-02 2.000000000000 +9 -6.000420132742E-02 2.000000000000 +10 2.017687334671E-02 2.000000000000 +11 2.087772333119E-01 2.000000000000 +12 2.547693173536E-01 2.000000000000 +13 3.124303931025E-01 2.000000000000 +14 4.580886968479E-01 0.000000000001 +15 5.368151604149E-01 0.000000000000 +16 5.764274228631E-01 0.000000000000 +17 7.109326917124E-01 0.000000000000 +18 8.743445758001E-01 0.000000000000 +19 9.311999734703E-01 0.000000000000 +20 1.011473104427E+00 0.000000000000 + +kred #59 = (0.277778,0.611111,0.611111) +n eigval occ +1 -3.561389618612E+00 2.000000000000 +2 -2.220274858861E+00 2.000000000000 +3 -2.106849718230E+00 2.000000000000 +4 -2.106683892506E+00 2.000000000000 +5 -3.061415055848E-01 2.000000000000 +6 -2.040464980423E-01 2.000000000000 +7 -1.969571396258E-01 2.000000000000 +8 -7.478653981067E-02 2.000000000000 +9 -6.008542012566E-02 2.000000000000 +10 1.285209894899E-02 2.000000000000 +11 2.045832160888E-01 2.000000000000 +12 2.565355830942E-01 2.000000000000 +13 3.222227354631E-01 2.000000000000 +14 4.595763358070E-01 0.000000000000 +15 5.494865862787E-01 0.000000000000 +16 5.975417950876E-01 0.000000000000 +17 7.407595635439E-01 0.000000000000 +18 8.510534151759E-01 0.000000000000 +19 9.100368135324E-01 0.000000000000 +20 9.969352107895E-01 0.000000000000 + +kred #60 = (0.250000,0.625000,0.625000) +n eigval occ +1 -3.561394950439E+00 2.000000000000 +2 -2.220246598116E+00 2.000000000000 +3 -2.106833534214E+00 2.000000000000 +4 -2.106635482266E+00 2.000000000000 +5 -3.055818975555E-01 2.000000000000 +6 -2.056699952808E-01 2.000000000000 +7 -1.972119766340E-01 2.000000000000 +8 -7.770475210063E-02 2.000000000000 +9 -6.018238124309E-02 2.000000000000 +10 5.275879400426E-03 2.000000000000 +11 2.014487393141E-01 2.000000000000 +12 2.582495383857E-01 2.000000000000 +13 3.330881091796E-01 2.000000000000 +14 4.624803196729E-01 0.000000000000 +15 5.631542770334E-01 0.000000000000 +16 6.200342956122E-01 0.000000000000 +17 7.710295013145E-01 0.000000000000 +18 8.287104197711E-01 0.000000000000 +19 8.884836568266E-01 0.000000000000 +20 9.818264615571E-01 0.000000000000 + +kred #61 = (0.250000,0.625000,0.625000) +n eigval occ +1 -3.561394950439E+00 2.000000000000 +2 -2.220246598116E+00 2.000000000000 +3 -2.106833534214E+00 2.000000000000 +4 -2.106635482266E+00 2.000000000000 +5 -3.055818975555E-01 2.000000000000 +6 -2.056699952808E-01 2.000000000000 +7 -1.972119766340E-01 2.000000000000 +8 -7.770475210063E-02 2.000000000000 +9 -6.018238124309E-02 2.000000000000 +10 5.275879400426E-03 2.000000000000 +11 2.014487393141E-01 2.000000000000 +12 2.582495383857E-01 2.000000000000 +13 3.330881091796E-01 2.000000000000 +14 4.624803196729E-01 0.000000000000 +15 5.631542770334E-01 0.000000000000 +16 6.200342956122E-01 0.000000000000 +17 7.710295013153E-01 0.000000000000 +18 8.287104197793E-01 0.000000000000 +19 8.884836585705E-01 0.000000000000 +20 9.818247932765E-01 0.000000000000 + +kred #62 = (0.250000,0.611111,0.638889) +n eigval occ +1 -3.561395049890E+00 2.000000000000 +2 -2.220245964388E+00 2.000000000000 +3 -2.106833471021E+00 2.000000000000 +4 -2.106634471249E+00 2.000000000000 +5 -3.055645583520E-01 2.000000000000 +6 -2.056954081842E-01 2.000000000000 +7 -1.974209616426E-01 2.000000000000 +8 -7.835368930719E-02 2.000000000000 +9 -5.946511970016E-02 2.000000000000 +10 5.562268972343E-03 2.000000000000 +11 2.021384142917E-01 2.000000000000 +12 2.560512983713E-01 2.000000000000 +13 3.353380406518E-01 2.000000000000 +14 4.618979090461E-01 0.000000000000 +15 5.638909913048E-01 0.000000000000 +16 6.189177249337E-01 0.000000000000 +17 7.707541453682E-01 0.000000000000 +18 8.285491710572E-01 0.000000000000 +19 8.838035970178E-01 0.000000000000 +20 9.863206079356E-01 0.000000000000 + +kred #63 = (0.250000,0.597222,0.652778) +n eigval occ +1 -3.561395345150E+00 2.000000000000 +2 -2.220244316393E+00 2.000000000000 +3 -2.106833639000E+00 2.000000000000 +4 -2.106630832263E+00 2.000000000000 +5 -3.055172276987E-01 2.000000000000 +6 -2.057628247751E-01 2.000000000000 +7 -1.976468963471E-01 2.000000000000 +8 -7.900959035428E-02 2.000000000000 +9 -5.884636270430E-02 2.000000000000 +10 5.646317660385E-03 2.000000000000 +11 2.008751518501E-01 2.000000000000 +12 2.560416847749E-01 2.000000000000 +13 3.378586470669E-01 2.000000000000 +14 4.618825560968E-01 0.000000000000 +15 5.632703944431E-01 0.000000000000 +16 6.199819907936E-01 0.000000000000 +17 7.713810490584E-01 0.000000000000 +18 8.279730989175E-01 0.000000000000 +19 8.785246917419E-01 0.000000000000 +20 9.903707231358E-01 0.000000000000 + +kred #64 = (0.250000,0.583333,0.666667) +n eigval occ +1 -3.561395834004E+00 2.000000000000 +2 -2.220241665255E+00 2.000000000000 +3 -2.106833919225E+00 2.000000000000 +4 -2.106624710554E+00 2.000000000000 +5 -3.054419825026E-01 2.000000000000 +6 -2.058757321490E-01 2.000000000000 +7 -1.978825713328E-01 2.000000000000 +8 -7.967151944418E-02 2.000000000000 +9 -5.833264362466E-02 2.000000000000 +10 5.528066233938E-03 2.000000000000 +11 1.979496563880E-01 2.000000000000 +12 2.579096216120E-01 2.000000000000 +13 3.406417463662E-01 2.000000000000 +14 4.624027006302E-01 0.000000000000 +15 5.616493118029E-01 0.000000000000 +16 6.229194437072E-01 0.000000000000 +17 7.728792856428E-01 0.000000000000 +18 8.269259989684E-01 0.000000000000 +19 8.729948484989E-01 0.000000000000 +20 9.933124506744E-01 0.000000000000 + +kred #65 = (0.250000,0.569444,0.680556) +n eigval occ +1 -3.561396512776E+00 2.000000000000 +2 -2.220238028977E+00 2.000000000000 +3 -2.106834129745E+00 2.000000000000 +4 -2.106616332304E+00 2.000000000000 +5 -3.053413902208E-01 2.000000000000 +6 -2.060381928483E-01 2.000000000000 +7 -1.981203258699E-01 2.000000000000 +8 -8.033904820377E-02 2.000000000000 +9 -5.792649792434E-02 2.000000000000 +10 5.196560925222E-03 2.000000000000 +11 1.939747864952E-01 2.000000000000 +12 2.610347326099E-01 2.000000000000 +13 3.436563034546E-01 2.000000000000 +14 4.634155428188E-01 0.000000000000 +15 5.596204475315E-01 0.000000000000 +16 6.271974637529E-01 0.000000000000 +17 7.752082984095E-01 0.000000000000 +18 8.253292642874E-01 0.000000000000 +19 8.675241088520E-01 0.000000000000 +20 9.948012066722E-01 0.000000000000 + +kred #66 = (0.250000,0.555556,0.694444) +n eigval occ +1 -3.561397376366E+00 2.000000000000 +2 -2.220233432379E+00 2.000000000000 +3 -2.106834058746E+00 2.000000000000 +4 -2.106605971143E+00 2.000000000000 +5 -3.052184381594E-01 2.000000000000 +6 -2.062542759642E-01 2.000000000000 +7 -1.983526887334E-01 2.000000000000 +8 -8.101219524503E-02 2.000000000000 +9 -5.762674965184E-02 2.000000000000 +10 4.631882633759E-03 2.000000000000 +11 1.895520262455E-01 2.000000000000 +12 2.648218401577E-01 2.000000000000 +13 3.468517904882E-01 2.000000000000 +14 4.648622137984E-01 0.000000000000 +15 5.577704771506E-01 0.000000000000 +16 6.323032051258E-01 0.000000000000 +17 7.783005618269E-01 0.000000000000 +18 8.230940734014E-01 0.000000000000 +19 8.624035367794E-01 0.000000000000 +20 9.945463066955E-01 0.000000000000 + +kred #67 = (0.250000,0.541667,0.708333) +n eigval occ +1 -3.561398418277E+00 2.000000000000 +2 -2.220227906988E+00 2.000000000000 +3 -2.106833493849E+00 2.000000000000 +4 -2.106593918386E+00 2.000000000000 +5 -3.050764518111E-01 2.000000000000 +6 -2.065273201093E-01 2.000000000000 +7 -1.985731686626E-01 2.000000000000 +8 -8.169145616030E-02 2.000000000000 +9 -5.742904778457E-02 2.000000000000 +10 3.808572639527E-03 2.000000000000 +11 1.851348866232E-01 2.000000000000 +12 2.688360019567E-01 2.000000000000 +13 3.501661230626E-01 2.000000000000 +14 4.666632978315E-01 0.000000000000 +15 5.565812675273E-01 0.000000000000 +16 6.378424357391E-01 0.000000000000 +17 7.820290387986E-01 0.000000000000 +18 8.201630282693E-01 0.000000000000 +19 8.579051919698E-01 0.000000000000 +20 9.925056614919E-01 0.000000000000 + +kred #68 = (0.250000,0.527778,0.722222) +n eigval occ +1 -3.561399630669E+00 2.000000000000 +2 -2.220221490908E+00 2.000000000000 +3 -2.106832242028E+00 2.000000000000 +4 -2.106580462536E+00 2.000000000000 +5 -3.049190045174E-01 2.000000000000 +6 -2.068591629118E-01 2.000000000000 +7 -1.987770584463E-01 2.000000000000 +8 -8.237790246948E-02 2.000000000000 +9 -5.732658380291E-02 2.000000000000 +10 2.700195642002E-03 2.000000000000 +11 1.810368904005E-01 2.000000000000 +12 2.727899549379E-01 2.000000000000 +13 3.535376728268E-01 2.000000000000 +14 4.687190420729E-01 0.000000000000 +15 5.564244275225E-01 0.000000000000 +16 6.435382343411E-01 0.000000000000 +17 7.861376000804E-01 0.000000000000 +18 8.166030533635E-01 0.000000000000 +19 8.542623877270E-01 0.000000000000 +20 9.888733022915E-01 0.000000000000 + +kred #69 = (0.250000,0.513889,0.736111) +n eigval occ +1 -3.561401004414E+00 2.000000000000 +2 -2.220214228648E+00 2.000000000000 +3 -2.106830140073E+00 2.000000000000 +4 -2.106565878097E+00 2.000000000000 +5 -3.047498211598E-01 2.000000000000 +6 -2.072495278535E-01 2.000000000000 +7 -1.989620608822E-01 2.000000000000 +8 -8.307333178278E-02 2.000000000000 +9 -5.731088889665E-02 2.000000000000 +10 1.284558196041E-03 2.000000000000 +11 1.774707993974E-01 2.000000000000 +12 2.764980342640E-01 2.000000000000 +13 3.569189348492E-01 2.000000000000 +14 4.709187367568E-01 0.000000000000 +15 5.575703866181E-01 0.000000000000 +16 6.492047630639E-01 0.000000000000 +17 7.900618506389E-01 0.000000000000 +18 8.127922193126E-01 0.000000000000 +19 8.516619740047E-01 0.000000000000 +20 9.839559287968E-01 0.000000000000 + +kred #70 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561402529160E+00 2.000000000000 +2 -2.220206170917E+00 2.000000000000 +3 -2.106827058194E+00 2.000000000000 +4 -2.106550421155E+00 2.000000000000 +5 -3.045726788826E-01 2.000000000000 +6 -2.076957347165E-01 2.000000000000 +7 -1.991285697593E-01 2.000000000000 +8 -8.378045057392E-02 2.000000000000 +9 -5.737260521222E-02 2.000000000000 +10 -4.511327149627E-04 2.000000000000 +11 1.745789258102E-01 2.000000000000 +12 2.798386287307E-01 2.000000000000 +13 3.602879870853E-01 2.000000000000 +14 4.731601440066E-01 0.000000000000 +15 5.601839608277E-01 0.000000000000 +16 6.547245673049E-01 0.000000000000 +17 7.924739311555E-01 0.000000000000 +18 8.098269556687E-01 0.000000000000 +19 8.502905317400E-01 0.000000000000 +20 9.781495615841E-01 0.000000000000 + +kred #71 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561402529160E+00 2.000000000000 +2 -2.220206170917E+00 2.000000000000 +3 -2.106827058194E+00 2.000000000000 +4 -2.106550421155E+00 2.000000000000 +5 -3.045726788826E-01 2.000000000000 +6 -2.076957347165E-01 2.000000000000 +7 -1.991285697593E-01 2.000000000000 +8 -8.378045057392E-02 2.000000000000 +9 -5.737260521222E-02 2.000000000000 +10 -4.511327149627E-04 2.000000000000 +11 1.745789258102E-01 2.000000000000 +12 2.798386287307E-01 2.000000000000 +13 3.602879870853E-01 2.000000000000 +14 4.731601440066E-01 0.000000000000 +15 5.601839608277E-01 0.000000000000 +16 6.547245673049E-01 0.000000000000 +17 7.924739311542E-01 0.000000000000 +18 8.098269556348E-01 0.000000000000 +19 8.502905316158E-01 0.000000000000 +20 9.781494545373E-01 0.000000000000 + +kred #72 = (0.277778,0.500000,0.722222) +n eigval occ +1 -3.561396176454E+00 2.000000000000 +2 -2.220239757345E+00 2.000000000000 +3 -2.106841407217E+00 2.000000000000 +4 -2.106613252518E+00 2.000000000000 +5 -3.052983517618E-01 2.000000000000 +6 -2.058142901356E-01 2.000000000000 +7 -1.985414013915E-01 2.000000000000 +8 -8.075908226853E-02 2.000000000000 +9 -5.717785634964E-02 2.000000000000 +10 7.433176556336E-03 2.000000000000 +11 1.848658190284E-01 2.000000000000 +12 2.681293711584E-01 2.000000000000 +13 3.469663841100E-01 2.000000000000 +14 4.652932787648E-01 0.000000000000 +15 5.473003561323E-01 0.000000000000 +16 6.311214258251E-01 0.000000000000 +17 7.706494859976E-01 0.000000000000 +18 8.297543810395E-01 0.000000000000 +19 8.616194261166E-01 0.000000000000 +20 1.002935053115E+00 0.000000000000 + +kred #73 = (0.305556,0.500000,0.694444) +n eigval occ +1 -3.561390018578E+00 2.000000000000 +2 -2.220272340943E+00 2.000000000000 +3 -2.106855311022E+00 2.000000000000 +4 -2.106673986775E+00 2.000000000000 +5 -3.060199914364E-01 2.000000000000 +6 -2.039894638042E-01 2.000000000000 +7 -1.980509849876E-01 2.000000000000 +8 -7.745473416087E-02 2.000000000000 +9 -5.730393457642E-02 2.000000000000 +10 1.563162789841E-02 2.000000000000 +11 1.953465417608E-01 2.000000000000 +12 2.582106069605E-01 2.000000000000 +13 3.341068119852E-01 2.000000000000 +14 4.596936745773E-01 0.000000000000 +15 5.357343904613E-01 0.000000000000 +16 6.057466724476E-01 0.000000000000 +17 7.387741504632E-01 0.000000000000 +18 8.563541344842E-01 0.000000000000 +19 8.807635518287E-01 0.000000000000 +20 1.026867624097E+00 0.000000000000 + +kred #74 = (0.333333,0.500000,0.666667) +n eigval occ +1 -3.561384242390E+00 2.000000000000 +2 -2.220302929253E+00 2.000000000000 +3 -2.106868348424E+00 2.000000000000 +4 -2.106730804252E+00 2.000000000000 +5 -3.067122916696E-01 2.000000000000 +6 -2.022770818175E-01 2.000000000000 +7 -1.976602827566E-01 2.000000000000 +8 -7.396934357656E-02 2.000000000000 +9 -5.764482580329E-02 2.000000000000 +10 2.367841075968E-02 2.000000000000 +11 2.056598778783E-01 2.000000000000 +12 2.503680788732E-01 2.000000000000 +13 3.219575087961E-01 2.000000000000 +14 4.565161607730E-01 0.000000000003 +15 5.255699018951E-01 0.000000000000 +16 5.806429774404E-01 0.000000000000 +17 7.063073705060E-01 0.000000000000 +18 8.843738260229E-01 0.000000000000 +19 9.023219955340E-01 0.000000000000 +20 1.048792253608E+00 0.000000000000 + +kred #75 = (0.361111,0.500000,0.638889) +n eigval occ +1 -3.561379023020E+00 2.000000000000 +2 -2.220330589171E+00 2.000000000000 +3 -2.106880125221E+00 2.000000000000 +4 -2.106782017833E+00 2.000000000000 +5 -3.073500360625E-01 2.000000000000 +6 -2.007293050454E-01 2.000000000000 +7 -1.973641620950E-01 2.000000000000 +8 -7.044967422362E-02 2.000000000000 +9 -5.810077569604E-02 2.000000000000 +10 3.108918887699E-02 2.000000000000 +11 2.154009450320E-01 2.000000000000 +12 2.448437122857E-01 2.000000000000 +13 3.107020731812E-01 2.000000000000 +14 4.558753394405E-01 0.000000000005 +15 5.168226146213E-01 0.000000000000 +16 5.570954456259E-01 0.000000000000 +17 6.751577801839E-01 0.000000000000 +18 9.126346237157E-01 0.000000000000 +19 9.247453567758E-01 0.000000000000 +20 1.069393247517E+00 0.000000000000 + +kred #76 = (0.388889,0.500000,0.611111) +n eigval occ +1 -3.561374518595E+00 2.000000000000 +2 -2.220354475747E+00 2.000000000000 +3 -2.106890285939E+00 2.000000000000 +4 -2.106826119485E+00 2.000000000000 +5 -3.079093299338E-01 2.000000000000 +6 -1.993931467392E-01 2.000000000000 +7 -1.971515601720E-01 2.000000000000 +8 -6.708611276164E-02 2.000000000000 +9 -5.858622095431E-02 2.000000000000 +10 3.743019444163E-02 2.000000000000 +11 2.241601821597E-01 2.000000000000 +12 2.417381870321E-01 2.000000000000 +13 3.004733161507E-01 2.000000000000 +14 4.577975587913E-01 0.000000000001 +15 5.094460758325E-01 0.000000000000 +16 5.360872545701E-01 0.000000000000 +17 6.463497643563E-01 0.000000000000 +18 9.401963743834E-01 0.000000000000 +19 9.472331222001E-01 0.000000000000 +20 1.090118482689E+00 0.000000000000 + +kred #77 = (0.416667,0.500000,0.583333) +n eigval occ +1 -3.561370865487E+00 2.000000000000 +2 -2.220373858398E+00 2.000000000000 +3 -2.106898524353E+00 2.000000000000 +4 -2.106861820288E+00 2.000000000000 +5 -3.083687725701E-01 2.000000000000 +6 -1.983091729061E-01 2.000000000000 +7 -1.970081106663E-01 2.000000000000 +8 -6.410366542437E-02 2.000000000000 +9 -5.903227836118E-02 2.000000000000 +10 4.239801447034E-02 2.000000000000 +11 2.315946182891E-01 2.000000000000 +12 2.408576778259E-01 2.000000000000 +13 2.914041802404E-01 2.000000000000 +14 4.621072360186E-01 0.000000000000 +15 5.033204525506E-01 0.000000000000 +16 5.184815509935E-01 0.000000000000 +17 6.208859981817E-01 0.000000000000 +18 9.660028595290E-01 0.000000000000 +19 9.690860382206E-01 0.000000000000 +20 1.096857545226E+00 0.000000000000 + +kred #78 = (0.444444,0.500000,0.555556) +n eigval occ +1 -3.561368174233E+00 2.000000000000 +2 -2.220388143686E+00 2.000000000000 +3 -2.106904592486E+00 2.000000000000 +4 -2.106888083449E+00 2.000000000000 +5 -3.087105100774E-01 2.000000000000 +6 -1.975103532887E-01 2.000000000000 +7 -1.969189224612E-01 2.000000000000 +8 -6.174136846093E-02 2.000000000000 +9 -5.938682596513E-02 2.000000000000 +10 4.587076141008E-02 2.000000000000 +11 2.374932522079E-01 2.000000000000 +12 2.415440487501E-01 2.000000000000 +13 2.837617137883E-01 2.000000000000 +14 4.682200505304E-01 0.000000000000 +15 4.982607853973E-01 0.000000000000 +16 5.050290426005E-01 0.000000000000 +17 6.001195254333E-01 0.000000000000 +18 9.884318633159E-01 0.000000000000 +19 9.892665326739E-01 0.000000000000 +20 1.086144298469E+00 0.000000000000 + +kred #79 = (0.472222,0.500000,0.527778) +n eigval occ +1 -3.561366526229E+00 2.000000000000 +2 -2.220396893892E+00 2.000000000000 +3 -2.106908307870E+00 2.000000000000 +4 -2.106904150047E+00 2.000000000000 +5 -3.089211167467E-01 2.000000000000 +6 -1.970210630398E-01 2.000000000000 +7 -1.968711835142E-01 2.000000000000 +8 -6.021839419583E-02 2.000000000000 +9 -5.961368213691E-02 2.000000000000 +10 4.788542691512E-02 2.000000000000 +11 2.416159977992E-01 2.000000000000 +12 2.426864144449E-01 2.000000000000 +13 2.782247532392E-01 2.000000000000 +14 4.747454554452E-01 0.000000000000 +15 4.943043843579E-01 0.000000000000 +16 4.961797081547E-01 0.000000000000 +17 5.860251169328E-01 0.000000000000 +18 1.005197716456E+00 0.000000000000 +19 1.005645015876E+00 0.000000000000 +20 1.078325220252E+00 0.000000000000 + +kred #80 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561365971302E+00 