cc-ade-eom.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bdced36f",
   "metadata": {},
   "source": [
    "### Algebraic Evaluation of Coupled-Cluster Diagrams - EOM"
   ]
  },
  {
   "attachments": {
    "feynman%283%29.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "7fc34978",
   "metadata": {},
   "source": [
    "The cc-ade code is easily extended to Equation-of-Motion coupled-cluster.\n",
    "\n",
    "__the exponential series__\n",
    "\n",
    "The series expansion for EOM CCSD is\n",
    "$S=R_1 + T_1 R_1 + T_2 R_1 + \\frac{1}{2} T_1^2 R_1 + R_2 + T_1 R_2$ or $R_1\\big(1 + T_1 + T_2 + \\frac{1}{2}T_1^2 \\big ) + R_2 \\big ( 1+ T_1 \\big)$. \n",
    "\n",
    "The CCSD singles expansion is $1 + T_1 + T_2 + \\frac{1}{2} T_1^2 + T_1 T_2 + \\frac{1}{6} T_1^3$ which is of order 3 in amplitudes. If we consider R to be an amplitude then the EOM-CCSD series is also of order 3 or CCSD to order 2 times $R_1$ plus CCSD to order 1 times $R_2$.\n",
    "\n",
    "The doubles are $D=R_1 + T_1 R_1 + T_2 R_1 + \\frac{1}{2} T_1^2 R_1 + T_1 T_2 R_1 + \\frac{1}{6} T_1^3 R_1 + R_2 + T_1 R_2 + T_2 R_2 + \\frac{1}{2} T_1^2 R_2$ = $R_1 \\big(1 + T_1 + T_2 + \\frac{1}{2}T_1^2 + T_1 T_2 + \\frac{1}{6}T_1^3 \\big ) + R_2 \\big (1 + T_1 + T_2 + \\frac{1}{2}T_1^2 \\big)$.\n",
    "\n",
    "This is CCSD order 3 times $R_1$ and again CCSD to order 2 times $R_2$. As we can already compute the $T_n$ series all we need to do is a multiplication by $R_n$ for the EOM series.\n",
    "\n",
    "__reference id__\n",
    "\n",
    "In cc-ade we referenced each term as eg '1100'. This is interpreted as $1xT_1 1xT_2 0xT_3 0xT_4$. For cc-eom-ade we reference as eg '1100n' where n is the degree of the r-amplitude, so '21002' would be a $T_1^2 T_2 R_2$ term.R is treated the same as T in the code with the convention that the last amplitude is always the (single) R one. This requires minor changes to the existing code. The same rules for determining the sign and factor of a diagram apply with caveat that when determining equivalant vertices $R_n$ and $T_n$ amplitudes should not be considered as equivalent.\n",
    "\n",
    "__labelling__\n",
    "\n",
    "Consider \n",
    "![feynman%283%29.png](attachment:feynman%283%29.png)\n",
    "\n",
    "This is a __+--__ as __+-|-__ contracted with __+-|++--__. If we forget that the first amplitude is an __r__ we would have algorithm a.24 $$\\boldsymbol{t^{(+)e}_{(-)m} t^{(+)}_{n[-)} \\scriptsize{\\langle mn\\Vert [e \\rangle}}~~~~~a.24$$\n",
    "\n",
    "So we would label $t^c_k t^{ab}_{lj} \\langle kl \\Vert ic \\rangle$. Our sign is + and $\\hat{P}(ij)$ If we keep the r-amplitude as the last term all we need do from cc-ade is rename the last 't' to 'r'. The *lablib* developed for cc-ade is completely compatible with eom-cc-ade.\n",
    "\n",
    "__validation__\n",
    "\n",
    "For S and D levels each diagram is referenced and a *reference.txt* file is provided in the *eom_validation* folder. The einsum expressions in the *reference.txt* folder are taken from Josh Goings pychem repo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7691d117",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}