2.000000000000 +2 -2.220399840750E+00 2.000000000000 +3 -2.106909558866E+00 2.000000000000 +4 -2.106909557387E+00 2.000000000000 +5 -3.089922604032E-01 2.000000000000 +6 -1.968562815600E-01 2.000000000000 +7 -1.968562806426E-01 2.000000000000 +8 -5.969162889398E-02 2.000000000000 +9 -5.969162787100E-02 2.000000000000 +10 4.854064954445E-02 2.000000000000 +11 2.432089087714E-01 2.000000000000 +12 2.432089126609E-01 2.000000000000 +13 2.760871374498E-01 2.000000000000 +14 4.782428122533E-01 0.000000000000 +15 4.926016304942E-01 0.000000000000 +16 4.926016348502E-01 0.000000000000 +17 5.809338513735E-01 0.000000000000 +18 1.011984749756E+00 0.000000000000 +19 1.011990082630E+00 0.000000000000 +20 1.074946401154E+00 0.000000000000 + +kred #81 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561365971302E+00 2.000000000000 +2 -2.220399840750E+00 2.000000000000 +3 -2.106909558866E+00 2.000000000000 +4 -2.106909557387E+00 2.000000000000 +5 -3.089922604032E-01 2.000000000000 +6 -1.968562815600E-01 2.000000000000 +7 -1.968562806426E-01 2.000000000000 +8 -5.969162889398E-02 2.000000000000 +9 -5.969162787100E-02 2.000000000000 +10 4.854064954445E-02 2.000000000000 +11 2.432089087714E-01 2.000000000000 +12 2.432089126609E-01 2.000000000000 +13 2.760871374498E-01 2.000000000000 +14 4.782428122533E-01 0.000000000000 +15 4.926016304942E-01 0.000000000000 +16 4.926016348502E-01 0.000000000000 +17 5.809338513736E-01 0.000000000000 +18 1.011984712380E+00 0.000000000000 +19 1.012374114287E+00 0.000000000000 +20 1.074946643586E+00 0.000000000000 + +kred #82 = (0.486111,0.486111,0.527778) +n eigval occ +1 -3.561366387613E+00 2.000000000000 +2 -2.220397644771E+00 2.000000000000 +3 -2.106908641871E+00 2.000000000000 +4 -2.106905461748E+00 2.000000000000 +5 -3.089374298902E-01 2.000000000000 +6 -1.969805504712E-01 2.000000000000 +7 -1.968457048929E-01 2.000000000000 +8 -5.999848121966E-02 2.000000000000 +9 -5.969992744664E-02 2.000000000000 +10 4.789273405620E-02 2.000000000000 +11 2.416494129321E-01 2.000000000000 +12 2.436073007234E-01 2.000000000000 +13 2.772787091288E-01 2.000000000000 +14 4.760644247677E-01 0.000000000000 +15 4.934943583034E-01 0.000000000000 +16 4.953787515720E-01 0.000000000000 +17 5.847512632639E-01 0.000000000000 +18 1.005281343420E+00 0.000000000000 +19 1.010634971754E+00 0.000000000000 +20 1.074074589126E+00 0.000000000000 + +kred #83 = (0.472222,0.472222,0.555556) +n eigval occ +1 -3.561367627126E+00 2.000000000000 +2 -2.220391105715E+00 2.000000000000 +3 -2.106905888016E+00 2.000000000000 +4 -2.106893288244E+00 2.000000000000 +5 -3.087750850453E-01 2.000000000000 +6 -1.973513289584E-01 2.000000000000 +7 -1.968165251758E-01 2.000000000000 +8 -6.090157089295E-02 2.000000000000 +9 -5.972408744596E-02 2.000000000000 +10 4.596603385696E-02 2.000000000000 +11 2.375592199684E-01 2.000000000000 +12 2.447478919522E-01 2.000000000000 +13 2.804030311363E-01 2.000000000000 +14 4.715337599916E-01 0.000000000000 +15 4.962172715980E-01 0.000000000000 +16 5.021974184676E-01 0.000000000000 +17 5.955319233934E-01 0.000000000000 +18 9.875434370565E-01 0.000000000000 +19 1.006408512141E+00 0.000000000000 +20 1.090375593988E+00 0.000000000000 + +kred #84 = (0.458333,0.458333,0.583333) +n eigval occ +1 -3.561369661835E+00 2.000000000000 +2 -2.220380368897E+00 2.000000000000 +3 -2.106901284270E+00 2.000000000000 +4 -2.106873378748E+00 2.000000000000 +5 -3.085115690273E-01 2.000000000000 +6 -1.979623827655E-01 2.000000000000 +7 -1.967762737637E-01 2.000000000000 +8 -6.235091439814E-02 2.000000000000 +9 -5.976209175655E-02 2.000000000000 +10 4.281210558640E-02 2.000000000000 +11 2.320110390991E-01 2.000000000000 +12 2.464745360636E-01 2.000000000000 +13 2.847735642518E-01 2.000000000000 +14 4.666985177120E-01 0.000000000000 +15 5.008207985777E-01 0.000000000000 +16 5.119943242816E-01 0.000000000000 +17 6.118559333102E-01 0.000000000000 +18 9.667142956808E-01 0.000000000000 +19 9.970942988069E-01 0.000000000000 +20 1.059643742524E+00 0.000000000000 + +kred #85 = (0.444444,0.444444,0.611111) +n eigval occ +1 -3.561372445919E+00 2.000000000000 +2 -2.220365672144E+00 2.000000000000 +3 -2.106894811090E+00 2.000000000000 +4 -2.106846291615E+00 2.000000000000 +5 -3.081571341103E-01 2.000000000000 +6 -1.988028528258E-01 2.000000000000 +7 -1.967371293935E-01 2.000000000000 +8 -6.427072803279E-02 2.000000000000 +9 -5.981118442801E-02 2.000000000000 +10 3.851779976888E-02 2.000000000000 +11 2.258546466468E-01 2.000000000000 +12 2.485572297731E-01 2.000000000000 +13 2.900968881124E-01 2.000000000000 +14 4.625476859395E-01 0.000000000000 +15 5.072840369590E-01 0.000000000000 +16 5.245392006323E-01 0.000000000000 +17 6.324002676499E-01 0.000000000000 +18 9.443529462949E-01 0.000000000000 +19 9.849927068405E-01 0.000000000000 +20 1.049322140147E+00 0.000000000000 + +kred #86 = (0.430556,0.430556,0.638889) +n eigval occ +1 -3.561375916998E+00 2.000000000000 +2 -2.220347339371E+00 2.000000000000 +3 -2.106886443927E+00 2.000000000000 +4 -2.106812786482E+00 2.000000000000 +5 -3.077254741412E-01 2.000000000000 +6 -1.998566547610E-01 2.000000000000 +7 -1.967153311643E-01 2.000000000000 +8 -6.656895124681E-02 2.000000000000 +9 -5.986868268819E-02 2.000000000000 +10 3.320528185748E-02 2.000000000000 +11 2.196729898679E-01 2.000000000000 +12 2.507469878878E-01 2.000000000000 +13 2.964017949951E-01 2.000000000000 +14 4.595982425955E-01 0.000000000000 +15 5.155260663154E-01 0.000000000000 +16 5.396341914719E-01 0.000000000000 +17 6.561983709978E-01 0.000000000000 +18 9.212633898313E-01 0.000000000000 +19 9.695068795124E-01 0.000000000000 +20 1.037761481976E+00 0.000000000000 + +kred #87 = (0.416667,0.416667,0.666667) +n eigval occ +1 -3.561379997839E+00 2.000000000000 +2 -2.220325771887E+00 2.000000000000 +3 -2.106876155905E+00 2.000000000000 +4 -2.106773802840E+00 2.000000000000 +5 -3.072330936935E-01 2.000000000000 +6 -2.011018369847E-01 2.000000000000 +7 -1.967303173361E-01 2.000000000000 +8 -6.914780375618E-02 2.000000000000 +9 -5.993292733350E-02 2.000000000000 +10 2.703013004389E-02 2.000000000000 +11 2.138798417240E-01 2.000000000000 +12 2.528475726219E-01 2.000000000000 +13 3.038182240829E-01 2.000000000000 +14 4.580884001576E-01 0.000000000001 +15 5.254240964495E-01 0.000000000000 +16 5.570247516885E-01 0.000000000000 +17 6.825592631008E-01 0.000000000000 +18 8.978417644029E-01 0.000000000000 +19 9.512925506377E-01 0.000000000000 +20 1.025103534614E+00 0.000000000000 + +kred #88 = (0.402778,0.402778,0.694444) +n eigval occ +1 -3.561384598466E+00 2.000000000000 +2 -2.220301437657E+00 2.000000000000 +3 -2.106863921061E+00 2.000000000000 +4 -2.106730433368E+00 2.000000000000 +5 -3.066985370550E-01 2.000000000000 +6 -2.025100758808E-01 2.000000000000 +7 -1.968035661322E-01 2.000000000000 +8 -7.191384642432E-02 2.000000000000 +9 -6.000420138397E-02 2.000000000000 +10 2.017687356731E-02 2.000000000000 +11 2.087772316662E-01 2.000000000000 +12 2.547693180167E-01 2.000000000000 +13 3.124303929779E-01 2.000000000000 +14 4.580886969223E-01 0.000000000001 +15 5.368151604525E-01 0.000000000000 +16 5.764274231559E-01 0.000000000000 +17 7.109326916772E-01 0.000000000000 +18 8.743445731444E-01 0.000000000000 +19 9.311998880276E-01 0.000000000000 +20 1.011463048769E+00 0.000000000000 + +kred #89 = (0.388889,0.388889,0.722222) +n eigval occ +1 -3.561389618612E+00 2.000000000000 +2 -2.220274858864E+00 2.000000000000 +3 -2.106849718031E+00 2.000000000000 +4 -2.106683892704E+00 2.000000000000 +5 -3.061415057140E-01 2.000000000000 +6 -2.040464981354E-01 2.000000000000 +7 -1.969571391704E-01 2.000000000000 +8 -7.478653948884E-02 2.000000000000 +9 -6.008542018284E-02 2.000000000000 +10 1.285209914547E-02 2.000000000000 +11 2.045832145614E-01 2.000000000000 +12 2.565355835106E-01 2.000000000000 +13 3.222227353369E-01 2.000000000000 +14 4.595763358466E-01 0.000000000000 +15 5.494865863697E-01 0.000000000000 +16 5.975417954054E-01 0.000000000000 +17 7.407595634842E-01 0.000000000000 +18 8.510534151048E-01 0.000000000000 +19 9.100368395277E-01 0.000000000000 +20 9.969420079742E-01 0.000000000000 + +kred #90 = (0.375000,0.375000,0.750000) +n eigval occ +1 -3.561394950439E+00 2.000000000000 +2 -2.220246598121E+00 2.000000000000 +3 -2.106833534016E+00 2.000000000000 +4 -2.106635482464E+00 2.000000000000 +5 -3.055818977030E-01 2.000000000000 +6 -2.056699952395E-01 2.000000000000 +7 -1.972119762448E-01 2.000000000000 +8 -7.770475174454E-02 2.000000000000 +9 -6.018238130383E-02 2.000000000000 +10 5.275879551723E-03 2.000000000000 +11 2.014487379246E-01 2.000000000000 +12 2.582495385957E-01 2.000000000000 +13 3.330881090287E-01 2.000000000000 +14 4.624803196882E-01 0.000000000000 +15 5.631542771388E-01 0.000000000000 +16 6.200342959805E-01 0.000000000000 +17 7.710295011444E-01 0.000000000000 +18 8.287104190206E-01 0.000000000000 +19 8.884836589088E-01 0.000000000000 +20 9.818245741722E-01 0.000000000000 diff --git a/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refout b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refout new file mode 100644 index 00000000..a53cd86b --- /dev/null +++ b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refout @@ -0,0 +1,149 @@ +*************************************************************************** +* SPARC (version Sep 20, 2023) * +* Copyright (c) 2020 Material Physics & Mechanics Group, Georgia Tech * +* Distributed under GNU General Public License 3 (GPL) * +* Start time: Wed Sep 20 18:04:51 2023 * +*************************************************************************** + Input parameters +*************************************************************************** +LATVEC_SCALE: 1 1 1 +LATVEC: +5.88590692979539 0 0 +0 5.88590692979539 0 +0 0 5.88590692979539 +FD_GRID: 30 30 30 +FD_ORDER: 12 +BC: P P P +KPOINT_GRID: 7 7 7 +KPOINT_SHIFT: 0 0 0 +SPIN_TYP: 0 +ELEC_TEMP_TYPE: Fermi-Dirac +SMEARING: 0.001000000336 +EXCHANGE_CORRELATION: GGA_PBE +NSTATES: 20 +CHEB_DEGREE: 35 +CHEFSI_BOUND_FLAG: 0 +CALC_STRESS: 0 +CALC_PRES: 0 +MAXIT_SCF: 1 +MINIT_SCF: 1 +MAXIT_POISSON: 3000 +TOL_SCF: 1.00E-06 +POISSON_SOLVER: AAR +TOL_POISSON: 1.00E-08 +TOL_LANCZOS: 1.00E-02 +TOL_PSEUDOCHARGE: 1.00E-09 +MIXING_VARIABLE: density +MIXING_PRECOND: none +MIXING_PARAMETER: 0.3 +MIXING_HISTORY: 7 +PULAY_FREQUENCY: 1 +PULAY_RESTART: 0 +REFERENCE_CUTOFF: 0.5 +RHO_TRIGGER: 10 +NUM_CHEFSI: 1 +FIX_RAND: 0 +VERBOSITY: 1 +PRINT_FORCES: 1 +PRINT_ATOMS: 1 +PRINT_EIGEN: 1 +PRINT_DENSITY: 0 +PRINT_ENERGY_DENSITY: 0 +BAND_STRUCTURE: 1 +KPT_PER_LINE: 10 +KPT_PATHS: 9 +0.000000 0.000000 0.000000 +0.000000 0.500000 0.500000 +0.000000 0.500000 0.500000 +0.250000 0.500000 0.750000 +0.250000 0.500000 0.750000 +0.375000 0.375000 0.750000 +0.375000 0.375000 0.750000 +0.000000 0.000000 0.000000 +0.000000 0.000000 0.000000 +0.500000 0.500000 0.500000 +0.500000 0.500000 0.500000 +0.250000 0.625000 0.625000 +0.250000 0.625000 0.625000 +0.250000 0.500000 0.750000 +0.250000 0.500000 0.750000 +0.500000 0.500000 0.500000 +0.500000 0.500000 0.500000 +0.375000 0.375000 0.750000 +OUTPUT_FILE: CdS +*************************************************************************** + Cell +*************************************************************************** +Lattice vectors (Bohr): +5.885906929795390 0.000000000000000 0.000000000000000 +0.000000000000000 5.885906929795390 0.000000000000000 +0.000000000000000 0.000000000000000 5.885906929795390 +Volume: 2.0391077336E+02 (Bohr^3) +Density: 7.0855255767E-01 (amu/Bohr^3), 7.9399500196E+00 (g/cc) +*************************************************************************** + Parallelization +*************************************************************************** +NP_SPIN_PARAL: 1 +NP_KPOINT_PARAL: 10 +NP_BAND_PARAL: 2 +NP_DOMAIN_PARAL: 1 1 1 +NP_DOMAIN_PHI_PARAL: 2 2 5 +EIG_SERIAL_MAXNS: 1500 +*************************************************************************** + Initialization +*************************************************************************** +Number of processors : 20 +Mesh spacing : 0.196197 (Bohr) +Number of symmetry adapted k-points: 90 +Output printed to : CdS.out_01 +Final eigenvalues printed to : CdS.eigen_01 +Total number of atom types : 2 +Total number of atoms : 2 +Total number of electrons : 26 +Atom type 1 (valence electrons) : Cd 20 +Pseudopotential : ../../../psps/48_Cd_20_2.2_2.3_pbe_n_v1.0.psp8 +Atomic mass : 112.414 +Pseudocharge radii of atom type 1 : 7.26 7.26 7.26 (x, y, z dir) +Number of atoms of type 1 : 1 +Atom type 2 (valence electrons) : S 6 +Pseudopotential : ../../../psps/16_S_6_1.8_1.9_pbe_n_v1.0.psp8 +Atomic mass : 32.0675 +Pseudocharge radii of atom type 2 : 7.26 7.26 7.26 (x, y, z dir) +Number of atoms of type 2 : 1 +Estimated total memory usage : 1.29 GB +Estimated memory per processor : 66.03 MB +=================================================================== + Self Consistent Field (SCF#1) +=================================================================== +Iteration Free Energy (Ha/atom) SCF Error Timing (sec) +1 -8.8865309044E+01 1.038E-02 33.894 +Total number of SCF: 1 +WARNING: SCF#1 did not converge to desired accuracy! +==================================================================== + Energy and force calculation +==================================================================== +Free energy per atom : -8.8865309044E+01 (Ha/atom) +Total free energy : -1.7773061809E+02 (Ha) +Band structure energy : -2.0021184766E+01 (Ha) +Exchange correlation energy : -2.5267856300E+01 (Ha) +Self and correction energy : -2.2141865764E+02 (Ha) +-Entropy*kb*T : -4.8922235902E-05 (Ha) +Fermi level : 4.2913354433E-01 (Ha) +RMS force : 2.1300362988E+00 (Ha/Bohr) +Maximum force : 2.1300362988E+00 (Ha/Bohr) +Time for force calculation : 0.168 (sec) +*************************************************************************** + Timing info +*************************************************************************** +Total walltime : 34.273 sec +___________________________________________________________________________ + +*************************************************************************** +* Material Physics & Mechanics Group, Georgia Tech * +* PI: Phanish Suryanarayana * +* List of contributors: See the documentation * +* Citation: See README.md or the documentation for details * +* Acknowledgements: U.S. DOE SC (DE-SC0019410), U.S. DOE NNSA (ASC) * +* {Preliminary developments: U.S. NSF (1333500,1663244,1553212)} * +*************************************************************************** + diff --git a/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refstatic b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refstatic new file mode 100644 index 00000000..b3b1a065 --- /dev/null +++ b/tests/CdS_bandstruct/high_accuracy/CdS_bandstruct.refstatic @@ -0,0 +1,11 @@ +*************************************************************************** + Atom positions +*************************************************************************** +Fractional coordinates of Cd: + 0.0000000000 0.0000000000 0.0000000000 +Fractional coordinates of S: + 0.7500000000 0.2500000000 0.7500000000 +Total free energy (Ha): -1.777306180882454E+02 +Atomic forces (Ha/Bohr): + 1.2139025036E+00 -1.2450300918E+00 1.2302013724E+00 + -1.2139025036E+00 1.2450300918E+00 -1.2302013724E+00 diff --git a/tests/CdS_bandstruct/standard/CdS_bandstruct.inpt b/tests/CdS_bandstruct/standard/CdS_bandstruct.inpt new file mode 100644 index 00000000..22283caf --- /dev/null +++ b/tests/CdS_bandstruct/standard/CdS_bandstruct.inpt @@ -0,0 +1,57 @@ +# Test: CdS band structure calculation +LATVEC: +5.8859069297953903 0.0 0.0 +0.0 5.8859069297953903 0.0 +0.0 0.0 5.8859069297953903 +LATVEC_SCALE: 1.0 1.0 1.0 +MESH_SPACING: 0.30 +FD_ORDER: 12 +BC: P P P +KPOINT_GRID: 7 7 7 +EXCHANGE_CORRELATION: GGA_PBE +ELEC_TEMP_TYPE: fermi-dirac +ELEC_TEMP: 315.775131 +TOL_SCF: 1e-6 +MAXIT_SCF: 50 +PRINT_EIGEN: 1 +PRINT_DENSITY: 1 +MIXING_VARIABLE: density +MIXING_PRECOND: none + +# RHO_TRIGGER: 40 + +# Band sturcture calculation +# First do a ground-state calculation with `BAND_STRUCTURE: 0` and `PRINT_DENSITY: 1`, +# then run a band structure calculation with `BAND_STRUCTURE: 1` and provide the k-path +# using the `KPT_PATHS` keyword. +BAND_STRUCTURE: 1 +INPUT_DENS_FILE: ../densfiles/CdS_standard.indens +KPT_PER_LINE: 10 # number of k-points on each high-symmetry line +KPT_PATHS: 9 +0.0 0.0 0.0 +0.0 0.5 0.5 + +0.0 0.5 0.5 +0.25 0.5 0.75 + +0.25 0.5 0.75 +0.375 0.375 0.75 + +0.375 0.375 0.75 +0.0 0.0 0.0 + +0.0 0.0 0.0 +0.5 0.5 0.5 + +0.5 0.5 0.5 +0.25 0.625 0.625 + +0.25 0.625 0.625 +0.25 0.5 0.75 + +0.25 0.5 0.75 +0.5 0.5 0.5 + +0.5 0.5 0.5 +0.375 0.375 0.75 + diff --git a/tests/CdS_bandstruct/standard/CdS_bandstruct.ion b/tests/CdS_bandstruct/standard/CdS_bandstruct.ion new file mode 100644 index 00000000..54da4349 --- /dev/null +++ b/tests/CdS_bandstruct/standard/CdS_bandstruct.ion @@ -0,0 +1,13 @@ +ATOM_TYPE: Cd +N_TYPE_ATOM: 1 +PSEUDO_POT: ../../../psps/48_Cd_20_2.2_2.3_pbe_n_v1.0.psp8 +COORD_FRAC: + 0.0000000000000000 0.0000000000000000 0.0000000000000000 + +ATOM_TYPE: S +N_TYPE_ATOM: 1 +PSEUDO_POT: ../../../psps/16_S_6_1.8_1.9_pbe_n_v1.0.psp8 +COORD_FRAC: + 0.7500000000000000 0.2500000000000000 0.7500000000000000 + + diff --git a/tests/CdS_bandstruct/standard/CdS_bandstruct.refeigen b/tests/CdS_bandstruct/standard/CdS_bandstruct.refeigen new file mode 100644 index 00000000..d01cd833 --- /dev/null +++ b/tests/CdS_bandstruct/standard/CdS_bandstruct.refeigen @@ -0,0 +1,2071 @@ +Final eigenvalues (Ha) and occupation numbers + +kred #1 = (0.000000,0.000000,0.000000) +n eigval occ +1 -3.561479749542E+00 2.000000000000 +2 -2.219738163480E+00 2.000000000000 +3 -2.106165282872E+00 2.000000000000 +4 -2.106165281944E+00 2.000000000000 +5 -3.026871987139E-01 2.000000000000 +6 -2.190312022910E-01 2.000000000000 +7 -2.190312007423E-01 2.000000000000 +8 -1.431692847298E-01 2.000000000000 +9 -5.981074971545E-02 2.000000000000 +10 -5.981074867070E-02 2.000000000000 +11 3.807541970765E-01 2.000000000000 +12 4.067720874084E-01 1.999999999605 +13 4.067720888883E-01 1.999999999605 +14 4.772984181526E-01 0.000000000000 +15 5.341976339732E-01 0.000000000000 +16 5.341976350567E-01 0.000000000000 +17 8.889413853335E-01 0.000000000000 +18 8.889421350363E-01 0.000000000000 +19 9.482962782180E-01 0.000000000000 +20 9.483216811854E-01 0.000000000000 + +kred #2 = (0.000000,0.055556,0.055556) +n eigval occ +1 -3.561477529894E+00 2.000000000000 +2 -2.219750105906E+00 2.000000000000 +3 -2.106187693800E+00 2.000000000000 +4 -2.106170500786E+00 2.000000000000 +5 -3.026142790862E-01 2.000000000000 +6 -2.188161696828E-01 2.000000000000 +7 -2.182124120219E-01 2.000000000000 +8 -1.408292371423E-01 2.000000000000 +9 -6.003531441096E-02 2.000000000000 +10 -5.943855008347E-02 2.000000000000 +11 3.538288107364E-01 2.000000000000 +12 3.998873686436E-01 2.000000000000 +13 4.203989530035E-01 1.999673139790 +14 4.702105873146E-01 0.000000000000 +15 5.432064878150E-01 0.000000000000 +16 5.600693836324E-01 0.000000000000 +17 8.661251353861E-01 0.000000000000 +18 8.702928941541E-01 0.000000000000 +19 9.522564401852E-01 0.000000000000 +20 9.587877623092E-01 0.000000000000 + +kred #3 = (0.000000,0.111111,0.111111) +n eigval occ +1 -3.561471139973E+00 2.000000000000 +2 -2.219784504708E+00 2.000000000000 +3 -2.106252087351E+00 2.000000000000 +4 -2.106185517406E+00 2.000000000000 +5 -3.024573370006E-01 2.000000000000 +6 -2.182268749170E-01 2.000000000000 +7 -2.158284586800E-01 2.000000000000 +8 -1.339977429167E-01 2.000000000000 +9 -6.066073331296E-02 2.000000000000 +10 -5.808827900014E-02 2.000000000000 +11 3.150826646136E-01 2.000000000000 +12 3.742150686472E-01 2.000000000000 +13 4.232479066631E-01 1.994370196255 +14 4.836538063810E-01 0.000000000000 +15 5.666983499583E-01 0.000000000000 +16 6.040364768388E-01 0.000000000000 +17 8.224673949633E-01 0.000000000000 +18 8.364349748407E-01 0.000000000000 +19 9.505258962502E-01 0.000000000000 +20 9.731774766825E-01 0.000000000000 + +kred #4 = (0.000000,0.166667,0.166667) +n eigval occ +1 -3.561461353792E+00 2.000000000000 +2 -2.219837241134E+00 2.000000000000 +3 -2.106350344729E+00 2.000000000000 +4 -2.106208501755E+00 2.000000000000 +5 -3.023570170785E-01 2.000000000000 +6 -2.174073399009E-01 2.000000000000 +7 -2.121059943757E-01 2.000000000000 +8 -1.234108566844E-01 2.000000000000 +9 -6.149810447449E-02 2.000000000000 +10 -5.503841747192E-02 2.000000000000 +11 2.770438549054E-01 2.000000000000 +12 3.398650942891E-01 2.000000000000 +13 4.242591432050E-01 1.984599505664 +14 5.063500612061E-01 0.000000000000 +15 5.902281865791E-01 0.000000000000 +16 6.472576713527E-01 0.000000000000 +17 7.861965071339E-01 0.000000000000 +18 8.018001873094E-01 0.000000000000 +19 9.439078569850E-01 0.000000000000 +20 9.723833622817E-01 0.000000000000 + +kred #5 = (0.000000,0.222222,0.222222) +n eigval occ +1 -3.561449355456E+00 2.000000000000 +2 -2.219901988713E+00 2.000000000000 +3 -2.106470216181E+00 2.000000000000 +4 -2.106236659223E+00 2.000000000000 +5 -3.024376883719E-01 2.000000000000 +6 -2.165355872200E-01 2.000000000000 +7 -2.074371045916E-01 2.000000000000 +8 -1.108175234027E-01 2.000000000000 +9 -6.209898756499E-02 2.000000000000 +10 -4.902763712078E-02 2.000000000000 +11 2.421254867296E-01 2.000000000000 +12 3.071146098520E-01 2.000000000000 +13 4.262302780995E-01 1.894463947133 +14 5.234917105910E-01 0.000000000000 +15 5.947540068848E-01 0.000000000000 +16 6.886038711892E-01 0.000000000000 +17 7.714292900629E-01 0.000000000000 +18 7.767702095543E-01 0.000000000000 +19 9.336120723376E-01 0.000000000000 +20 9.595334642444E-01 0.000000000000 + +kred #6 = (0.000000,0.277778,0.277778) +n eigval occ +1 -3.561436594587E+00 2.000000000000 +2 -2.219970960231E+00 2.000000000000 +3 -2.106596984341E+00 2.000000000000 +4 -2.106266579114E+00 2.000000000000 +5 -3.027357790089E-01 2.000000000000 +6 -2.157673755024E-01 2.000000000000 +7 -2.023630250066E-01 2.000000000000 +8 -9.926694934551E-02 2.000000000000 +9 -6.162808409026E-02 2.000000000000 +10 -3.856111094732E-02 2.000000000000 +11 2.118985343708E-01 2.000000000000 +12 2.790009341136E-01 2.000000000000 +13 4.281486976729E-01 1.449927857891 +14 5.093597545574E-01 0.000000000000 +15 6.046662166721E-01 0.000000000000 +16 7.250413320210E-01 0.000000000000 +17 7.525174970965E-01 0.000000000000 +18 7.843874362208E-01 0.000000000000 +19 9.203583274264E-01 0.000000000000 +20 9.495993087153E-01 0.000000000000 + +kred #7 = (0.000000,0.333333,0.333333) +n eigval occ +1 -3.561424610336E+00 2.000000000000 +2 -2.220035836582E+00 2.000000000000 +3 -2.106715360272E+00 2.000000000000 +4 -2.106294652776E+00 2.000000000000 +5 -3.031879282141E-01 2.000000000000 +6 -2.151964758010E-01 2.000000000000 +7 -1.975163047502E-01 2.000000000000 +8 -9.168400157250E-02 2.000000000000 +9 -5.912972241468E-02 2.000000000000 +10 -2.373127523301E-02 2.000000000000 +11 1.882780300400E-01 2.000000000000 +12 2.561978477624E-01 2.000000000000 +13 4.268531411659E-01 1.811834919860 +14 4.707774754983E-01 0.000000000000 +15 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2.000000000000 +3 -2.106895321054E+00 2.000000000000 +4 -2.106337585773E+00 2.000000000000 +5 -3.041580630046E-01 2.000000000000 +6 -2.146135057225E-01 2.000000000000 +7 -1.900011243874E-01 2.000000000000 +8 -8.695064609436E-02 2.000000000000 +9 -4.867261281532E-02 2.000000000000 +10 6.471854465981E-03 2.000000000000 +11 1.694020282503E-01 2.000000000000 +12 2.201572991156E-01 2.000000000000 +13 3.687736259367E-01 2.000000000000 +14 4.440605534025E-01 0.000000647930 +15 7.144824851333E-01 0.000000000000 +16 7.188340496020E-01 0.000000000000 +17 7.801681598460E-01 0.000000000000 +18 8.063697091234E-01 0.000000000000 +19 8.794687755591E-01 0.000000000000 +20 9.103432815176E-01 0.000000000000 + +kred #11 = (0.000000,0.500000,0.500000) +n eigval occ +1 -3.561406262640E+00 2.000000000000 +2 -2.220135353536E+00 2.000000000000 +3 -2.106895321054E+00 2.000000000000 +4 -2.106337585773E+00 2.000000000000 +5 -3.041580630046E-01 2.000000000000 +6 -2.146135057225E-01 2.000000000000 +7 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2.000000000000 +12 2.206404958330E-01 2.000000000000 +13 3.704788943885E-01 2.000000000000 +14 4.429022183245E-01 0.000002063411 +15 7.095874903737E-01 0.000000000000 +16 7.168421423303E-01 0.000000000000 +17 7.774204540727E-01 0.000000000000 +18 8.098600341318E-01 0.000000000000 +19 8.737538799218E-01 0.000000000000 +20 9.176685930549E-01 0.000000000000 + +kred #13 = (0.055556,0.500000,0.555556) +n eigval occ +1 -3.561406268995E+00 2.000000000000 +2 -2.220135038488E+00 2.000000000000 +3 -2.106882779532E+00 2.000000000000 +4 -2.106350198022E+00 2.000000000000 +5 -3.041964224789E-01 2.000000000000 +6 -2.140715052375E-01 2.000000000000 +7 -1.907692208338E-01 2.000000000000 +8 -8.666630967981E-02 2.000000000000 +9 -4.956088329259E-02 2.000000000000 +10 5.464510151505E-03 2.000000000000 +11 1.719024287857E-01 2.000000000000 +12 2.224067755878E-01 2.000000000000 +13 3.753471251696E-01 2.000000000000 +14 4.395475055076E-01 0.000059088944 +15 6.959473872344E-01 0.000000000000 +16 7.118232666247E-01 0.000000000000 +17 7.707386058913E-01 0.000000000000 +18 8.181795244007E-01 0.000000000000 +19 8.642048139984E-01 0.000000000000 +20 9.325550541317E-01 0.000000000000 + +kred #14 = (0.083333,0.500000,0.583333) +n eigval occ +1 -3.561406276221E+00 2.000000000000 +2 -2.220134680228E+00 2.000000000000 +3 -2.106867753771E+00 2.000000000000 +4 -2.106365304213E+00 2.000000000000 +5 -3.042407764053E-01 2.000000000000 +6 -2.134083872057E-01 2.000000000000 +7 -1.916878895192E-01 2.000000000000 +8 -8.631844409704E-02 2.000000000000 +9 -5.060110946629E-02 2.000000000000 +10 4.395415215258E-03 2.000000000000 +11 1.739583217064E-01 2.000000000000 +12 2.262422170013E-01 2.000000000000 +13 3.824957173706E-01 2.000000000000 +14 4.345694623421E-01 0.008542716827 +15 6.776189620070E-01 0.000000000000 +16 7.022904967953E-01 0.000000000000 +17 7.651821150157E-01 0.000000000000 +18 8.273183233828E-01 0.000000000000 +19 8.555357573891E-01 0.000000000000 +20 9.497245731501E-01 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2.000000000000 +4 -2.106408373372E+00 2.000000000000 +5 -3.043565756657E-01 2.000000000000 +6 -2.114148975814E-01 2.000000000000 +7 -1.943211912734E-01 2.000000000000 +8 -8.529829949716E-02 2.000000000000 +9 -5.339586625261E-02 2.000000000000 +10 2.002312294677E-03 2.000000000000 +11 1.759193387789E-01 2.000000000000 +12 2.423557367806E-01 2.000000000000 +13 3.912291475277E-01 2.000000000000 +14 4.310076448304E-01 0.262551301885 +15 6.329357579939E-01 0.000000000000 +16 6.769433645374E-01 0.000000000000 +17 7.671231311764E-01 0.000000000000 +18 8.388389458378E-01 0.000000000000 +19 8.420966675301E-01 0.000000000000 +20 9.749375982357E-01 0.000000000000 + +kred #17 = (0.166667,0.500000,0.666667) +n eigval occ +1 -3.561406303384E+00 2.000000000000 +2 -2.220133333611E+00 2.000000000000 +3 -2.106800545699E+00 2.000000000000 +4 -2.106432814595E+00 2.000000000000 +5 -3.044144758842E-01 2.000000000000 +6 -2.101896793164E-01 2.000000000000 +7 -1.958527014853E-01 2.000000000000 +8 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2.000000000000 +13 3.738482241621E-01 2.000000000000 +14 4.544815079053E-01 0.000000000019 +15 5.857528683859E-01 0.000000000000 +16 6.600521378324E-01 0.000000000000 +17 7.802028919642E-01 0.000000000000 +18 8.227835522718E-01 0.000000000000 +19 8.482565013908E-01 0.000000000000 +20 9.786434984260E-01 0.000000000000 + +kred #19 = (0.222222,0.500000,0.722222) +n eigval occ +1 -3.561406315327E+00 2.000000000000 +2 -2.220132741514E+00 2.000000000000 +3 -2.106761384097E+00 2.000000000000 +4 -2.106472109118E+00 2.000000000000 +5 -3.044943437121E-01 2.000000000000 +6 -2.079465522512E-01 2.000000000000 +7 -1.985047989273E-01 2.000000000000 +8 -8.380795436440E-02 2.000000000000 +9 -5.692938383328E-02 2.000000000000 +10 -2.710670084205E-04 2.000000000000 +11 1.747370842018E-01 2.000000000000 +12 2.757471506758E-01 2.000000000000 +13 3.642868433782E-01 2.000000000000 +14 4.673940693892E-01 0.000000000000 +15 5.676375646990E-01 0.000000000000 +16 6.560209863613E-01 0.000000000000 +17 7.879582275245E-01 0.000000000000 +18 8.144076028896E-01 0.000000000000 +19 8.497699074019E-01 0.000000000000 +20 9.783088365176E-01 0.000000000000 + +kred #20 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561406316965E+00 2.000000000000 +2 -2.220132660304E+00 2.000000000000 +3 -2.106755148361E+00 2.000000000000 +4 -2.106478363083E+00 2.000000000000 +5 -3.045054646766E-01 2.000000000000 +6 -2.075316918634E-01 2.000000000000 +7 -1.989754265406E-01 2.000000000000 +8 -8.367038246447E-02 2.000000000000 +9 -5.722848631773E-02 2.000000000000 +10 -4.329960095212E-04 2.000000000000 +11 1.745634512575E-01 2.000000000000 +12 2.798142086068E-01 2.000000000000 +13 3.602719902321E-01 2.000000000000 +14 4.731454796350E-01 0.000000000000 +15 5.601709578851E-01 0.000000000000 +16 6.547022602985E-01 0.000000000000 +17 7.923929304676E-01 0.000000000000 +18 8.097821329996E-01 0.000000000000 +19 8.502542722631E-01 0.000000000000 +20 9.781345234811E-01 0.000000000000 + +kred #21 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561406316965E+00 2.000000000000 +2 -2.220132660304E+00 2.000000000000 +3 -2.106755148361E+00 2.000000000000 +4 -2.106478363083E+00 2.000000000000 +5 -3.045054646766E-01 2.000000000000 +6 -2.075316918634E-01 2.000000000000 +7 -1.989754265406E-01 2.000000000000 +8 -8.367038246447E-02 2.000000000000 +9 -5.722848631773E-02 2.000000000000 +10 -4.329960095208E-04 2.000000000000 +11 1.745634512575E-01 2.000000000000 +12 2.798142086068E-01 2.000000000000 +13 3.602719902321E-01 2.000000000000 +14 4.731454796350E-01 0.000000000000 +15 5.601709578851E-01 0.000000000000 +16 6.547022602985E-01 0.000000000000 +17 7.923929304676E-01 0.000000000000 +18 8.097821329998E-01 0.000000000000 +19 8.502542722664E-01 0.000000000000 +20 9.781345758929E-01 0.000000000000 + +kred #22 = (0.263889,0.486111,0.750000) +n eigval occ +1 -3.561404793081E+00 2.000000000000 +2 -2.220140726440E+00 2.000000000000 +3 -2.106758232262E+00 2.000000000000 +4 -2.106493828650E+00 2.000000000000 +5 -3.046824806719E-01 2.000000000000 +6 -2.070867021786E-01 2.000000000000 +7 -1.988095843808E-01 2.000000000000 +8 -8.296098387600E-02 2.000000000000 +9 -5.716557660716E-02 2.000000000000 +10 1.300320792867E-03 2.000000000000 +11 1.774550899974E-01 2.000000000000 +12 2.764738191845E-01 2.000000000000 +13 3.569028215751E-01 2.000000000000 +14 4.709043609397E-01 0.000000000000 +15 5.575578408209E-01 0.000000000000 +16 6.491835589457E-01 0.000000000000 +17 7.900015303585E-01 0.000000000000 +18 8.127352256515E-01 0.000000000000 +19 8.516140903137E-01 0.000000000000 +20 9.839381446690E-01 0.000000000000 + +kred #23 = (0.277778,0.472222,0.750000) +n eigval occ +1 -3.561403420113E+00 2.000000000000 +2 -2.220147996276E+00 2.000000000000 +3 -2.106760335673E+00 2.000000000000 +4 -2.106508421223E+00 2.000000000000 +5 -3.048515622642E-01 2.000000000000 +6 -2.066973930328E-01 2.000000000000 +7 -1.986252008756E-01 2.000000000000 +8 -8.226362676578E-02 2.000000000000 +9 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2.000000000000 +8 -1.431692847298E-01 2.000000000000 +9 -5.981074971545E-02 2.000000000000 +10 -5.981074867070E-02 2.000000000000 +11 3.807541970765E-01 2.000000000000 +12 4.067720874084E-01 1.999999999605 +13 4.067720888883E-01 1.999999999605 +14 4.772984181526E-01 0.000000000000 +15 5.341976339732E-01 0.000000000000 +16 5.341976350567E-01 0.000000000000 +17 8.889413858541E-01 0.000000000000 +18 8.889414671263E-01 0.000000000000 +19 9.482962694840E-01 0.000000000000 +20 9.483518859252E-01 0.000000000000 + +kred #41 = (0.000000,0.000000,0.000000) +n eigval occ +1 -3.561479749542E+00 2.000000000000 +2 -2.219738163480E+00 2.000000000000 +3 -2.106165282872E+00 2.000000000000 +4 -2.106165281944E+00 2.000000000000 +5 -3.026871987139E-01 2.000000000000 +6 -2.190312022910E-01 2.000000000000 +7 -2.190312007423E-01 2.000000000000 +8 -1.431692847298E-01 2.000000000000 +9 -5.981074971545E-02 2.000000000000 +10 -5.981074867070E-02 2.000000000000 +11 3.807541970765E-01 2.000000000000 +12 4.067720874084E-01 1.999999999605 +13 4.067720888883E-01 1.999999999605 +14 4.772984181526E-01 0.000000000000 +15 5.341976339732E-01 0.000000000000 +16 5.341976350567E-01 0.000000000000 +17 8.889413856844E-01 0.000000000000 +18 8.889414530909E-01 0.000000000000 +19 9.482962700924E-01 0.000000000000 +20 9.483510782759E-01 0.000000000000 + +kred #42 = (0.055556,0.055556,0.055556) +n eigval occ +1 -3.561476419675E+00 2.000000000000 +2 -2.219756137196E+00 2.000000000000 +3 -2.106186226863E+00 2.000000000000 +4 -2.106185709828E+00 2.000000000000 +5 -3.025290718035E-01 2.000000000000 +6 -2.183298364193E-01 2.000000000000 +7 -2.181441900624E-01 2.000000000000 +8 -1.397532075932E-01 2.000000000000 +9 -5.987528704196E-02 2.000000000000 +10 -5.963523117704E-02 2.000000000000 +11 3.491017110994E-01 2.000000000000 +12 3.915383179492E-01 2.000000000000 +13 4.184353124460E-01 1.999954119821 +14 4.747538302575E-01 0.000000000000 +15 5.530802579253E-01 0.000000000000 +16 5.643628197371E-01 0.000000000000 +17 8.596640916109E-01 0.000000000000 +18 8.650498182341E-01 0.000000000000 +19 9.516627231429E-01 0.000000000000 +20 9.610208160648E-01 0.000000000000 + +kred #43 = (0.111111,0.111111,0.111111) +n eigval occ +1 -3.561466836545E+00 2.000000000000 +2 -2.219807809443E+00 2.000000000000 +3 -2.106246295207E+00 2.000000000000 +4 -2.106244475463E+00 2.000000000000 +5 -3.022467566110E-01 2.000000000000 +6 -2.163049400489E-01 2.000000000000 +7 -2.156331174116E-01 2.000000000000 +8 -1.298334975223E-01 2.000000000000 +9 -6.006516364516E-02 2.000000000000 +10 -5.851477854271E-02 2.000000000000 +11 3.097800109017E-01 2.000000000000 +12 3.608692593316E-01 2.000000000000 +13 3.932420578455E-01 2.000000000000 +14 5.068488389086E-01 0.000000000000 +15 5.936896338717E-01 0.000000000000 +16 6.133414400417E-01 0.000000000000 +17 8.107949405610E-01 0.000000000000 +18 8.177337564176E-01 0.000000000000 +19 9.382756603009E-01 0.000000000000 +20 9.679176458403E-01 0.000000000000 + +kred #44 = 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0.000000000000 +17 7.751837455891E-01 0.000000000000 +18 8.252514272003E-01 0.000000000000 +19 8.674561196600E-01 0.000000000000 +20 9.947480148068E-01 0.000000000000 + +kred #66 = (0.250000,0.555556,0.694444) +n eigval occ +1 -3.561401167083E+00 2.000000000000 +2 -2.220159950207E+00 2.000000000000 +3 -2.106762153562E+00 2.000000000000 +4 -2.106533944377E+00 2.000000000000 +5 -3.051508567255E-01 2.000000000000 +6 -2.060940700816E-01 2.000000000000 +7 -1.982019235709E-01 2.000000000000 +8 -8.089504046871E-02 2.000000000000 +9 -5.747858891926E-02 2.000000000000 +10 4.642696779723E-03 2.000000000000 +11 1.895351361410E-01 2.000000000000 +12 2.647990298747E-01 2.000000000000 +13 3.468345932520E-01 2.000000000000 +14 4.648484500821E-01 0.000000000000 +15 5.577596155431E-01 0.000000000000 +16 6.322837896254E-01 0.000000000000 +17 7.782712487273E-01 0.000000000000 +18 8.230197698397E-01 0.000000000000 +19 8.623370012303E-01 0.000000000000 +20 9.945033679628E-01 0.000000000000 + +kred #67 = (0.250000,0.541667,0.708333) +n eigval occ +1 -3.561402208406E+00 2.000000000000 +2 -2.220154419050E+00 2.000000000000 +3 -2.106761588213E+00 2.000000000000 +4 -2.106521884813E+00 2.000000000000 +5 -3.050089299678E-01 2.000000000000 +6 -2.063664273436E-01 2.000000000000 +7 -1.984218827624E-01 2.000000000000 +8 -8.157558476306E-02 2.000000000000 +9 -5.728167183241E-02 2.000000000000 +10 3.820672915635E-03 2.000000000000 +11 1.851184680595E-01 2.000000000000 +12 2.688125937043E-01 2.000000000000 +13 3.501493908312E-01 2.000000000000 +14 4.666493810616E-01 0.000000000000 +15 5.565697778648E-01 0.000000000000 +16 6.378226335579E-01 0.000000000000 +17 7.819931179046E-01 0.000000000000 +18 8.200926478819E-01 0.000000000000 +19 8.578422841105E-01 0.000000000000 +20 9.924848022568E-01 0.000000000000 + +kred #68 = (0.250000,0.527778,0.722222) +n eigval occ +1 -3.561403420113E+00 2.000000000000 +2 -2.220147996275E+00 2.000000000000 +3 -2.106760335521E+00 2.000000000000 +4 -2.106508421376E+00 2.000000000000 +5 -3.048515622073E-01 2.000000000000 +6 -2.066973932806E-01 2.000000000000 +7 -1.986252007600E-01 2.000000000000 +8 -8.226362693417E-02 2.000000000000 +9 -5.718017154929E-02 2.000000000000 +10 2.713945749179E-03 2.000000000000 +11 1.810208661718E-01 2.000000000000 +12 2.727660770135E-01 2.000000000000 +13 3.535213094199E-01 2.000000000000 +14 4.687049186311E-01 0.000000000000 +15 5.564123793325E-01 0.000000000000 +16 6.435178495365E-01 0.000000000000 +17 7.860920481891E-01 0.000000000000 +18 8.165378097339E-01 0.000000000000 +19 8.542056209909E-01 0.000000000000 +20 9.888463707544E-01 0.000000000000 + +kred #69 = (0.250000,0.513889,0.736111) +n eigval occ +1 -3.561404793081E+00 2.000000000000 +2 -2.220140726439E+00 2.000000000000 +3 -2.106758232190E+00 2.000000000000 +4 -2.106493828723E+00 2.000000000000 +5 -3.046824806432E-01 2.000000000000 +6 -2.070867023072E-01 2.000000000000 +7 -1.988095843183E-01 2.000000000000 +8 -8.296098396026E-02 2.000000000000 +9 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2.000000000000 +14 4.731454796350E-01 0.000000000000 +15 5.601709578851E-01 0.000000000000 +16 6.547022602985E-01 0.000000000000 +17 7.923929304677E-01 0.000000000000 +18 8.097821329998E-01 0.000000000000 +19 8.502542722655E-01 0.000000000000 +20 9.781346056477E-01 0.000000000000 + +kred #71 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561406316965E+00 2.000000000000 +2 -2.220132660304E+00 2.000000000000 +3 -2.106755148361E+00 2.000000000000 +4 -2.106478363083E+00 2.000000000000 +5 -3.045054646766E-01 2.000000000000 +6 -2.075316918634E-01 2.000000000000 +7 -1.989754265406E-01 2.000000000000 +8 -8.367038246447E-02 2.000000000000 +9 -5.722848631773E-02 2.000000000000 +10 -4.329960095211E-04 2.000000000000 +11 1.745634512575E-01 2.000000000000 +12 2.798142086068E-01 2.000000000000 +13 3.602719902321E-01 2.000000000000 +14 4.731454796350E-01 0.000000000000 +15 5.601709578851E-01 0.000000000000 +16 6.547022602985E-01 0.000000000000 +17 7.923929304676E-01 0.000000000000 +18 8.097821329995E-01 0.000000000000 +19 8.502542722631E-01 0.000000000000 +20 9.781345190389E-01 0.000000000000 + +kred #72 = (0.277778,0.500000,0.722222) +n eigval occ +1 -3.561399967852E+00 2.000000000000 +2 -2.220166281778E+00 2.000000000000 +3 -2.106769506513E+00 2.000000000000 +4 -2.106541229661E+00 2.000000000000 +5 -3.052306053210E-01 2.000000000000 +6 -2.056553164634E-01 2.000000000000 +7 -1.983910264872E-01 2.000000000000 +8 -8.063962577101E-02 2.000000000000 +9 -5.702931198812E-02 2.000000000000 +10 7.441908691196E-03 2.000000000000 +11 1.848495548067E-01 2.000000000000 +12 2.681056053267E-01 2.000000000000 +13 3.469501701301E-01 2.000000000000 +14 4.652797689781E-01 0.000000000000 +15 5.472888450640E-01 0.000000000000 +16 6.311029042935E-01 0.000000000000 +17 7.706227969910E-01 0.000000000000 +18 8.296776538201E-01 0.000000000000 +19 8.615474957836E-01 0.000000000000 +20 1.002887460914E+00 0.000000000000 + +kred #73 = (0.305556,0.500000,0.694444) +n eigval occ +1 -3.561393813457E+00 2.000000000000 +2 -2.220198899406E+00 2.000000000000 +3 -2.106783419152E+00 2.000000000000 +4 -2.106601998028E+00 2.000000000000 +5 -3.059517688100E-01 2.000000000000 +6 -2.038352688041E-01 2.000000000000 +7 -1.979033159743E-01 2.000000000000 +8 -7.732677578677E-02 2.000000000000 +9 -5.715188994240E-02 2.000000000000 +10 1.563238928407E-02 2.000000000000 +11 1.953294728045E-01 2.000000000000 +12 2.581876893744E-01 2.000000000000 +13 3.340903131552E-01 2.000000000000 +14 4.596811672880E-01 0.000000000000 +15 5.357239909778E-01 0.000000000000 +16 6.057303023465E-01 0.000000000000 +17 7.387597086768E-01 0.000000000000 +18 8.562687057486E-01 0.000000000000 +19 8.806752905389E-01 0.000000000000 +20 1.028832236383E+00 0.000000000000 + +kred #74 = (0.333333,0.500000,0.666667) +n eigval occ +1 -3.561388040534E+00 2.000000000000 +2 -2.220229519690E+00 2.000000000000 +3 -2.106796464826E+00 2.000000000000 +4 -2.106658847476E+00 2.000000000000 +5 -3.066436551228E-01 2.000000000000 +6 -2.021272371037E-01 2.000000000000 +7 -1.975151633683E-01 2.000000000000 +8 -7.383371241640E-02 2.000000000000 +9 -5.749006819340E-02 2.000000000000 +10 2.367227403635E-02 2.000000000000 +11 2.056420124478E-01 2.000000000000 +12 2.503462179336E-01 2.000000000000 +13 3.219406407972E-01 2.000000000000 +14 4.565044266792E-01 0.000000000003 +15 5.255604636507E-01 0.000000000000 +16 5.806279760908E-01 0.000000000000 +17 7.062973610882E-01 0.000000000000 +18 8.842810809634E-01 0.000000000000 +19 9.022229492278E-01 0.000000000000 +20 1.048491780641E+00 0.000000000000 + +kred #75 = (0.361111,0.500000,0.638889) +n eigval occ +1 -3.561382824114E+00 2.000000000000 +2 -2.220257208544E+00 2.000000000000 +3 -2.106808249087E+00 2.000000000000 +4 -2.106710089926E+00 2.000000000000 +5 -3.072810507294E-01 2.000000000000 +6 -2.005832718398E-01 2.000000000000 +7 -1.972213503481E-01 2.000000000000 +8 -7.030716885550E-02 2.000000000000 +9 -5.794393624982E-02 2.000000000000 +10 3.107692086030E-02 2.000000000000 +11 2.153823450472E-01 2.000000000000 +12 2.448231135680E-01 2.000000000000 +13 3.106847194972E-01 2.000000000000 +14 4.558640275370E-01 0.000000000005 +15 5.168141746928E-01 0.000000000000 +16 5.570814367006E-01 0.000000000000 +17 6.751498911110E-01 0.000000000000 +18 9.125330491856E-01 0.000000000000 +19 9.246335171726E-01 0.000000000000 +20 1.066443990646E+00 0.000000000000 + +kred #76 = (0.388889,0.500000,0.611111) +n eigval occ +1 -3.561378322234E+00 2.000000000000 +2 -2.220281120125E+00 2.000000000000 +3 -2.106818416238E+00 2.000000000000 +4 -2.106754216477E+00 2.000000000000 +5 -3.078400615397E-01 2.000000000000 +6 -1.992503051906E-01 2.000000000000 +7 -1.970107394091E-01 2.000000000000 +8 -6.693756204133E-02 2.000000000000 +9 -5.842780583750E-02 2.000000000000 +10 3.741242230588E-02 2.000000000000 +11 2.241410225177E-01 2.000000000000 +12 2.417189869286E-01 2.000000000000 +13 3.004553099394E-01 2.000000000000 +14 4.577861208231E-01 0.000000000001 +15 5.094388812378E-01 0.000000000000 +16 5.360740640087E-01 0.000000000000 +17 6.463430424925E-01 0.000000000000 +18 9.400822568626E-01 0.000000000000 +19 9.471149827289E-01 0.000000000000 +20 1.079530370943E+00 0.000000000000 + +kred #77 = (0.416667,0.500000,0.583333) +n eigval occ +1 -3.561374671190E+00 2.000000000000 +2 -2.220300523078E+00 2.000000000000 +3 -2.106826659862E+00 2.000000000000 +4 -2.106789937463E+00 2.000000000000 +5 -3.082992861021E-01 2.000000000000 +6 -1.981688494011E-01 2.000000000000 +7 -1.968689023896E-01 2.000000000000 +8 -6.395001610733E-02 2.000000000000 +9 -5.887270669034E-02 2.000000000000 +10 4.237543941678E-02 2.000000000000 +11 2.315753001396E-01 2.000000000000 +12 2.408398043712E-01 2.000000000000 +13 2.913852878315E-01 2.000000000000 +14 4.620947699576E-01 0.000000000000 +15 5.033150307486E-01 0.000000000000 +16 5.184691807053E-01 0.000000000000 +17 6.208799315498E-01 0.000000000000 +18 9.658440109031E-01 0.000000000000 +19 9.689561453958E-01 0.000000000000 +20 1.083813019925E+00 0.000000000000 + +kred #78 = (0.444444,0.500000,0.555556) +n eigval occ +1 -3.561371981457E+00 2.000000000000 +2 -2.220314823336E+00 2.000000000000 +3 -2.106832731831E+00 2.000000000000 +4 -2.106816215487E+00 2.000000000000 +5 -3.086408692186E-01 2.000000000000 +6 -1.973718427052E-01 2.000000000000 +7 -1.967809000513E-01 2.000000000000 +8 -6.158377771842E-02 2.000000000000 +9 -5.922646072906E-02 2.000000000000 +10 4.584435055063E-02 2.000000000000 +11 2.374745070958E-01 2.000000000000 +12 2.415270681144E-01 2.000000000000 +13 2.837416485571E-01 2.000000000000 +14 4.682049290044E-01 0.000000000000 +15 4.982578848677E-01 0.000000000000 +16 5.050180528778E-01 0.000000000000 +17 6.001137469730E-01 0.000000000000 +18 9.882819602934E-01 0.000000000000 +19 9.891256268730E-01 0.000000000000 +20 1.083702366746E+00 0.000000000000 + +kred #79 = (0.472222,0.500000,0.527778) +n eigval occ +1 -3.561370334383E+00 2.000000000000 +2 -2.220323582714E+00 2.000000000000 +3 -2.106836449563E+00 2.000000000000 +4 -2.106832291184E+00 2.000000000000 +5 -3.088513838754E-01 2.000000000000 +6 -1.968836444217E-01 2.000000000000 +7 -1.967338861833E-01 2.000000000000 +8 -6.005828314078E-02 2.000000000000 +9 -5.945285255809E-02 2.000000000000 +10 4.785650679695E-02 2.000000000000 +11 2.415985137620E-01 2.000000000000 +12 2.426697100175E-01 2.000000000000 +13 2.782033667529E-01 2.000000000000 +14 4.747245439588E-01 0.000000000000 +15 4.943038230469E-01 0.000000000000 +16 4.961730739200E-01 0.000000000000 +17 5.860193464950E-01 0.000000000000 +18 1.004940108261E+00 0.000000000000 +19 1.005255991049E+00 0.000000000000 +20 1.079758040857E+00 0.000000000000 + +kred #80 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561369779770E+00 2.000000000000 +2 -2.220326532662E+00 2.000000000000 +3 -2.106837701935E+00 2.000000000000 +4 -2.106837701002E+00 2.000000000000 +5 -3.089224969717E-01 2.000000000000 +6 -1.967192275762E-01 2.000000000000 +7 -1.967192271490E-01 2.000000000000 +8 -5.953064656144E-02 2.000000000000 +9 -5.953064601912E-02 2.000000000000 +10 4.851085297996E-02 2.000000000000 +11 2.431922026240E-01 2.000000000000 +12 2.431922046682E-01 2.000000000000 +13 2.760650554176E-01 2.000000000000 +14 4.782153040558E-01 0.000000000000 +15 4.926015126225E-01 0.000000000000 +16 4.926015148824E-01 0.000000000000 +17 5.809280240372E-01 0.000000000000 +18 1.011807861289E+00 0.000000000000 +19 1.012291663753E+00 0.000000000000 +20 1.074907920808E+00 0.000000000000 + +kred #81 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561369779770E+00 2.000000000000 +2 -2.220326532662E+00 2.000000000000 +3 -2.106837701935E+00 2.000000000000 +4 -2.106837701002E+00 2.000000000000 +5 -3.089224969717E-01 2.000000000000 +6 -1.967192275762E-01 2.000000000000 +7 -1.967192271490E-01 2.000000000000 +8 -5.953064656144E-02 2.000000000000 +9 -5.953064601912E-02 2.000000000000 +10 4.851085297996E-02 2.000000000000 +11 2.431922026240E-01 2.000000000000 +12 2.431922046681E-01 2.000000000000 +13 2.760650554176E-01 2.000000000000 +14 4.782153040558E-01 0.000000000000 +15 4.926015126225E-01 0.000000000000 +16 4.926015148824E-01 0.000000000000 +17 5.809280240372E-01 0.000000000000 +18 1.011807967522E+00 0.000000000000 +19 1.011874813820E+00 0.000000000000 +20 1.074998162920E+00 0.000000000000 + +kred #82 = (0.486111,0.486111,0.527778) +n eigval occ +1 -3.561370195846E+00 2.000000000000 +2 -2.220324334381E+00 2.000000000000 +3 -2.106836784691E+00 2.000000000000 +4 -2.106833602709E+00 2.000000000000 +5 -3.088676891955E-01 2.000000000000 +6 -1.968431765793E-01 2.000000000000 +7 -1.967084932688E-01 2.000000000000 +8 -5.983803190562E-02 2.000000000000 +9 -5.953911514621E-02 2.000000000000 +10 4.786348839009E-02 2.000000000000 +11 2.416323643676E-01 2.000000000000 +12 2.435905000383E-01 2.000000000000 +13 2.772570155553E-01 2.000000000000 +14 4.760414751172E-01 0.000000000000 +15 4.934938532706E-01 0.000000000000 +16 4.953742869303E-01 0.000000000000 +17 5.847453913586E-01 0.000000000000 +18 1.004369757640E+00 0.000000000000 +19 1.011518161280E+00 0.000000000000 +20 1.073673010986E+00 0.000000000000 + +kred #83 = (0.472222,0.472222,0.555556) +n eigval occ +1 -3.561371434656E+00 2.000000000000 +2 -2.220317788469E+00 2.000000000000 +3 -2.106834029047E+00 2.000000000000 +4 -2.106821422355E+00 2.000000000000 +5 -3.087054131239E-01 2.000000000000 +6 -1.972130006387E-01 2.000000000000 +7 -1.966788394184E-01 2.000000000000 +8 -6.074271227145E-02 2.000000000000 +9 -5.956378423135E-02 2.000000000000 +10 4.593842073608E-02 2.000000000000 +11 2.375414818893E-01 2.000000000000 +12 2.447308269493E-01 2.000000000000 +13 2.803821524638E-01 2.000000000000 +14 4.715159636174E-01 0.000000000000 +15 4.962159245774E-01 0.000000000000 +16 5.021881554405E-01 0.000000000000 +17 5.955258957485E-01 0.000000000000 +18 9.873564239215E-01 0.000000000000 +19 1.005372911180E+00 0.000000000000 +20 1.068912139411E+00 0.000000000000 + +kred #84 = (0.458333,0.458333,0.583333) +n eigval occ +1 -3.561373468213E+00 2.000000000000 +2 -2.220307040399E+00 2.000000000000 +3 -2.106829422322E+00 2.000000000000 +4 -2.106801501657E+00 2.000000000000 +5 -3.084420135839E-01 2.000000000000 +6 -1.978224811928E-01 2.000000000000 +7 -1.966377997667E-01 2.000000000000 +8 -6.219468794534E-02 2.000000000000 +9 -5.960263157932E-02 2.000000000000 +10 4.278715275106E-02 2.000000000000 +11 2.319926733888E-01 2.000000000000 +12 2.464570883668E-01 2.000000000000 +13 2.847534685575E-01 2.000000000000 +14 4.666835686797E-01 0.000000000000 +15 5.008185606810E-01 0.000000000000 +16 5.119823492147E-01 0.000000000000 +17 6.118496199966E-01 0.000000000000 +18 9.665764253555E-01 0.000000000000 +19 9.969372086888E-01 0.000000000000 +20 1.059513892142E+00 0.000000000000 + +kred #85 = (0.444444,0.444444,0.611111) +n eigval occ +1 -3.561376250721E+00 2.000000000000 +2 -2.220292328249E+00 2.000000000000 +3 -2.106822944977E+00 2.000000000000 +4 -2.106774399283E+00 2.000000000000 +5 -3.080877455574E-01 2.000000000000 +6 -1.986607876958E-01 2.000000000000 +7 -1.965975567148E-01 2.000000000000 +8 -6.411815383439E-02 2.000000000000 +9 -5.965289198843E-02 2.000000000000 +10 3.849646408063E-02 2.000000000000 +11 2.258358383110E-01 2.000000000000 +12 2.485393525215E-01 2.000000000000 +13 2.900773567790E-01 2.000000000000 +14 4.625341408492E-01 0.000000000000 +15 5.072809681857E-01 0.000000000000 +16 5.245256432430E-01 0.000000000000 +17 6.323935515560E-01 0.000000000000 +18 9.442260982621E-01 0.000000000000 +19 9.848697658690E-01 0.000000000000 +20 1.049229674209E+00 0.000000000000 + +kred #86 = (0.430556,0.430556,0.638889) +n eigval occ +1 -3.561379719836E+00 2.000000000000 +2 -2.220273976279E+00 2.000000000000 +3 -2.106814572469E+00 2.000000000000 +4 -2.106740875302E+00 2.000000000000 +5 -3.076563065092E-01 2.000000000000 +6 -1.997118795869E-01 2.000000000000 +7 -1.965743558767E-01 2.000000000000 +8 -6.642103027862E-02 2.000000000000 +9 -5.971186780915E-02 2.000000000000 +10 3.318845267867E-02 2.000000000000 +11 2.196539150799E-01 2.000000000000 +12 2.507287026013E-01 2.000000000000 +13 2.963825617909E-01 2.000000000000 +14 4.595852782863E-01 0.000000000000 +15 5.155221864135E-01 0.000000000000 +16 5.396195959588E-01 0.000000000000 +17 6.561911480828E-01 0.000000000000 +18 9.211434048875E-01 0.000000000000 +19 9.694042853411E-01 0.000000000000 +20 1.037646589355E+00 0.000000000000 + +kred #87 = (0.416667,0.416667,0.666667) +n eigval occ +1 -3.561383798368E+00 2.000000000000 +2 -2.220252386223E+00 2.000000000000 +3 -2.106804277931E+00 2.000000000000 +4 -2.106701869733E+00 2.000000000000 +5 -3.071642053269E-01 2.000000000000 +6 -2.009538666362E-01 2.000000000000 +7 -1.965876462249E-01 2.000000000000 +8 -6.900552522166E-02 2.000000000000 +9 -5.977787796028E-02 2.000000000000 +10 2.701864986924E-02 2.000000000000 +11 2.138606405332E-01 2.000000000000 +12 2.528289407335E-01 2.000000000000 +13 3.037990334457E-01 2.000000000000 +14 4.580755289762E-01 0.000000000001 +15 5.254193595236E-01 0.000000000000 +16 5.570093700152E-01 0.000000000000 +17 6.825514076404E-01 0.000000000000 +18 8.977280352070E-01 0.000000000000 +19 9.512067354270E-01 0.000000000000 +20 1.025005152507E+00 0.000000000000 + +kred #88 = (0.402778,0.402778,0.694444) +n eigval occ +1 -3.561388396393E+00 2.000000000000 +2 -2.220228026540E+00 2.000000000000 +3 -2.106792035414E+00 2.000000000000 +4 -2.106658475869E+00 2.000000000000 +5 -3.066299909798E-01 2.000000000000 +6 -2.023585050783E-01 2.000000000000 +7 -1.966589224635E-01 2.000000000000 +8 -7.177819675551E-02 2.000000000000 +9 -5.985117545681E-02 2.000000000000 +10 2.017156869885E-02 2.000000000000 +11 2.087580086754E-01 2.000000000000 +12 2.547504017599E-01 2.000000000000 +13 3.124110393485E-01 2.000000000000 +14 4.580756161108E-01 0.000000000001 +15 5.368094510267E-01 0.000000000000 +16 5.764113379159E-01 0.000000000000 +17 7.109239686892E-01 0.000000000000 +18 8.742371220124E-01 0.000000000000 +19 9.311265371333E-01 0.000000000000 +20 1.011361634505E+00 0.000000000000 + +kred #89 = (0.388889,0.388889,0.722222) +n eigval occ +1 -3.561393413700E+00 2.000000000000 +2 -2.220201419966E+00 2.000000000000 +3 -2.106777823573E+00 2.000000000000 +4 -2.106611909033E+00 2.000000000000 +5 -3.060733695410E-01 2.000000000000 +6 -2.038910188476E-01 2.000000000000 +7 -1.968102699845E-01 2.000000000000 +8 -7.465850884944E-02 2.000000000000 +9 -5.993463684758E-02 2.000000000000 +10 1.285381146285E-02 2.000000000000 +11 2.045640436389E-01 2.000000000000 +12 2.565164187418E-01 2.000000000000 +13 3.222030857649E-01 2.000000000000 +14 4.595628496466E-01 0.000000000000 +15 5.494796989359E-01 0.000000000000 +16 5.975249554894E-01 0.000000000000 +17 7.407493363853E-01 0.000000000000 +18 8.509529681776E-01 0.000000000000 +19 9.099722665970E-01 0.000000000000 +20 9.968380268200E-01 0.000000000000 + +kred #90 = (0.375000,0.375000,0.750000) +n eigval occ +1 -3.561398742514E+00 2.000000000000 +2 -2.220173129701E+00 2.000000000000 +3 -2.106761629629E+00 2.000000000000 +4 -2.106563471573E+00 2.000000000000 +5 -3.055142429170E-01 2.000000000000 +6 -2.055104106320E-01 2.000000000000 +7 -1.970626607163E-01 2.000000000000 +8 -7.758533284111E-02 2.000000000000 +9 -6.003401193068E-02 2.000000000000 +10 5.285489194548E-03 2.000000000000 +11 2.014296653111E-01 2.000000000000 +12 2.582301288679E-01 2.000000000000 +13 3.330681066841E-01 2.000000000000 +14 4.624662967587E-01 0.000000000000 +15 5.631458610181E-01 0.000000000000 +16 6.200164917577E-01 0.000000000000 +17 7.710148274740E-01 0.000000000000 +18 8.286201600668E-01 0.000000000000 +19 8.884252361081E-01 0.000000000000 +20 9.817330993677E-01 0.000000000000 diff --git a/tests/CdS_bandstruct/standard/CdS_bandstruct.refout b/tests/CdS_bandstruct/standard/CdS_bandstruct.refout new file mode 100644 index 00000000..c5b72473 --- /dev/null +++ b/tests/CdS_bandstruct/standard/CdS_bandstruct.refout @@ -0,0 +1,150 @@ +*************************************************************************** +* SPARC (version Sep 20, 2023) * +* Copyright (c) 2020 Material Physics & Mechanics Group, Georgia Tech * +* Distributed under GNU General Public License 3 (GPL) * +* Start time: Wed Sep 20 19:57:43 2023 * +*************************************************************************** + Input parameters +*************************************************************************** +LATVEC_SCALE: 1 1 1 +LATVEC: +5.88590692979539 0 0 +0 5.88590692979539 0 +0 0 5.88590692979539 +FD_GRID: 20 20 20 +FD_ORDER: 12 +BC: P P P +KPOINT_GRID: 7 7 7 +KPOINT_SHIFT: 0 0 0 +SPIN_TYP: 0 +ELEC_TEMP_TYPE: Fermi-Dirac +SMEARING: 0.001000000336 +EXCHANGE_CORRELATION: GGA_PBE +NSTATES: 20 +CHEB_DEGREE: 26 +CHEFSI_BOUND_FLAG: 0 +CALC_STRESS: 0 +CALC_PRES: 0 +MAXIT_SCF: 1 +MINIT_SCF: 1 +MAXIT_POISSON: 3000 +TOL_SCF: 1.00E-06 +POISSON_SOLVER: AAR +TOL_POISSON: 1.00E-08 +TOL_LANCZOS: 1.00E-02 +TOL_PSEUDOCHARGE: 1.00E-09 +MIXING_VARIABLE: density +MIXING_PRECOND: none +MIXING_PARAMETER: 0.3 +MIXING_HISTORY: 7 +PULAY_FREQUENCY: 1 +PULAY_RESTART: 0 +REFERENCE_CUTOFF: 0.5 +RHO_TRIGGER: 10 +NUM_CHEFSI: 1 +FIX_RAND: 0 +VERBOSITY: 1 +PRINT_FORCES: 1 +PRINT_ATOMS: 1 +PRINT_EIGEN: 1 +PRINT_DENSITY: 0 +PRINT_ENERGY_DENSITY: 0 +BAND_STRUCTURE: 1 +INPUT_DENS_FILE: CdS.indens +KPT_PER_LINE: 10 +KPT_PATHS: 9 +0.000000 0.000000 0.000000 +0.000000 0.500000 0.500000 +0.000000 0.500000 0.500000 +0.250000 0.500000 0.750000 +0.250000 0.500000 0.750000 +0.375000 0.375000 0.750000 +0.375000 0.375000 0.750000 +0.000000 0.000000 0.000000 +0.000000 0.000000 0.000000 +0.500000 0.500000 0.500000 +0.500000 0.500000 0.500000 +0.250000 0.625000 0.625000 +0.250000 0.625000 0.625000 +0.250000 0.500000 0.750000 +0.250000 0.500000 0.750000 +0.500000 0.500000 0.500000 +0.500000 0.500000 0.500000 +0.375000 0.375000 0.750000 +OUTPUT_FILE: CdS +*************************************************************************** + Cell +*************************************************************************** +Lattice vectors (Bohr): +5.885906929795390 0.000000000000000 0.000000000000000 +0.000000000000000 5.885906929795390 0.000000000000000 +0.000000000000000 0.000000000000000 5.885906929795390 +Volume: 2.0391077336E+02 (Bohr^3) +Density: 7.0855255767E-01 (amu/Bohr^3), 7.9399500196E+00 (g/cc) +*************************************************************************** + Parallelization +*************************************************************************** +NP_SPIN_PARAL: 1 +NP_KPOINT_PARAL: 2 +NP_BAND_PARAL: 4 +NP_DOMAIN_PARAL: 1 1 1 +NP_DOMAIN_PHI_PARAL: 2 2 2 +EIG_SERIAL_MAXNS: 1500 +*************************************************************************** + Initialization +*************************************************************************** +Number of processors : 8 +Mesh spacing : 0.294295 (Bohr) +Number of symmetry adapted k-points: 90 +Output printed to : CdS.out +Final eigenvalues printed to : CdS.eigen +Total number of atom types : 2 +Total number of atoms : 2 +Total number of electrons : 26 +Atom type 1 (valence electrons) : Cd 20 +Pseudopotential : ../../../psps/48_Cd_20_2.2_2.3_pbe_n_v1.0.psp8 +Atomic mass : 112.414 +Pseudocharge radii of atom type 1 : 7.95 7.95 7.95 (x, y, z dir) +Number of atoms of type 1 : 1 +Atom type 2 (valence electrons) : S 6 +Pseudopotential : ../../../psps/16_S_6_1.8_1.9_pbe_n_v1.0.psp8 +Atomic mass : 32.0675 +Pseudocharge radii of atom type 2 : 7.95 7.95 7.95 (x, y, z dir) +Number of atoms of type 2 : 1 +Estimated total memory usage : 273.13 MB +Estimated memory per processor : 34.14 MB +=================================================================== + Self Consistent Field (SCF#1) +=================================================================== +Iteration Free Energy (Ha/atom) SCF Error Timing (sec) +1 -8.8867518454E+01 1.038E-02 55.420 +Total number of SCF: 1 +WARNING: SCF#1 did not converge to desired accuracy! +==================================================================== + Energy and force calculation +==================================================================== +Free energy per atom : -8.8867518454E+01 (Ha/atom) +Total free energy : -1.7773503691E+02 (Ha) +Band structure energy : -2.0019558158E+01 (Ha) +Exchange correlation energy : -2.5269251882E+01 (Ha) +Self and correction energy : -2.2142441770E+02 (Ha) +-Entropy*kb*T : -4.8879887433E-05 (Ha) +Fermi level : 4.2911791764E-01 (Ha) +RMS force : 2.1295386361E+00 (Ha/Bohr) +Maximum force : 2.1295386361E+00 (Ha/Bohr) +Time for force calculation : 0.225 (sec) +*************************************************************************** + Timing info +*************************************************************************** +Total walltime : 55.722 sec +___________________________________________________________________________ + +*************************************************************************** +* Material Physics & Mechanics Group, Georgia Tech * +* PI: Phanish Suryanarayana * +* List of contributors: See the documentation * +* Citation: See README.md or the documentation for details * +* Acknowledgements: U.S. DOE SC (DE-SC0019410), U.S. DOE NNSA (ASC) * +* {Preliminary developments: U.S. NSF (1333500,1663244,1553212)} * +*************************************************************************** + diff --git a/tests/CdS_bandstruct/standard/CdS_bandstruct.refstatic b/tests/CdS_bandstruct/standard/CdS_bandstruct.refstatic new file mode 100644 index 00000000..712d0dc4 --- /dev/null +++ b/tests/CdS_bandstruct/standard/CdS_bandstruct.refstatic @@ -0,0 +1,11 @@ +*************************************************************************** + Atom positions +*************************************************************************** +Fractional coordinates of Cd: + 0.0000000000 0.0000000000 0.0000000000 +Fractional coordinates of S: + 0.7500000000 0.2500000000 0.7500000000 +Total free energy (Ha): -1.777350369073562E+02 +Atomic forces (Ha/Bohr): + 1.2136001462E+00 -1.2447536994E+00 1.2299177679E+00 + -1.2136001462E+00 1.2447536994E+00 -1.2299177679E+00 diff --git a/tests/SPARC_testing_script.py b/tests/SPARC_testing_script.py index 1408c664..f7ff2069 100644 --- a/tests/SPARC_testing_script.py +++ b/tests/SPARC_testing_script.py @@ -381,6 +381,10 @@ SYSTEMS["Tags"].append(['bulk', 'gga','noncollinear','spin']) SYSTEMS["Tols"].append([tols["E_tol"], tols["F_tol"], tols["stress_tol"]]) # E_tol(Ha/atom), F_tol(Ha/Bohr), stress_tol(%) ################################################################################################################## +SYSTEMS["systemname"].append('CdS_bandstruct') +SYSTEMS["Tags"].append(['bulk', 'gga', 'denmix', 'kerker', 'orth', 'smear_fd', 'bandstruct']) +SYSTEMS["Tols"].append([1e-5, 1e-4, 0.5]) # E_tol(Ha/atom), F_tol(Ha/Bohr), stress_tol(%) +################################################################################################################## # < Uncomment 3 lines below and fill in the details for the new systems> # SYSTEMS["systemname"].append('??type the system name??') # SYSTEMS["Tols"].append([??type the E_tol, F_tol and stress_tol separated by comma??]) # E_tol(Ha/atom), F_tol(Ha/Bohr), stress_tol(%) diff --git a/utils/bandstruct/README.md b/utils/bandstruct/README.md new file mode 100644 index 00000000..34ff2e55 --- /dev/null +++ b/utils/bandstruct/README.md @@ -0,0 +1,28 @@ +# `band_structure_plot` – Band Structure Visualization Tool + +## Overview + +`band_structure_plot.py` is a Python script that provides a set of tools for processing `.eigen` files generated by [**SPARC**](https://github.com/SPARC-X/SPARC/) and visualizing the band structure of a given system. + +## Requirements + +To use `band_structure_plot.py`, you need the following: + +- Python 3.6 or later +- Numpy +- Matplotlib + +## Usage + +### Plotting Band Structure + +You can use the `plot_band_structure` function to create visualizations of the band structure from your provided `.eigen` file. + +### Reading Eigen Files + +The `read_eigen_file` function is a separate utility that enables you to read and extract data from a `.eigen` file. + +## Example + +Explore an example of how to use `plot_band_structure` to visualize the band structure of a CdS system in the `example/` directory. + diff --git a/utils/bandstruct/band_structure_plot.py b/utils/bandstruct/band_structure_plot.py new file mode 100644 index 00000000..79b380df --- /dev/null +++ b/utils/bandstruct/band_structure_plot.py @@ -0,0 +1,378 @@ +import re +import numpy as np +import matplotlib.pyplot as plt + +Ha2eV = 27.211386245988 # 1 Ha = 27.211386245988 eV + +def read_eigen_file(fname, unit="Ha"): + """Read eigenvlaues and occupations from the given .eigen file + generated by SPARC. + + Parameters + ---------- + fname : string + File name (can be a path, relative or absolute) of the + eigenvalue file generated by SPARC. + unit : string, optional + Unit of the returned eigenvalues. + + Returns + ------- + eigdata : dict + Eigenvalue information dictionary. + + * eigdata['spin_polarization'] is + - True if the test system is spin-polarized, + - False if the test system is spin-unpolarized. + * eigdata['eigunit'] is the unit of the eigenvalues stored. + * eigdata['nkpt'] is the number of k-points. + * eigdata['data'] is a list of information dictionaries with keys: + "kred" : k-point coordinates (reduced). + "weight" : weight of the k-point. + "eigvals" : eigenvalues of the k-point, + size=(1,nkpt) w/o spin, or (2,nkpt) w/ spin. + "occs" : occupations of the bands corresponding to the k-point, + size=(1,nkpt) w/o spin, or (2,nkpt) w/ spin. + """ + + with open(fname, 'r') as f: + content = f.read() + f.seek(0) + lines = f.readlines() + + match = re.search(r"Spin-down", content) + if match: + spin_polarization = True + else: + spin_polarization = False + + eigdata = { + "eig_unit": unit, + "spin_polarization": spin_polarization, + "nkpt" : 0, + "data" : []} + + if (eigdata["eig_unit"].lower() == "ha"): + unit_trans = 1.0 + elif (unit.lower() == "ev"): + unit_trans = Ha2eV + + for line in lines: + if line.startswith("kred"): + kred_value = list(map(float, line.split("=")[1].strip().strip("()").split(","))) + eigdata["data"].append({ + "kred": kred_value, + "weight": 1.0, + "eigvals": ([[],[]] if spin_polarization else [[]]), + "occs": ([[],[]] if spin_polarization else [[]]) + }) + eigdata["nkpt"] += 1 + elif line.startswith("weight"): + eigdata["data"][-1]["weight"] = float(line.split("=")[1].strip()) + elif line.strip(): + try: + parts = line.split() + #n = int(parts[0]) + eigdata["data"][-1]["eigvals"][0].append(float(parts[1])*unit_trans) + eigdata["data"][-1]["occs"][0].append(float(parts[2])) + if spin_polarization: + eigdata["data"][-1]["eigvals"][1].append(float(parts[3])*unit_trans) + eigdata["data"][-1]["occs"][1].append(float(parts[4])) + except: + pass # Skip lines that don't match the expected format + #print(json.dumps(eigdata,separators=(',',':'),skipkeys = True,indent = 6)) + return eigdata + + +def process_band_data(eigdata): + """Process band data created by read_eigen_file(). Calculate k-point + distances in the band structure plot. + + Parameters + ---------- + eigdata : dict + Eigenvalue information dictionary. + + * eigdata['spin_polarization'] is + - True if the test system is spin-polarized, + - False if the test system is spin-unpolarized. + * eigdata['eigunit'] is the unit of the eigenvalues stored. + * eigdata['nkpt'] is the number of k-points. + * eigdata['data'] is a list of information dictionaries with keys: + "kred" : k-point coordinates (reduced). + "weight" : weight of the k-point. + "eigvals" : eigenvalues of the k-point, + size=(1,nkpt) w/o spin, or (2,nkpt) w/ spin. + "occs" : occupations of the bands corresponding to the k-point, + size=(1,nkpt) w/o spin, or (2,nkpt) w/ spin. + + Returns + ------- + kpt_dist : list + Distances of the k-points on the k-point path. + eigvals : numpy array + Eigenvalues of all the k-points. When spin is present, eigvals[0] + contains the eigenvalues for spin-up values and eigvals[1] for spin- + down. + kpt_coords : k-point coordinates. + """ + + spin_polarization = eigdata["spin_polarization"] + data = eigdata["data"] + + kpt_coords = [] + kpt_dist = [] + eigvals = [[],[]] if spin_polarization else [[]] + ref = data[0]["kred"] + pos = 0.0 + for i in data: + kpt_coords.append(i["kred"]) + dis = ((ref[0]-i["kred"][0])**2 + (ref[1]-i["kred"][1])**2 + (ref[2]-i["kred"][2])**2)**0.5 + ref = i["kred"] + pos += dis + kpt_dist.append(pos) + for spin in range(len(eigvals)): + eigvals[spin].append(i["eigvals"][spin]) + + for spin in range(len(eigvals)): + eigvals[spin] = np.array(eigvals[spin]).T + + return kpt_dist, np.array(eigvals), kpt_coords + + +def change_extension(input_filename, new_extension): + """Change the extension of input_filename to a given + extension. + """ + # Split the input filename by '.' + parts = input_filename.split('.') + + # Check if there's an extension to replace + if len(parts) > 1: + # Replace the last part (extension) with new_extension + parts[-1] = new_extension + # Join the parts back together to create the new filename + output_filename = '.'.join(parts) + else: + # If there was no extension, just append new_extension to the filename + output_filename = input_filename + '.' + new_extension + + return output_filename + + +class InvalidInputError(Exception): + pass + + +def create_band_structure_plot( + kpt_dist, eigvals, nkpt_per_line, outfname, highsym_points='', unit='eV', + Efermi_Ha = None, Efermi_eV = None, ylim = None, dpi = 300., plotstyles={}): + """Plot band structure using the data processed by `process_band_data()`. + + Parameters + ---------- + kpt_dist : list + Distances of the k-points on the k-point path. + eigvals : numpy array + Eigenvalues of all the k-points. + nkpt_per_line : int + Number of k-points on each line segment (between two high symmetry + points). + highsym_points : string + Symbols of the high-symmetry points, used for xticks. + Example: 'G-X-W-K', 'G-X-W|G-K' + unit : string + unit of the energy in the final plot. + Efermi_Ha : float + Fermi level in Hartree. Cannot be specified together with Efermi_eV. + Efermi_eV : float + Fermi level in eV. Cannot be specified together with Efermi_Ha. + outfname : string + Output band structure plot file name. Default is set to fname with + extension changed to "png". + ylim : tuple -> (float, float) + Y limits of the final plot. + dpi : float + Dots Per Inch (dpi) of the resulting plot. + plotstyles : dict + Plot style controls, currently supports: + "linewidth" : (float) line width of the bands. + "vlinewidth" : (float) line width of the vertical lines. + "spin_style" : (list of strings) line styles that discreminates the spin-up + and spin-down bands. + "xlabel" : (string) x label. + "ylabel" : (string) y label. + """ + + # define plot styles + linewidth = 1.0 if 'linewidth' not in plotstyles else plotstyles['linewidth'] + vlinewidth = 0.75 if 'vlinewidth' not in plotstyles else plotstyles['vlinewidth'] + if 'spin_style' in plotstyles: + if isinstance(plotstyles['spin_style'], str): + spin_style = [plotstyles['spin_style'], plotstyles['spin_style']] + elif isinstance(plotstyles['spin_style'], list): + if len(plotstyles['spin_style'])==1: + spin_style = [plotstyles['spin_style'][0], plotstyles['spin_style'][0]] + else: + spin_style = [plotstyles['spin_style'][0], plotstyles['spin_style'][1]] + else: + spin_style = ['k-', 'r--'] + + xlabel = 'Wave vector' if 'xlabel' not in plotstyles else plotstyles['xlabel'] + ylabel = 'Energy' + if 'ylabel' in plotstyles: + ylabel = plotstyles['ylabel'] + else: + if unit.lower() == 'ha': + ylabel = "Energy (Ha)" + elif unit.lower() == 'ev': + ylabel = "Energy (eV)" + + # check if Efermi is provided properly + if (Efermi_eV != None and Efermi_Ha != None): + raise InvalidInputError("`Efermi_eV` and `Efermi_Ha` cannot be set simultaneously") + elif (Efermi_eV != None): + Efermi = Efermi_eV + if unit.lower() == 'ha': + Efermi /= Ha2eV + elif (Efermi_Ha != None): + Efermi = Efermi_Ha + if unit.lower() == 'ev': + Efermi *= Ha2eV + else: + Efermi = None + + _, ax = plt.subplots() + + if (Efermi != None): + ax.axhline(y = Efermi, color = 'g', linestyle = '--') + + spin_polarization = len(eigvals) > 1 + + if len(highsym_points) == 0: + for spin in range(len(eigvals)): + for y in range(len(eigvals[spin])): + label = None + if spin_polarization and y == 0: + label = 'spin-up' if (spin == 0) else 'spin-down' + ax.plot(kpt_dist, eigvals[spin, y, :], spin_style[spin], linewidth=linewidth, label = label) + else: + highsym_points = highsym_points.split() + #Connect different lines + len_flag = 0 + for e in highsym_points[:len(highsym_points)-1]: + edge_len = len(e.split('-'))-1 + len_flag += edge_len*nkpt_per_line + diff = kpt_dist[len_flag]-kpt_dist[len_flag-1] + for i in range(len_flag,len(kpt_dist)): + kpt_dist[i] = kpt_dist[i] - diff + + for spin in range(len(eigvals)): + for y in range(len(eigvals[spin])): + label = None + if spin_polarization and y == 0: + label = 'spin-up' if (spin == 0) else 'spin-down' + + ax.plot(kpt_dist, eigvals[spin, y, :], spin_style[spin], linewidth=linewidth, label = label) + + # Make high symmteric vertical lines + tick_x = [] + for i in range(0,len(kpt_dist)-1,nkpt_per_line): + tick_x.append(kpt_dist[i]) + plt.axvline(kpt_dist[i], linewidth=vlinewidth, linestyle ="--", color='k', alpha=0.5) + + tick_x.append(kpt_dist[-1]) + plt.axvline(kpt_dist[-1], linewidth=vlinewidth, linestyle ="--", color='k', alpha=0.5) + + # Make x tick + tick_kpt = '|'.join(highsym_points) + tick_kpt = tick_kpt.split('-') + tick_kpt = [item.replace('G', r"$\Gamma$") for item in tick_kpt] + # tick_kpt = [item.replace('|', r"$|$") for item in tick_kpt] + plt.xticks(ticks=tick_x, labels=tick_kpt) + + plt.xlim(min(kpt_dist), max(kpt_dist)) + + if ylim != None: + plt.ylim(ylim) + + plt.xlabel(xlabel=xlabel) + plt.ylabel(ylabel=ylabel) + + # Customize the tick parameters + ax.tick_params(axis='both', direction='in', which='both') + + if spin_polarization: + plt.legend(loc="upper right") + + plt.savefig(outfname, format="png", dpi=dpi) + + +def plot_band_structure( + fname, nkpt_per_line, highsym_points='', unit='eV', + Efermi_Ha = None, Efermi_eV = None, outfname=None, + ylim = None, dpi = 300., plotstyles={}): + """Plot band structure using the data from the given file. + + Parameters + ---------- + fname : string + File name of the .eigen file generated by SPARC. + nkpt_per_line : int + Number of k-points on each line segment (between two high symmetry + points). + highsym_points : string, optional + Symbols of the high-symmetry points, used for xticks. + Example: 'G-X-W-K', 'G-X-W|G-K' + unit : string, optional + unit of the energy in the final plot. + Efermi_Ha : float, optional + Fermi level in Hartree. Cannot be specified together with Efermi_eV. + Efermi_eV : float, optional + Fermi level in eV. Cannot be specified together with Efermi_Ha. + outfname : string, optional + Output band structure plot file name. Default is set to fname with + extension changed to "png". + ylim : tuple -> (float, float), optional + Y limits of the final plot. + dpi : float, optional + Dots Per Inch (dpi) of the resulting plot. + plotstyles : dict + Plot style controls, currently supports: + "linewidth" : (float) line width of the bands. + "vlinewidth" : (float) line width of the vertical lines. + "spin_style" : (list of strings) line styles that discreminates the spin-up + and spin-down bands. + "xlabel" : (string) x label. + "ylabel" : (string) y label. + """ + # read data from .eigen file + data = read_eigen_file(fname, unit=unit) + + # process the data, find k-point distances + kpt_dist, eigvals, _ = process_band_data(data) + + if outfname == None: + outfname = change_extension(fname, new_extension="png") + + # create band structure plot and save to file + create_band_structure_plot(kpt_dist, eigvals, nkpt_per_line, + outfname, highsym_points, unit, + Efermi_Ha, Efermi_eV, ylim, dpi, + plotstyles) + + + +if __name__ == '__main__': + + fname = 'example/CdS.eigen_01' + highsym_points = 'G-X-W-K-G-L-U-W-L-K' + + Efermi = 0.42712 # in Ha + nkpt_per_line = 10 + + # plot_band_structure(fname, nkpt_per_line, highsym_points, Efermi_Ha=Efermi) + # plot_band_structure(fname, nkpt_per_line, highsym_points, plotstyles = {"xlabel": None}) + plot_band_structure(fname, nkpt_per_line, highsym_points, + unit='eV', Efermi_Ha=Efermi, ylim=(-10,30), dpi=200) + diff --git a/utils/bandstruct/example/CdS.eigen_01 b/utils/bandstruct/example/CdS.eigen_01 new file mode 100644 index 00000000..36538d76 --- /dev/null +++ b/utils/bandstruct/example/CdS.eigen_01 @@ -0,0 +1,2071 @@ +Final eigenvalues (Ha) and occupation numbers + +kred #1 = (0.000000,0.000000,0.000000) +n eigval occ +1 -3.561393125981E+00 2.000000000000 +2 -2.219689852351E+00 2.000000000000 +3 -2.106183474506E+00 2.000000000000 +4 -2.106183461063E+00 2.000000000000 +5 -3.026660023647E-01 2.000000000000 +6 -2.191315729812E-01 2.000000000000 +7 -2.191315608511E-01 2.000000000000 +8 -1.432035399416E-01 2.000000000000 +9 -5.990204450168E-02 2.000000000000 +10 -5.990204049633E-02 2.000000000000 +11 3.807378101614E-01 2.000000000000 +12 4.066701407766E-01 1.999999999627 +13 4.066701480198E-01 1.999999999627 +14 4.773645767966E-01 0.000000000000 +15 5.342432284692E-01 0.000000000000 +16 5.342432344175E-01 0.000000000000 +17 8.889877243600E-01 0.000000000000 +18 8.889877296037E-01 0.000000000000 +19 9.481915144597E-01 0.000000000000 +20 9.481927230166E-01 0.000000000000 + +kred #2 = (0.000000,0.055556,0.055556) +n eigval occ +1 -3.561390904993E+00 2.000000000000 +2 -2.219701783408E+00 2.000000000000 +3 -2.106205860568E+00 2.000000000000 +4 -2.106188688910E+00 2.000000000000 +5 -3.025935595247E-01 2.000000000000 +6 -2.189158366241E-01 2.000000000000 +7 -2.183111770600E-01 2.000000000000 +8 -1.408640656358E-01 2.000000000000 +9 -6.012714495738E-02 2.000000000000 +10 -5.952982592200E-02 2.000000000000 +11 3.537845122383E-01 2.000000000000 +12 3.997995005956E-01 2.000000000000 +13 4.203522690931E-01 1.999673671639 +14 4.702376292703E-01 0.000000000000 +15 5.432466765341E-01 0.000000000000 +16 5.601198591826E-01 0.000000000000 +17 8.661346686377E-01 0.000000000000 +18 8.703089412865E-01 0.000000000000 +19 9.521720996282E-01 0.000000000000 +20 9.587069084342E-01 0.000000000000 + +kred #3 = (0.000000,0.111111,0.111111) +n eigval occ +1 -3.561384511215E+00 2.000000000000 +2 -2.219736149452E+00 2.000000000000 +3 -2.106270218385E+00 2.000000000000 +4 -2.106203695599E+00 2.000000000000 +5 -3.024379608070E-01 2.000000000000 +6 -2.183245252996E-01 2.000000000000 +7 -2.159226653551E-01 2.000000000000 +8 -1.340345240848E-01 2.000000000000 +9 -6.075414642774E-02 2.000000000000 +10 -5.817917430096E-02 2.000000000000 +11 3.150346372467E-01 2.000000000000 +12 3.741754476707E-01 2.000000000000 +13 4.232174879651E-01 1.994287426919 +14 4.836340643125E-01 0.000000000000 +15 5.667272407745E-01 0.000000000000 +16 6.040887184932E-01 0.000000000000 +17 8.224537510128E-01 0.000000000000 +18 8.364299746799E-01 0.000000000000 +19 9.504806138360E-01 0.000000000000 +20 9.731151772027E-01 0.000000000000 + +kred #4 = (0.000000,0.166667,0.166667) +n eigval occ +1 -3.561374719128E+00 2.000000000000 +2 -2.219788835615E+00 2.000000000000 +3 -2.106368421012E+00 2.000000000000 +4 -2.106226664750E+00 2.000000000000 +5 -3.023396073263E-01 2.000000000000 +6 -2.175019302110E-01 2.000000000000 +7 -2.121933013316E-01 2.000000000000 +8 -1.234519003223E-01 2.000000000000 +9 -6.159403640189E-02 2.000000000000 +10 -5.512742610759E-02 2.000000000000 +11 2.769970782243E-01 2.000000000000 +12 3.398511776323E-01 2.000000000000 +13 4.242201102380E-01 1.984507201546 +14 5.063245887289E-01 0.000000000000 +15 5.902560427761E-01 0.000000000000 +16 6.473006960116E-01 0.000000000000 +17 7.861817158407E-01 0.000000000000 +18 8.017856916191E-01 0.000000000000 +19 9.438453736995E-01 0.000000000000 +20 9.720232690673E-01 0.000000000000 + +kred #5 = (0.000000,0.222222,0.222222) +n eigval occ +1 -3.561362713555E+00 2.000000000000 +2 -2.219853521417E+00 2.000000000000 +3 -2.106488225300E+00 2.000000000000 +4 -2.106254803600E+00 2.000000000000 +5 -3.024225337756E-01 2.000000000000 +6 -2.166264698743E-01 2.000000000000 +7 -2.075160597312E-01 2.000000000000 +8 -1.108670855931E-01 2.000000000000 +9 -6.219815371075E-02 2.000000000000 +10 -4.911111166213E-02 2.000000000000 +11 2.420811212963E-01 2.000000000000 +12 3.071113149199E-01 2.000000000000 +13 4.261875441923E-01 1.894231656027 +14 5.234599631753E-01 0.000000000000 +15 5.947932005802E-01 0.000000000000 +16 6.886258293209E-01 0.000000000000 +17 7.714171807258E-01 0.000000000000 +18 7.767583549260E-01 0.000000000000 +19 9.335834803128E-01 0.000000000000 +20 9.595901134101E-01 0.000000000000 + +kred #6 = (0.000000,0.277778,0.277778) +n eigval occ +1 -3.561349944995E+00 2.000000000000 +2 -2.219922427046E+00 2.000000000000 +3 -2.106614921981E+00 2.000000000000 +4 -2.106284703711E+00 2.000000000000 +5 -3.027228422462E-01 2.000000000000 +6 -2.158543591999E-01 2.000000000000 +7 -2.024332170830E-01 2.000000000000 +8 -9.933043933277E-02 2.000000000000 +9 -6.173086715570E-02 2.000000000000 +10 -3.863414616112E-02 2.000000000000 +11 2.118571143955E-01 2.000000000000 +12 2.790027317128E-01 2.000000000000 +13 4.281077182323E-01 1.448301038981 +14 5.093298706214E-01 0.000000000000 +15 6.047040331065E-01 0.000000000000 +16 7.250407969956E-01 0.000000000000 +17 7.525015753759E-01 0.000000000000 +18 7.843849937225E-01 0.000000000000 +19 9.201579596386E-01 0.000000000000 +20 9.483271137743E-01 0.000000000000 + +kred #7 = (0.000000,0.333333,0.333333) +n eigval occ +1 -3.561337953525E+00 2.000000000000 +2 -2.219987241343E+00 2.000000000000 +3 -2.106733230738E+00 2.000000000000 +4 -2.106312758815E+00 2.000000000000 +5 -3.031769229388E-01 2.000000000000 +6 -2.152798310183E-01 2.000000000000 +7 -1.975784099018E-01 2.000000000000 +8 -9.176251353912E-02 2.000000000000 +9 -5.923627423337E-02 2.000000000000 +10 -2.379305305857E-02 2.000000000000 +11 1.882397396256E-01 2.000000000000 +12 2.562024364584E-01 2.000000000000 +13 4.268274371989E-01 1.808510263910 +14 4.707418422669E-01 0.000000000000 +15 6.356805047330E-01 0.000000000000 +16 7.256370017484E-01 0.000000000000 +17 7.697993142103E-01 0.000000000000 +18 7.889393468300E-01 0.000000000000 +19 9.061966777400E-01 0.000000000000 +20 9.537032874673E-01 0.000000000000 + +kred #8 = (0.000000,0.388889,0.388889) +n eigval occ +1 -3.561328183046E+00 2.000000000000 +2 -2.220040124373E+00 2.000000000000 +3 -2.106829142066E+00 2.000000000000 +4 -2.106335599660E+00 2.000000000000 +5 -3.036557203143E-01 2.000000000000 +6 -2.149219753185E-01 2.000000000000 +7 -1.935814581930E-01 2.000000000000 +8 -8.835079032981E-02 2.000000000000 +9 -5.488811726905E-02 2.000000000000 +10 -8.262781030918E-03 2.000000000000 +11 1.736681258343E-01 2.000000000000 +12 2.384244256042E-01 2.000000000000 +13 4.081973462563E-01 1.999999998282 +14 4.474507741168E-01 0.000000020874 +15 6.725712317878E-01 0.000000000000 +16 7.181105486495E-01 0.000000000000 +17 7.856596238532E-01 0.000000000000 +18 7.913309530962E-01 0.000000000000 +19 8.934847347762E-01 0.000000000000 +20 9.547410412589E-01 0.000000000000 + +kred #9 = (0.000000,0.444444,0.444444) +n eigval occ +1 -3.561321808268E+00 2.000000000000 +2 -2.220074663538E+00 2.000000000000 +3 -2.106891484932E+00 2.000000000000 +4 -2.106350493520E+00 2.000000000000 +5 -3.040162016687E-01 2.000000000000 +6 -2.147431689450E-01 2.000000000000 +7 -1.909618968670E-01 2.000000000000 +8 -8.725988945146E-02 2.000000000000 +9 -5.060061050082E-02 2.000000000000 +10 2.709940971778E-03 2.000000000000 +11 1.690523805368E-01 2.000000000000 +12 2.255476786611E-01 2.000000000000 +13 3.802288883884E-01 2.000000000000 +14 4.442325557127E-01 0.000000521508 +15 7.048969495988E-01 0.000000000000 +16 7.150631740169E-01 0.000000000000 +17 7.819240449817E-01 0.000000000000 +18 8.022165694771E-01 0.000000000000 +19 8.837180242995E-01 0.000000000000 +20 9.255420581851E-01 0.000000000000 + +kred #10 = (0.000000,0.500000,0.500000) +n eigval occ +1 -3.561319594784E+00 2.000000000000 +2 -2.220086662965E+00 2.000000000000 +3 -2.106913088594E+00 2.000000000000 +4 -2.106355663438E+00 2.000000000000 +5 -3.041497822989E-01 2.000000000000 +6 -2.146913602661E-01 2.000000000000 +7 -1.900513167789E-01 2.000000000000 +8 -8.704640970530E-02 2.000000000000 +9 -4.878744756822E-02 2.000000000000 +10 6.420829083711E-03 2.000000000000 +11 1.693652406247E-01 2.000000000000 +12 2.201688374653E-01 2.000000000000 +13 3.687855631949E-01 2.000000000000 +14 4.439990877702E-01 0.000000658650 +15 7.144191218887E-01 0.000000000000 +16 7.189063663901E-01 0.000000000000 +17 7.801512045788E-01 0.000000000000 +18 8.063255980535E-01 0.000000000000 +19 8.794376529597E-01 0.000000000000 +20 9.103082638774E-01 0.000000000000 + +kred #11 = (0.000000,0.500000,0.500000) +n eigval occ +1 -3.561319594784E+00 2.000000000000 +2 -2.220086662965E+00 2.000000000000 +3 -2.106913088594E+00 2.000000000000 +4 -2.106355663438E+00 2.000000000000 +5 -3.041497822989E-01 2.000000000000 +6 -2.146913602661E-01 2.000000000000 +7 -1.900513167789E-01 2.000000000000 +8 -8.704640970530E-02 2.000000000000 +9 -4.878744756822E-02 2.000000000000 +10 6.420829083711E-03 2.000000000000 +11 1.693652406247E-01 2.000000000000 +12 2.201688374653E-01 2.000000000000 +13 3.687855631949E-01 2.000000000000 +14 4.439990877702E-01 0.000000658650 +15 7.144191218887E-01 0.000000000000 +16 7.189063663901E-01 0.000000000000 +17 7.801512045788E-01 0.000000000000 +18 8.063255980535E-01 0.000000000000 +19 8.794376530941E-01 0.000000000000 +20 9.103082635618E-01 0.000000000000 + +kred #12 = (0.027778,0.500000,0.527778) +n eigval occ +1 -3.561319596421E+00 2.000000000000 +2 -2.220086581825E+00 2.000000000000 +3 -2.106909912317E+00 2.000000000000 +4 -2.106358857915E+00 2.000000000000 +5 -3.041595935415E-01 2.000000000000 +6 -2.145547447764E-01 2.000000000000 +7 -1.902463021274E-01 2.000000000000 +8 -8.697508923983E-02 2.000000000000 +9 -4.901406086008E-02 2.000000000000 +10 6.154954740236E-03 2.000000000000 +11 1.700712600256E-01 2.000000000000 +12 2.206513048291E-01 2.000000000000 +13 3.704913525829E-01 2.000000000000 +14 4.428410371182E-01 0.000002096956 +15 7.095362487798E-01 0.000000000000 +16 7.169016087773E-01 0.000000000000 +17 7.774024284709E-01 0.000000000000 +18 8.098161833720E-01 0.000000000000 +19 8.737317704137E-01 0.000000000000 +20 9.176244354812E-01 0.000000000000 + +kred #13 = (0.055556,0.500000,0.555556) +n eigval occ +1 -3.561319601133E+00 2.000000000000 +2 -2.220086348192E+00 2.000000000000 +3 -2.106900553713E+00 2.000000000000 +4 -2.106368268928E+00 2.000000000000 +5 -3.041880678562E-01 2.000000000000 +6 -2.141485405521E-01 2.000000000000 +7 -1.908200969040E-01 2.000000000000 +8 -8.676268537005E-02 2.000000000000 +9 -4.967543412829E-02 2.000000000000 +10 5.414092897899E-03 2.000000000000 +11 1.718668526477E-01 2.000000000000 +12 2.224150524258E-01 2.000000000000 +13 3.753612882201E-01 2.000000000000 +14 4.394870544432E-01 0.000060005682 +15 6.959122287866E-01 0.000000000000 +16 7.118629767443E-01 0.000000000000 +17 7.707217262709E-01 0.000000000000 +18 8.181354484438E-01 0.000000000000 +19 8.641926258483E-01 0.000000000000 +20 9.325096424025E-01 0.000000000000 + +kred #14 = (0.083333,0.500000,0.583333) +n eigval occ +1 -3.561319608354E+00 2.000000000000 +2 -2.220085990245E+00 2.000000000000 +3 -2.106885535918E+00 2.000000000000 +4 -2.106383367016E+00 2.000000000000 +5 -3.042323381538E-01 2.000000000000 +6 -2.134844417915E-01 2.000000000000 +7 -1.917395919201E-01 2.000000000000 +8 -8.641554386792E-02 2.000000000000 +9 -5.071527242144E-02 2.000000000000 +10 4.345593816353E-03 2.000000000000 +11 1.739252294184E-01 2.000000000000 +12 2.262454758080E-01 2.000000000000 +13 3.825130881815E-01 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2.000000000000 +8 -7.769050888892E-02 2.000000000000 +9 -6.014825005972E-02 2.000000000000 +10 5.238862652117E-03 2.000000000000 +11 2.013933017796E-01 2.000000000000 +12 2.582209240038E-01 2.000000000000 +13 3.330745427087E-01 2.000000000000 +14 4.624424119461E-01 0.000000000000 +15 5.631201602195E-01 0.000000000000 +16 6.200167603588E-01 0.000000000000 +17 7.710141139932E-01 0.000000000000 +18 8.286329601601E-01 0.000000000000 +19 8.884010089529E-01 0.000000000000 +20 9.817902507869E-01 0.000000000000 + +kred #31 = (0.375000,0.375000,0.750000) +n eigval occ +1 -3.561312070036E+00 2.000000000000 +2 -2.220124402587E+00 2.000000000000 +3 -2.106779475814E+00 2.000000000000 +4 -2.106581414939E+00 2.000000000000 +5 -3.055063624259E-01 2.000000000000 +6 -2.055750236059E-01 2.000000000000 +7 -1.971172227792E-01 2.000000000000 +8 -7.769050888891E-02 2.000000000000 +9 -6.014825005972E-02 2.000000000000 +10 5.238862652117E-03 2.000000000000 +11 2.013933017796E-01 2.000000000000 +12 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2.000000000000 +6 -2.191315729812E-01 2.000000000000 +7 -2.191315608511E-01 2.000000000000 +8 -1.432035399416E-01 2.000000000000 +9 -5.990204450168E-02 2.000000000000 +10 -5.990204049633E-02 2.000000000000 +11 3.807378101614E-01 2.000000000000 +12 4.066701407766E-01 1.999999999627 +13 4.066701480198E-01 1.999999999627 +14 4.773645767966E-01 0.000000000000 +15 5.342432284692E-01 0.000000000000 +16 5.342432344175E-01 0.000000000000 +17 8.889877245492E-01 0.000000000000 +18 8.889877294652E-01 0.000000000000 +19 9.481915144469E-01 0.000000000000 +20 9.481919919617E-01 0.000000000000 + +kred #42 = (0.055556,0.055556,0.055556) +n eigval occ +1 -3.561389794105E+00 2.000000000000 +2 -2.219707808976E+00 2.000000000000 +3 -2.106204398125E+00 2.000000000000 +4 -2.106203885544E+00 2.000000000000 +5 -3.025085777948E-01 2.000000000000 +6 -2.184286490983E-01 2.000000000000 +7 -2.182427169730E-01 2.000000000000 +8 -1.397882254665E-01 2.000000000000 +9 -5.996753059772E-02 2.000000000000 +10 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0.000000000000 +15 5.937083245225E-01 0.000000000000 +16 6.134008286308E-01 0.000000000000 +17 8.107669980167E-01 0.000000000000 +18 8.177308186987E-01 0.000000000000 +19 9.382435188886E-01 0.000000000000 +20 9.679644484189E-01 0.000000000000 + +kred #44 = (0.166667,0.166667,0.166667) +n eigval occ +1 -3.561365528058E+00 2.000000000000 +2 -2.219838290298E+00 2.000000000000 +3 -2.106355726891E+00 2.000000000000 +4 -2.106352447461E+00 2.000000000000 +5 -3.022383114185E-01 2.000000000000 +6 -2.132831081993E-01 2.000000000000 +7 -2.120302807935E-01 2.000000000000 +8 -1.149737158794E-01 2.000000000000 +9 -6.045074524734E-02 2.000000000000 +10 -5.446848315003E-02 2.000000000000 +11 2.754594227628E-01 2.000000000000 +12 3.291865537303E-01 2.000000000000 +13 3.638774868330E-01 2.000000000000 +14 5.321446874045E-01 0.000000000000 +15 6.347427254399E-01 0.000000000000 +16 6.574419596530E-01 0.000000000000 +17 7.572676155063E-01 0.000000000000 +18 7.898348580274E-01 0.000000000000 +19 8.845876481766E-01 0.000000000000 +20 9.979764110565E-01 0.000000000000 + +kred #45 = (0.222222,0.222222,0.222222) +n eigval occ +1 -3.561347546854E+00 2.000000000000 +2 -2.219934640138E+00 2.000000000000 +3 -2.106466601850E+00 2.000000000000 +4 -2.106462390962E+00 2.000000000000 +5 -3.028544934221E-01 2.000000000000 +6 -2.094760418971E-01 2.000000000000 +7 -2.078372279025E-01 2.000000000000 +8 -9.896278890780E-02 2.000000000000 +9 -6.074909651932E-02 2.000000000000 +10 -4.331522426065E-02 2.000000000000 +11 2.479152846246E-01 2.000000000000 +12 3.014691172757E-01 2.000000000000 +13 3.405735670527E-01 2.000000000000 +14 5.273247141686E-01 0.000000000000 +15 6.375032690241E-01 0.000000000000 +16 6.792128918937E-01 0.000000000000 +17 7.492061777142E-01 0.000000000000 +18 7.712781877975E-01 0.000000000000 +19 8.820580752830E-01 0.000000000000 +20 9.594839038900E-01 0.000000000000 + +kred #46 = (0.277778,0.277778,0.277778) +n eigval occ +1 -3.561328439376E+00 2.000000000000 +2 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2.000000000000 +7 -2.006839116209E-01 2.000000000000 +8 -7.635998936652E-02 2.000000000000 +9 -6.076022243519E-02 2.000000000000 +10 4.739100686894E-03 2.000000000000 +11 2.186816425977E-01 2.000000000000 +12 2.626525268984E-01 2.000000000000 +13 3.100053135173E-01 2.000000000000 +14 4.783647644007E-01 0.000000000000 +15 5.546091030497E-01 0.000000000000 +16 5.872668143660E-01 0.000000000000 +17 7.609095082887E-01 0.000000000000 +18 8.521004920172E-01 0.000000000000 +19 8.758452794840E-01 0.000000000000 +20 9.883856797048E-01 0.000000000000 + +kred #48 = (0.388889,0.388889,0.388889) +n eigval occ +1 -3.561295912759E+00 2.000000000000 +2 -2.220209713732E+00 2.000000000000 +3 -2.106779171232E+00 2.000000000000 +4 -2.106777418278E+00 2.000000000000 +5 -3.073286718968E-01 2.000000000000 +6 -1.990791769233E-01 2.000000000000 +7 -1.984605364060E-01 2.000000000000 +8 -6.809328762013E-02 2.000000000000 +9 -6.033748536781E-02 2.000000000000 +10 2.886219580051E-02 2.000000000000 +11 2.208835046801E-01 2.000000000000 +12 2.515156426797E-01 2.000000000000 +13 2.976184963322E-01 2.000000000000 +14 4.653234570645E-01 0.000000000000 +15 5.210560797280E-01 0.000000000000 +16 5.409999216889E-01 0.000000000000 +17 6.761083411562E-01 0.000000000000 +18 9.133079492000E-01 0.000000000000 +19 9.397477583963E-01 0.000000000000 +20 1.033876333339E+00 0.000000000000 + +kred #49 = (0.444444,0.444444,0.444444) +n eigval occ +1 -3.561286393936E+00 2.000000000000 +2 -2.220260164020E+00 2.000000000000 +3 -2.106835872573E+00 2.000000000000 +4 -2.106835381655E+00 2.000000000000 +5 -3.084928430437E-01 2.000000000000 +6 -1.973468545362E-01 2.000000000000 +7 -1.971813684435E-01 2.000000000000 +8 -6.197403216463E-02 2.000000000000 +9 -5.986077609469E-02 2.000000000000 +10 4.377995634399E-02 2.000000000000 +11 2.333270060196E-01 2.000000000000 +12 2.451943164065E-01 2.000000000000 +13 2.845604417287E-01 2.000000000000 +14 4.681480309734E-01 0.000000000000 +15 4.998217852497E-01 0.000000000000 +16 5.084513192292E-01 0.000000000000 +17 6.092370557424E-01 0.000000000000 +18 9.732862096512E-01 0.000000000000 +19 9.912096687529E-01 0.000000000000 +20 1.067931785666E+00 0.000000000000 + +kred #50 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561283089740E+00 2.000000000000 +2 -2.220277657479E+00 2.000000000000 +3 -2.106855498122E+00 2.000000000000 +4 -2.106855484650E+00 2.000000000000 +5 -3.089176619771E-01 2.000000000000 +6 -1.967661940924E-01 2.000000000000 +7 -1.967661895453E-01 2.000000000000 +8 -5.965106303093E-02 2.000000000000 +9 -5.965105950296E-02 2.000000000000 +10 4.845659024410E-02 2.000000000000 +11 2.431579815404E-01 2.000000000000 +12 2.431580033011E-01 2.000000000000 +13 2.761243004536E-01 2.000000000000 +14 4.782236274737E-01 0.000000000000 +15 4.925598918892E-01 0.000000000000 +16 4.925599113006E-01 0.000000000000 +17 5.809337943160E-01 0.000000000000 +18 1.011913786547E+00 0.000000000000 +19 1.011928191369E+00 0.000000000000 +20 1.074893161452E+00 0.000000000000 + +kred #51 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561283089740E+00 2.000000000000 +2 -2.220277657479E+00 2.000000000000 +3 -2.106855498122E+00 2.000000000000 +4 -2.106855484650E+00 2.000000000000 +5 -3.089176619771E-01 2.000000000000 +6 -1.967661940924E-01 2.000000000000 +7 -1.967661895453E-01 2.000000000000 +8 -5.965106303093E-02 2.000000000000 +9 -5.965105950296E-02 2.000000000000 +10 4.845659024410E-02 2.000000000000 +11 2.431579815404E-01 2.000000000000 +12 2.431580033011E-01 2.000000000000 +13 2.761243004536E-01 2.000000000000 +14 4.782236274737E-01 0.000000000000 +15 4.925598918892E-01 0.000000000000 +16 4.925599113006E-01 0.000000000000 +17 5.809337943160E-01 0.000000000000 +18 1.011913778681E+00 0.000000000000 +19 1.011941451377E+00 0.000000000000 +20 1.074893160544E+00 0.000000000000 + +kred #52 = (0.472222,0.513889,0.513889) +n eigval occ +1 -3.561283506068E+00 2.000000000000 +2 -2.220275461325E+00 2.000000000000 +3 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2.464251168267E-01 2.000000000000 +13 2.847999911984E-01 2.000000000000 +14 4.666701403763E-01 0.000000000000 +15 5.007811807927E-01 0.000000000000 +16 5.119637450497E-01 0.000000000000 +17 6.118520429931E-01 0.000000000000 +18 9.666388303724E-01 0.000000000000 +19 9.970015770696E-01 0.000000000000 +20 1.059487329649E+00 0.000000000000 + +kred #55 = (0.388889,0.555556,0.555556) +n eigval occ +1 -3.561289564616E+00 2.000000000000 +2 -2.220243486138E+00 2.000000000000 +3 -2.106840738456E+00 2.000000000000 +4 -2.106792232562E+00 2.000000000000 +5 -3.080822718445E-01 2.000000000000 +6 -1.987115045513E-01 2.000000000000 +7 -1.966459424416E-01 2.000000000000 +8 -6.423627784121E-02 2.000000000000 +9 -5.977220066650E-02 2.000000000000 +10 3.844656995710E-02 2.000000000000 +11 2.258067679735E-01 2.000000000000 +12 2.485097951437E-01 2.000000000000 +13 2.901182541362E-01 2.000000000000 +14 4.625176016678E-01 0.000000000000 +15 5.072452928030E-01 0.000000000000 +16 5.245111469488E-01 0.000000000000 +17 6.323948283746E-01 0.000000000000 +18 9.442787185536E-01 0.000000000000 +19 9.849105795425E-01 0.000000000000 +20 1.049260979942E+00 0.000000000000 + +kred #56 = (0.361111,0.569444,0.569444) +n eigval occ +1 -3.561293035833E+00 2.000000000000 +2 -2.220225151897E+00 2.000000000000 +3 -2.106832371845E+00 2.000000000000 +4 -2.106758727826E+00 2.000000000000 +5 -3.076504816934E-01 2.000000000000 +6 -1.997646690854E-01 2.000000000000 +7 -1.966235649547E-01 2.000000000000 +8 -6.653767350083E-02 2.000000000000 +9 -5.983051488050E-02 2.000000000000 +10 3.314019226188E-02 2.000000000000 +11 2.196236754900E-01 2.000000000000 +12 2.507026371201E-01 2.000000000000 +13 2.964171675671E-01 2.000000000000 +14 4.595665576899E-01 0.000000000000 +15 5.154881768776E-01 0.000000000000 +16 5.396084035452E-01 0.000000000000 +17 6.561915525541E-01 0.000000000000 +18 9.211877114457E-01 0.000000000000 +19 9.694218951638E-01 0.000000000000 +20 1.037694423579E+00 0.000000000000 + +kred #57 = (0.333333,0.583333,0.583333) +n eigval occ +1 -3.561297116837E+00 2.000000000000 +2 -2.220203582684E+00 2.000000000000 +3 -2.106822084466E+00 2.000000000000 +4 -2.106719744643E+00 2.000000000000 +5 -3.071579591941E-01 2.000000000000 +6 -2.010091379521E-01 2.000000000000 +7 -1.966378801900E-01 2.000000000000 +8 -6.912019726140E-02 2.000000000000 +9 -5.989568803929E-02 2.000000000000 +10 2.697173963325E-02 2.000000000000 +11 2.138288286001E-01 2.000000000000 +12 2.528071590224E-01 2.000000000000 +13 3.038266784568E-01 2.000000000000 +14 4.580551134198E-01 0.000000000001 +15 5.253870773946E-01 0.000000000000 +16 5.570010985307E-01 0.000000000000 +17 6.825511465096E-01 0.000000000000 +18 8.977646990567E-01 0.000000000000 +19 9.512062725464E-01 0.000000000000 +20 1.025058584943E+00 0.000000000000 + +kred #58 = (0.305556,0.597222,0.597222) +n eigval occ +1 -3.561301717649E+00 2.000000000000 +2 -2.220179246502E+00 2.000000000000 +3 -2.106809850340E+00 2.000000000000 +4 -2.106676375680E+00 2.000000000000 +5 -3.066232578659E-01 2.000000000000 +6 -2.024166207925E-01 2.000000000000 +7 -1.967103888511E-01 2.000000000000 +8 -7.189033915488E-02 2.000000000000 +9 -5.996796819768E-02 2.000000000000 +10 2.012549477332E-02 2.000000000000 +11 2.087245488674E-01 2.000000000000 +12 2.547331656321E-01 2.000000000000 +13 3.124314167215E-01 2.000000000000 +14 4.580538160100E-01 0.000000000001 +15 5.367790526495E-01 0.000000000000 +16 5.764058246700E-01 0.000000000000 +17 7.109231930407E-01 0.000000000000 +18 8.742663185130E-01 0.000000000000 +19 9.311137658230E-01 0.000000000000 +20 1.011422005283E+00 0.000000000000 + +kred #59 = (0.277778,0.611111,0.611111) +n eigval occ +1 -3.561306737996E+00 2.000000000000 +2 -2.220152665572E+00 2.000000000000 +3 -2.106795648085E+00 2.000000000000 +4 -2.106629835562E+00 2.000000000000 +5 -3.060660891765E-01 2.000000000000 +6 -2.039522775920E-01 2.000000000000 +7 -1.968631787030E-01 2.000000000000 +8 -7.476750305338E-02 2.000000000000 +9 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2.000000000000 +14 4.624424175889E-01 0.000000000000 +15 5.631201602145E-01 0.000000000000 +16 6.200167507242E-01 0.000000000000 +17 7.710141161201E-01 0.000000000000 +18 8.286329550527E-01 0.000000000000 +19 8.884010204710E-01 0.000000000000 +20 9.817902472373E-01 0.000000000000 + +kred #61 = (0.250000,0.625000,0.625000) +n eigval occ +1 -3.561312070037E+00 2.000000000000 +2 -2.220124402551E+00 2.000000000000 +3 -2.106779464879E+00 2.000000000000 +4 -2.106581425894E+00 2.000000000000 +5 -3.055063614028E-01 2.000000000000 +6 -2.055750303818E-01 2.000000000000 +7 -1.971172183323E-01 2.000000000000 +8 -7.769051475316E-02 2.000000000000 +9 -6.014824894585E-02 2.000000000000 +10 5.238863501144E-03 2.000000000000 +11 2.013933162166E-01 2.000000000000 +12 2.582209231830E-01 2.000000000000 +13 3.330745366064E-01 2.000000000000 +14 4.624424175889E-01 0.000000000000 +15 5.631201602145E-01 0.000000000000 +16 6.200167507242E-01 0.000000000000 +17 7.710141161201E-01 0.000000000000 +18 8.286329550527E-01 0.000000000000 +19 8.884010204710E-01 0.000000000000 +20 9.817902472170E-01 0.000000000000 + +kred #62 = (0.250000,0.611111,0.638889) +n eigval occ +1 -3.561312169491E+00 2.000000000000 +2 -2.220123768752E+00 2.000000000000 +3 -2.106779401789E+00 2.000000000000 +4 -2.106580414825E+00 2.000000000000 +5 -3.054889697572E-01 2.000000000000 +6 -2.056005260863E-01 2.000000000000 +7 -1.973263265610E-01 2.000000000000 +8 -7.833967920051E-02 2.000000000000 +9 -5.943061378355E-02 2.000000000000 +10 5.525298002641E-03 2.000000000000 +11 2.020838815392E-01 2.000000000000 +12 2.560189468685E-01 2.000000000000 +13 3.353286481151E-01 2.000000000000 +14 4.618598306274E-01 0.000000000000 +15 5.638579789742E-01 0.000000000000 +16 6.188972861890E-01 0.000000000000 +17 7.707396124784E-01 0.000000000000 +18 8.284699047757E-01 0.000000000000 +19 8.837198692825E-01 0.000000000000 +20 9.862795321671E-01 0.000000000000 + +kred #63 = (0.250000,0.597222,0.652778) +n eigval occ +1 -3.561312464764E+00 2.000000000000 +2 -2.220122120611E+00 2.000000000000 +3 -2.106779570043E+00 2.000000000000 +4 -2.106576775659E+00 2.000000000000 +5 -3.054415785198E-01 2.000000000000 +6 -2.056679785329E-01 2.000000000000 +7 -1.975523657313E-01 2.000000000000 +8 -7.899592542438E-02 2.000000000000 +9 -5.881158821972E-02 2.000000000000 +10 5.609548468252E-03 2.000000000000 +11 2.008238896243E-01 2.000000000000 +12 2.560029493778E-01 2.000000000000 +13 3.378533048146E-01 2.000000000000 +14 4.618446977177E-01 0.000000000000 +15 5.632392443601E-01 0.000000000000 +16 6.199575463023E-01 0.000000000000 +17 7.713673951695E-01 0.000000000000 +18 8.278923623450E-01 0.000000000000 +19 8.784400768654E-01 0.000000000000 +20 9.902968212661E-01 0.000000000000 + +kred #64 = (0.250000,0.583333,0.666667) +n eigval occ +1 -3.561312953636E+00 2.000000000000 +2 -2.220119469252E+00 2.000000000000 +3 -2.106779850691E+00 2.000000000000 +4 -2.106570653666E+00 2.000000000000 +5 -3.053662665263E-01 2.000000000000 +6 -2.057808735712E-01 2.000000000000 +7 -1.977881248392E-01 2.000000000000 +8 -7.965831390509E-02 2.000000000000 +9 -5.829771672077E-02 2.000000000000 +10 5.491669610278E-03 2.000000000000 +11 1.979027757504E-01 2.000000000000 +12 2.578632567409E-01 2.000000000000 +13 3.406401677911E-01 2.000000000000 +14 4.623654584619E-01 0.000000000000 +15 5.616201095592E-01 0.000000000000 +16 6.228906157608E-01 0.000000000000 +17 7.728664173152E-01 0.000000000000 +18 8.268442270995E-01 0.000000000000 +19 8.729093938531E-01 0.000000000000 +20 9.932805649366E-01 0.000000000000 + +kred #65 = (0.250000,0.569444,0.680556) +n eigval occ +1 -3.561313632436E+00 2.000000000000 +2 -2.220115832681E+00 2.000000000000 +3 -2.106780061748E+00 2.000000000000 +4 -2.106562275062E+00 2.000000000000 +5 -3.052656034138E-01 2.000000000000 +6 -2.059432739559E-01 2.000000000000 +7 -1.980259414625E-01 2.000000000000 +8 -8.032641531605E-02 2.000000000000 +9 -5.789153763559E-02 2.000000000000 +10 5.160723094355E-03 2.000000000000 +11 1.939321153888E-01 2.000000000000 +12 2.609809406575E-01 2.000000000000 +13 3.436580208799E-01 2.000000000000 +14 4.633792876446E-01 0.000000000000 +15 5.595927933647E-01 0.000000000000 +16 6.271644419756E-01 0.000000000000 +17 7.751959252061E-01 0.000000000000 +18 8.252470399560E-01 0.000000000000 +19 8.674378433243E-01 0.000000000000 +20 9.947801624821E-01 0.000000000000 + +kred #66 = (0.250000,0.555556,0.694444) +n eigval occ +1 -3.561314496060E+00 2.000000000000 +2 -2.220111235717E+00 2.000000000000 +3 -2.106779991365E+00 2.000000000000 +4 -2.106551913508E+00 2.000000000000 +5 -3.051425788655E-01 2.000000000000 +6 -2.061592508668E-01 2.000000000000 +7 -1.982583421600E-01 2.000000000000 +8 -8.100024936480E-02 2.000000000000 +9 -5.759187067589E-02 2.000000000000 +10 4.596805589541E-03 2.000000000000 +11 1.895128264554E-01 2.000000000000 +12 2.647615688988E-01 2.000000000000 +13 3.468561535439E-01 2.000000000000 +14 4.648272533205E-01 0.000000000000 +15 5.577438530603E-01 0.000000000000 +16 6.322664066909E-01 0.000000000000 +17 7.782880563611E-01 0.000000000000 +18 8.230122241318E-01 0.000000000000 +19 8.623165486683E-01 0.000000000000 +20 9.945292669861E-01 0.000000000000 + +kred #67 = (0.250000,0.541667,0.708333) +n eigval occ +1 -3.561315538013E+00 2.000000000000 +2 -2.220105709889E+00 2.000000000000 +3 -2.106779427135E+00 2.000000000000 +4 -2.106539860349E+00 2.000000000000 +5 -3.050005208862E-01 2.000000000000 +6 -2.064321471254E-01 2.000000000000 +7 -1.984788326494E-01 2.000000000000 +8 -8.168031436343E-02 2.000000000000 +9 -5.739435469828E-02 2.000000000000 +10 3.774473421433E-03 2.000000000000 +11 1.850983388389E-01 2.000000000000 +12 2.687704528261E-01 2.000000000000 +13 3.501723238735E-01 2.000000000000 +14 4.666298272800E-01 0.000000000000 +15 5.565552580020E-01 0.000000000000 +16 6.378023159698E-01 0.000000000000 +17 7.820151385246E-01 0.000000000000 +18 8.200828185744E-01 0.000000000000 +19 8.578177354912E-01 0.000000000000 +20 9.924959872068E-01 0.000000000000 + +kred #68 = (0.250000,0.527778,0.722222) +n eigval occ +1 -3.561316750454E+00 2.000000000000 +2 -2.220099293302E+00 2.000000000000 +3 -2.106778176010E+00 2.000000000000 +4 -2.106526404105E+00 2.000000000000 +5 -3.048430053927E-01 2.000000000000 +6 -2.067638065611E-01 2.000000000000 +7 -1.986827019549E-01 2.000000000000 +8 -8.236768594269E-02 2.000000000000 +9 -5.729216701486E-02 2.000000000000 +10 2.667304451343E-03 2.000000000000 +11 1.810022562935E-01 2.000000000000 +12 2.727203959675E-01 2.000000000000 +13 3.535447933497E-01 2.000000000000 +14 4.686870920180E-01 0.000000000000 +15 5.563988008866E-01 0.000000000000 +16 6.434952315604E-01 0.000000000000 +17 7.861196756061E-01 0.000000000000 +18 8.165267432736E-01 0.000000000000 +19 8.541750739327E-01 0.000000000000 +20 9.888635545470E-01 0.000000000000 + +kred #69 = (0.250000,0.513889,0.736111) +n eigval occ +1 -3.561318124254E+00 2.000000000000 +2 -2.220092030470E+00 2.000000000000 +3 -2.106776074768E+00 2.000000000000 +4 -2.106511819294E+00 2.000000000000 +5 -3.046737598299E-01 2.000000000000 +6 -2.071539602886E-01 2.000000000000 +7 -1.988676488411E-01 2.000000000000 +8 -8.306416708699E-02 2.000000000000 +9 -5.727682237968E-02 2.000000000000 +10 1.253115175413E-03 2.000000000000 +11 1.774374428333E-01 2.000000000000 +12 2.764257428279E-01 2.000000000000 +13 3.569260041620E-01 2.000000000000 +14 4.708881374217E-01 0.000000000000 +15 5.575451057209E-01 0.000000000000 +16 6.491592930387E-01 0.000000000000 +17 7.900339738157E-01 0.000000000000 +18 8.127247536923E-01 0.000000000000 +19 8.515760333168E-01 0.000000000000 +20 9.839539998594E-01 0.000000000000 + +kred #70 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561319649061E+00 2.000000000000 +2 -2.220083972104E+00 2.000000000000 +3 -2.106772993608E+00 2.000000000000 +4 -2.106496362007E+00 2.000000000000 +5 -3.044965638141E-01 2.000000000000 +6 -2.075999363041E-01 2.000000000000 +7 -1.990340635450E-01 2.000000000000 +8 -8.377247079957E-02 2.000000000000 +9 -5.733894580383E-02 2.000000000000 +10 -4.808820492233E-04 2.000000000000 +11 1.745462978811E-01 2.000000000000 +12 2.797648664902E-01 2.000000000000 +13 3.602940352983E-01 2.000000000000 +14 4.731305298458E-01 0.000000000000 +15 5.601591481103E-01 0.000000000000 +16 6.546770247087E-01 0.000000000000 +17 7.924242599693E-01 0.000000000000 +18 8.097783107463E-01 0.000000000000 +19 8.502081061872E-01 0.000000000000 +20 9.781502020074E-01 0.000000000000 + +kred #71 = (0.250000,0.500000,0.750000) +n eigval occ +1 -3.561319649061E+00 2.000000000000 +2 -2.220083972104E+00 2.000000000000 +3 -2.106772993608E+00 2.000000000000 +4 -2.106496362007E+00 2.000000000000 +5 -3.044965638141E-01 2.000000000000 +6 -2.075999363041E-01 2.000000000000 +7 -1.990340635450E-01 2.000000000000 +8 -8.377247079957E-02 2.000000000000 +9 -5.733894580383E-02 2.000000000000 +10 -4.808820492236E-04 2.000000000000 +11 1.745462978811E-01 2.000000000000 +12 2.797648664902E-01 2.000000000000 +13 3.602940352983E-01 2.000000000000 +14 4.731305298458E-01 0.000000000000 +15 5.601591481103E-01 0.000000000000 +16 6.546770247087E-01 0.000000000000 +17 7.924242599693E-01 0.000000000000 +18 8.097783107463E-01 0.000000000000 +19 8.502081061872E-01 0.000000000000 +20 9.781502015188E-01 0.000000000000 + +kred #72 = (0.277778,0.500000,0.722222) +n eigval occ +1 -3.561313296100E+00 2.000000000000 +2 -2.220117561199E+00 2.000000000000 +3 -2.106787341723E+00 2.000000000000 +4 -2.106559192695E+00 2.000000000000 +5 -3.052224446676E-01 2.000000000000 +6 -2.057194474571E-01 2.000000000000 +7 -1.984474107077E-01 2.000000000000 +8 -8.074613666874E-02 2.000000000000 +9 -5.714260821631E-02 2.000000000000 +10 7.396153877388E-03 2.000000000000 +11 1.848312544953E-01 2.000000000000 +12 2.680591515402E-01 2.000000000000 +13 3.469778414624E-01 2.000000000000 +14 4.652611561927E-01 0.000000000000 +15 5.472734260254E-01 0.000000000000 +16 6.310796328992E-01 0.000000000000 +17 7.706420544973E-01 0.000000000000 +18 8.296678231801E-01 0.000000000000 +19 8.615314339228E-01 0.000000000000 +20 1.002901814206E+00 0.000000000000 + +kred #73 = (0.305556,0.500000,0.694444) +n eigval occ +1 -3.561307137977E+00 2.000000000000 +2 -2.220150147395E+00 2.000000000000 +3 -2.106801244641E+00 2.000000000000 +4 -2.106619926263E+00 2.000000000000 +5 -3.059443107843E-01 2.000000000000 +6 -2.038955670445E-01 2.000000000000 +7 -1.979576019028E-01 2.000000000000 +8 -7.743693305673E-02 2.000000000000 +9 -5.726736065455E-02 2.000000000000 +10 1.558725640076E-02 2.000000000000 +11 1.953100307040E-01 2.000000000000 +12 2.581442158550E-01 2.000000000000 +13 3.341225366779E-01 2.000000000000 +14 4.596600561027E-01 0.000000000000 +15 5.357055867505E-01 0.000000000000 +16 6.057083564544E-01 0.000000000000 +17 7.387688758454E-01 0.000000000000 +18 8.562644859707E-01 0.000000000000 +19 8.806775455880E-01 0.000000000000 +20 1.026848042169E+00 0.000000000000 + +kred #74 = (0.333333,0.500000,0.666667) +n eigval occ +1 -3.561301361558E+00 2.000000000000 +2 -2.220180738155E+00 2.000000000000 +3 -2.106814281202E+00 2.000000000000 +4 -2.106676743060E+00 2.000000000000 +5 -3.066368437590E-01 2.000000000000 +6 -2.021840871762E-01 2.000000000000 +7 -1.975675611227E-01 2.000000000000 +8 -7.394682179205E-02 2.000000000000 +9 -5.760716060486E-02 2.000000000000 +10 2.362653611273E-02 2.000000000000 +11 2.056214744934E-01 2.000000000000 +12 2.503057251261E-01 2.000000000000 +13 3.219764788506E-01 2.000000000000 +14 4.564820149065E-01 0.000000000002 +15 5.255393812478E-01 0.000000000000 +16 5.806069928943E-01 0.000000000000 +17 7.063020770633E-01 0.000000000000 +18 8.842846823395E-01 0.000000000000 +19 9.022381889935E-01 0.000000000000 +20 1.048395820147E+00 0.000000000000 + +kred #75 = (0.361111,0.500000,0.638889) +n eigval occ +1 -3.561296141979E+00 2.000000000000 +2 -2.220208400297E+00 2.000000000000 +3 -2.106826057231E+00 2.000000000000 +4 -2.106727956000E+00 2.000000000000 +5 -3.072748140894E-01 2.000000000000 +6 -2.006371351961E-01 2.000000000000 +7 -1.972721108273E-01 2.000000000000 +8 -7.042262594733E-02 2.000000000000 +9 -5.806221735829E-02 2.000000000000 +10 3.102970343635E-02 2.000000000000 +11 2.153607881745E-01 2.000000000000 +12 2.447853613300E-01 2.000000000000 +13 3.107235369116E-01 2.000000000000 +14 4.558415001552E-01 0.000000000005 +15 5.167904090584E-01 0.000000000000 +16 5.570611158637E-01 0.000000000000 +17 6.751524684136E-01 0.000000000000 +18 9.125471860742E-01 0.000000000000 +19 9.246601377598E-01 0.000000000000 +20 1.066103895036E+00 0.000000000000 + +kred #76 = (0.388889,0.500000,0.611111) +n eigval occ +1 -3.561291637374E+00 2.000000000000 +2 -2.220232288800E+00 2.000000000000 +3 -2.106836217283E+00 2.000000000000 +4 -2.106772057079E+00 2.000000000000 +5 -3.078343140877E-01 2.000000000000 +6 -1.993016937967E-01 2.000000000000 +7 -1.970601407080E-01 2.000000000000 +8 -6.705484777711E-02 2.000000000000 +9 -5.854694201683E-02 2.000000000000 +10 3.736325609711E-02 2.000000000000 +11 2.241184720101E-01 2.000000000000 +12 2.416833515002E-01 2.000000000000 +13 3.004969484746E-01 2.000000000000 +14 4.577646929874E-01 0.000000000001 +15 5.094120359627E-01 0.000000000000 +16 5.360540747472E-01 0.000000000000 +17 6.463447924443E-01 0.000000000000 +18 9.401101354535E-01 0.000000000000 +19 9.471530205644E-01 0.000000000000 +20 1.079431660093E+00 0.000000000000 + +kred #77 = (0.416667,0.500000,0.583333) +n eigval occ +1 -3.561287984120E+00 2.000000000000 +2 -2.220251673019E+00 2.000000000000 +3 -2.106844455153E+00 2.000000000000 +4 -2.106807757402E+00 2.000000000000 +5 -3.082939310541E-01 2.000000000000 +6 -1.982183033307E-01 2.000000000000 +7 -1.969172386340E-01 2.000000000000 +8 -6.406868045449E-02 2.000000000000 +9 -5.899243894756E-02 2.000000000000 +10 4.232428121282E-02 2.000000000000 +11 2.315514239891E-01 2.000000000000 +12 2.408053068452E-01 2.000000000000 +13 2.914302763730E-01 2.000000000000 +14 4.620759260657E-01 0.000000000000 +15 5.032841778100E-01 0.000000000000 +16 5.184490027992E-01 0.000000000000 +17 6.208819008248E-01 0.000000000000 +18 9.658896874573E-01 0.000000000000 +19 9.690073022940E-01 0.000000000000 +20 1.087575231021E+00 0.000000000000 + +kred #78 = (0.444444,0.500000,0.555556) +n eigval occ +1 -3.561285292759E+00 2.000000000000 +2 -2.220265959466E+00 2.000000000000 +3 -2.106850522884E+00 2.000000000000 +4 -2.106834020201E+00 2.000000000000 +5 -3.086358009159E-01 2.000000000000 +6 -1.974199138310E-01 2.000000000000 +7 -1.968284732665E-01 2.000000000000 +8 -6.170341446726E-02 2.000000000000 +9 -5.934658336272E-02 2.000000000000 +10 4.579153205704E-02 2.000000000000 +11 2.374479868114E-01 2.000000000000 +12 2.414928272068E-01 2.000000000000 +13 2.837913423800E-01 2.000000000000 +14 4.681911628161E-01 0.000000000000 +15 4.982217310410E-01 0.000000000000 +16 5.049961631558E-01 0.000000000000 +17 6.001169025721E-01 0.000000000000 +18 9.883513533410E-01 0.000000000000 +19 9.891906099185E-01 0.000000000000 +20 1.086826531177E+00 0.000000000000 + +kred #79 = (0.472222,0.500000,0.527778) +n eigval occ +1 -3.561283644689E+00 2.000000000000 +2 -2.220274710382E+00 2.000000000000 +3 -2.106854238028E+00 2.000000000000 +4 -2.106850086567E+00 2.000000000000 +5 -3.088464902260E-01 2.000000000000 +6 -1.969308868615E-01 2.000000000000 +7 -1.967810012734E-01 2.000000000000 +8 -6.017850351518E-02 2.000000000000 +9 -5.957319564011E-02 2.000000000000 +10 4.780261299606E-02 2.000000000000 +11 2.415673527018E-01 2.000000000000 +12 2.426354728598E-01 2.000000000000 +13 2.782591121428E-01 2.000000000000 +14 4.747210773329E-01 0.000000000000 +15 4.942630164929E-01 0.000000000000 +16 4.961434607055E-01 0.000000000000 +17 5.860242126697E-01 0.000000000000 +18 1.005031838048E+00 0.000000000000 +19 1.005348855027E+00 0.000000000000 +20 1.078868825545E+00 0.000000000000 + +kred #80 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561283089740E+00 2.000000000000 +2 -2.220277657479E+00 2.000000000000 +3 -2.106855498122E+00 2.000000000000 +4 -2.106855484650E+00 2.000000000000 +5 -3.089176619771E-01 2.000000000000 +6 -1.967661940924E-01 2.000000000000 +7 -1.967661895453E-01 2.000000000000 +8 -5.965106303093E-02 2.000000000000 +9 -5.965105950296E-02 2.000000000000 +10 4.845659024410E-02 2.000000000000 +11 2.431579815404E-01 2.000000000000 +12 2.431580033011E-01 2.000000000000 +13 2.761243004536E-01 2.000000000000 +14 4.782236274737E-01 0.000000000000 +15 4.925598918892E-01 0.000000000000 +16 4.925599113006E-01 0.000000000000 +17 5.809337943160E-01 0.000000000000 +18 1.011913776962E+00 0.000000000000 +19 1.011944931749E+00 0.000000000000 +20 1.074893163086E+00 0.000000000000 + +kred #81 = (0.500000,0.500000,0.500000) +n eigval occ +1 -3.561283089740E+00 2.000000000000 +2 -2.220277657479E+00 2.000000000000 +3 -2.106855498122E+00 2.000000000000 +4 -2.106855484650E+00 2.000000000000 +5 -3.089176619771E-01 2.000000000000 +6 -1.967661940924E-01 2.000000000000 +7 -1.967661895453E-01 2.000000000000 +8 -5.965106303093E-02 2.000000000000 +9 -5.965105950296E-02 2.000000000000 +10 4.845659024410E-02 2.000000000000 +11 2.431579815404E-01 2.000000000000 +12 2.431580033011E-01 2.000000000000 +13 2.761243004536E-01 2.000000000000 +14 4.782236274737E-01 0.000000000000 +15 4.925598918892E-01 0.000000000000 +16 4.925599113006E-01 0.000000000000 +17 5.809337943160E-01 0.000000000000 +18 1.011913777299E+00 0.000000000000 +19 1.011975220917E+00 0.000000000000 +20 1.074893179914E+00 0.000000000000 + +kred #82 = (0.486111,0.486111,0.527778) +n eigval occ +1 -3.561283506068E+00 2.000000000000 +2 -2.220275461325E+00 2.000000000000 +3 -2.106854579239E+00 2.000000000000 +4 -2.106851391015E+00 2.000000000000 +5 -3.088628137436E-01 2.000000000000 +6 -1.968903765884E-01 2.000000000000 +7 -1.967555454720E-01 2.000000000000 +8 -5.995831813702E-02 2.000000000000 +9 -5.965946374879E-02 2.000000000000 +10 4.780956244536E-02 2.000000000000 +11 2.415997468674E-01 2.000000000000 +12 2.435564838898E-01 2.000000000000 +13 2.773138675645E-01 2.000000000000 +14 4.760419165155E-01 0.000000000000 +15 4.934529908220E-01 0.000000000000 +16 4.953406544020E-01 0.000000000000 +17 5.847505625608E-01 0.000000000000 +18 1.004449557380E+00 0.000000000000 +19 1.010355562597E+00 0.000000000000 +20 1.073802970166E+00 0.000000000000 + +kred #83 = (0.472222,0.472222,0.555556) +n eigval occ +1 -3.561284745630E+00 2.000000000000 +2 -2.220268921747E+00 2.000000000000 +3 -2.106851825576E+00 2.000000000000 +4 -2.106839217663E+00 2.000000000000 +5 -3.087004167495E-01 2.000000000000 +6 -1.972609077354E-01 2.000000000000 +7 -1.967261548559E-01 2.000000000000 +8 -6.086259897947E-02 2.000000000000 +9 -5.968393237153E-02 2.000000000000 +10 4.588545024128E-02 2.000000000000 +11 2.375114365872E-01 2.000000000000 +12 2.446974704140E-01 2.000000000000 +13 2.804340219171E-01 2.000000000000 +14 4.715076134738E-01 0.000000000000 +15 4.961767366780E-01 0.000000000000 +16 5.021637157378E-01 0.000000000000 +17 5.955297190412E-01 0.000000000000 +18 9.874303676602E-01 0.000000000000 +19 1.005432625006E+00 0.000000000000 +20 1.067689934426E+00 0.000000000000 + +kred #84 = (0.458333,0.458333,0.583333) +n eigval occ +1 -3.561286780420E+00 2.000000000000 +2 -2.220258184073E+00 2.000000000000 +3 -2.106847222154E+00 2.000000000000 +4 -2.106819308407E+00 2.000000000000 +5 -3.084368171560E-01 2.000000000000 +6 -1.978715625531E-01 2.000000000000 +7 -1.966855585090E-01 2.000000000000 +8 -6.231387072537E-02 2.000000000000 +9 -5.972243695554E-02 2.000000000000 +10 4.273560188533E-02 2.000000000000 +11 2.319638469755E-01 2.000000000000 +12 2.464251301657E-01 2.000000000000 +13 2.847999924684E-01 2.000000000000 +14 4.666701371545E-01 0.000000000000 +15 5.007811757428E-01 0.000000000000 +16 5.119637551411E-01 0.000000000000 +17 6.118520415075E-01 0.000000000000 +18 9.666388309034E-01 0.000000000000 +19 9.970015981138E-01 0.000000000000 +20 1.059479247728E+00 0.000000000000 + +kred #85 = (0.444444,0.444444,0.611111) +n eigval occ +1 -3.561289564615E+00 2.000000000000 +2 -2.220243486146E+00 2.000000000000 +3 -2.106840749416E+00 2.000000000000 +4 -2.106792221596E+00 2.000000000000 +5 -3.080822721278E-01 2.000000000000 +6 -1.987115012713E-01 2.000000000000 +7 -1.966459451203E-01 2.000000000000 +8 -6.423627607673E-02 2.000000000000 +9 -5.977220120618E-02 2.000000000000 +10 3.844657064061E-02 2.000000000000 +11 2.258067514570E-01 2.000000000000 +12 2.485098062607E-01 2.000000000000 +13 2.901182565870E-01 2.000000000000 +14 4.625175974706E-01 0.000000000000 +15 5.072452899334E-01 0.000000000000 +16 5.245111564725E-01 0.000000000000 +17 6.323948264474E-01 0.000000000000 +18 9.442787214502E-01 0.000000000000 +19 9.849105805396E-01 0.000000000000 +20 1.049260816873E+00 0.000000000000 + +kred #86 = (0.430556,0.430556,0.638889) +n eigval occ +1 -3.561293035833E+00 2.000000000000 +2 -2.220225151910E+00 2.000000000000 +3 -2.106832382802E+00 2.000000000000 +4 -2.106758716861E+00 2.000000000000 +5 -3.076504821172E-01 2.000000000000 +6 -1.997646652331E-01 2.000000000000 +7 -1.966235679007E-01 2.000000000000 +8 -6.653767106273E-02 2.000000000000 +9 -5.983051547514E-02 2.000000000000 +10 3.314019302703E-02 2.000000000000 +11 2.196236589875E-01 2.000000000000 +12 2.507026457796E-01 2.000000000000 +13 2.964171712969E-01 2.000000000000 +14 4.595665528416E-01 0.000000000000 +15 5.154881753997E-01 0.000000000000 +16 5.396084128016E-01 0.000000000000 +17 6.561915503543E-01 0.000000000000 +18 9.211877156673E-01 0.000000000000 +19 9.694218917722E-01 0.000000000000 +20 1.037694355171E+00 0.000000000000 + +kred #87 = (0.416667,0.416667,0.666667) +n eigval occ +1 -3.561297116837E+00 2.000000000000 +2 -2.220203582703E+00 2.000000000000 +3 -2.106822095418E+00 2.000000000000 +4 -2.106719733680E+00 2.000000000000 +5 -3.071579597720E-01 2.000000000000 +6 -2.010091334398E-01 2.000000000000 +7 -1.966378834540E-01 2.000000000000 +8 -6.912019405000E-02 2.000000000000 +9 -5.989568871228E-02 2.000000000000 +10 2.697174029758E-02 2.000000000000 +11 2.138288123002E-01 2.000000000000 +12 2.528071652625E-01 2.000000000000 +13 3.038266833127E-01 2.000000000000 +14 4.580551081494E-01 0.000000000001 +15 5.253870767315E-01 0.000000000000 +16 5.570011077325E-01 0.000000000000 +17 6.825511441712E-01 0.000000000000 +18 8.977647041015E-01 0.000000000000 +19 9.512062656428E-01 0.000000000000 +20 1.025058577854E+00 0.000000000000 + +kred #88 = (0.402778,0.402778,0.694444) +n eigval occ +1 -3.561301717648E+00 2.000000000000 +2 -2.220179246526E+00 2.000000000000 +3 -2.106809861287E+00 2.000000000000 +4 -2.106676364718E+00 2.000000000000 +5 -3.066232586019E-01 2.000000000000 +6 -2.024166155555E-01 2.000000000000 +7 -1.967103924773E-01 2.000000000000 +8 -7.189033509495E-02 2.000000000000 +9 -5.996796897871E-02 2.000000000000 +10 2.012549512385E-02 2.000000000000 +11 2.087245329916E-01 2.000000000000 +12 2.547331697065E-01 2.000000000000 +13 3.124314223734E-01 2.000000000000 +14 4.580538104860E-01 0.000000000001 +15 5.367790524157E-01 0.000000000000 +16 5.764058339467E-01 0.000000000000 +17 7.109231906597E-01 0.000000000000 +18 8.742663239879E-01 0.000000000000 +19 9.311137564412E-01 0.000000000000 +20 1.011422004178E+00 0.000000000000 + +kred #89 = (0.388889,0.388889,0.722222) +n eigval occ +1 -3.561306737995E+00 2.000000000000 +2 -2.220152665602E+00 2.000000000000 +3 -2.106795659026E+00 2.000000000000 +4 -2.106629824603E+00 2.000000000000 +5 -3.060660900642E-01 2.000000000000 +6 -2.039522715914E-01 2.000000000000 +7 -1.968631827270E-01 2.000000000000 +8 -7.476749809777E-02 2.000000000000 +9 -6.005023546942E-02 2.000000000000 +10 1.280787588341E-02 2.000000000000 +11 2.045290282540E-01 2.000000000000 +12 2.565034813314E-01 2.000000000000 +13 3.222163133738E-01 2.000000000000 +14 4.595399001928E-01 0.000000000000 +15 5.494514451069E-01 0.000000000000 +16 5.975222213491E-01 0.000000000000 +17 7.407482279657E-01 0.000000000000 +18 8.509744878410E-01 0.000000000000 +19 9.099519909049E-01 0.000000000000 +20 9.968978389944E-01 0.000000000000 + +kred #90 = (0.375000,0.375000,0.750000) +n eigval occ +1 -3.561312070036E+00 2.000000000000 +2 -2.220124402587E+00 2.000000000000 +3 -2.106779475814E+00 2.000000000000 +4 -2.106581414939E+00 2.000000000000 +5 -3.055063624259E-01 2.000000000000 +6 -2.055750236059E-01 2.000000000000 +7 -1.971172227792E-01 2.000000000000 +8 -7.769050888891E-02 2.000000000000 +9 -6.014825005972E-02 2.000000000000 +10 5.238862652117E-03 2.000000000000 +11 2.013933017796E-01 2.000000000000 +12 2.582209240038E-01 2.000000000000 +13 3.330745427087E-01 2.000000000000 +14 4.624424119461E-01 0.000000000000 +15 5.631201602195E-01 0.000000000000 +16 6.200167603588E-01 0.000000000000 +17 7.710141139932E-01 0.000000000000 +18 8.286329601601E-01 0.000000000000 +19 8.884010089529E-01 0.000000000000 +20 9.817902507511E-01 0.000000000000 diff --git a/utils/bandstruct/example/CdS_ref.png b/utils/bandstruct/example/CdS_ref.png new file mode 100644 index 00000000..e6cc6efd Binary files /dev/null and b/utils/bandstruct/example/CdS_ref.png differ diff --git a/utils/bandstruct/example/plot_BS_CdS.py b/utils/bandstruct/example/plot_BS_CdS.py new file mode 100644 index 00000000..99d67cd4 --- /dev/null +++ b/utils/bandstruct/example/plot_BS_CdS.py @@ -0,0 +1,13 @@ +import sys +sys.path.append('..') +from band_structure_plot import * + +nkpt_per_line = 10 +fname = 'CdS.eigen_01' +highsym_points = 'G-X-W-K-G-L-U-W-L-K' +Efermi = 0.42712 # in Ha +outfname = 'CdS_bandstruct.png' +plot_band_structure(fname, nkpt_per_line, highsym_points, + unit='eV', Efermi_Ha=Efermi, ylim=(-10,30), + outfname=outfname, dpi=200) +