{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of F12 matrix elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- : unit = ()\n",
      "Findlib has been successfully loaded. Additional directives:\n",
      "  #require \"package\";;      to load a package\n",
      "  #list;;                   to list the available packages\n",
      "  #camlp4o;;                to load camlp4 (standard syntax)\n",
      "  #camlp4r;;                to load camlp4 (revised syntax)\n",
      "  #predicates \"p,q,...\";;   to set these predicates\n",
      "  Topfind.reset();;         to force that packages will be reloaded\n",
      "  #thread;;                 to enable threads\n",
      "\n",
      "- : unit = ()\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/scemama/qp2/external/opam/4.07.1/lib/bytes: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/base64: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/base64/base64.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/result: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/result/result.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/unix.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm/uuidm.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format/easy_format.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/biniou: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/biniou/biniou.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/yojson: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/yojson/yojson.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/jupyter.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/bigarray.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/lacaml.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/astring: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/astring/astring.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner/cmdliner.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/seq: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims/stdlib_shims.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_cli.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_tty.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest/alcotest.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/str.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/zarith: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/zarith/zarith.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/getopt: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/getopt/getopt.cma: loaded\n"
     ]
    }
   ],
   "source": [
    "#cd \"/home/scemama/QCaml\";;\n",
    "#use \"topfind\";;\n",
    "#require \"jupyter.notebook\";;\n",
    "\n",
    "#require \"lacaml\";;\n",
    "#require \"alcotest\";;\n",
    "#require \"str\";;\n",
    "#require \"bigarray\";;\n",
    "#require \"zarith\";;\n",
    "#require \"getopt\";;\n",
    "#directory \"_build\";;\n",
    "#directory \"_build/Basis\";;\n",
    "#directory \"_build/CI\";;\n",
    "#directory \"_build/MOBasis\";;\n",
    "#directory \"_build/Nuclei\";;\n",
    "#directory \"_build/Parallel\";;\n",
    "#directory \"_build/Perturbation\";;\n",
    "#directory \"_build/SCF\";;\n",
    "#directory \"_build/Utils\";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modules to load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#load \"Constants.cmo\";;\n",
    "#load_rec \"Util.cma\";;\n",
    "#load_rec \"Matrix.cmo\";;\n",
    "#load_rec \"Simulation.cmo\";;\n",
    "#load_rec \"Simulation.cmo\";;\n",
    "#load_rec \"HartreeFock.cmo\";;\n",
    "\n",
    "open Lacaml.D;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Printers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install_printer AngularMomentum.pp_string ;;\n",
    "#install_printer Basis.pp ;;\n",
    "#install_printer Charge.pp ;;\n",
    "#install_printer Coordinate.pp ;;\n",
    "#install_printer Vector.pp;;\n",
    "#install_printer Matrix.pp;;\n",
    "#install_printer Util.pp_float_2darray;;\n",
    "#install_printer Util.pp_float_array;;\n",
    "#install_printer Util.pp_matrix;;\n",
    "#install_printer HartreeFock.pp ;;\n",
    "#install_printer Fock.pp ;;\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvtz\"\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val nuclei : Nuclei.t = [|(Element.Be,   0.0000   0.0000   0.0000)|]\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val basis : Basis.t =\n",
       "  \n",
       "                          Atomic Basis set\n",
       "                          ----------------\n",
       "\n",
       "-----------------------------------------------------------------------\n",
       " #   Angular   Coordinates (Bohr)       Exponents       Coefficients\n",
       "    Momentum  X        Y        Z\n",
       "-----------------------------------------------------------------------\n",
       "  1-3  S   0.0000   0.0000   0.0000   2.94000000e+03    6.80000000e-04\n",
       "                                      4.41200000e+02    5.23600000e-03\n",
       "                                      1.00500000e+02    2.66060000e-02\n",
       "                                      2.84300000e+01    9.99930000e-02\n",
       "                                      9.16900000e+00    2.69702000e-01\n",
       "                                      3.19600000e+00    4.51469000e-01\n",
       "                                      1.15900000e+00    2.95074000e-01\n",
       "                                      1.81100000e-01    1.25870000e-02\n",
       "                                    \n",
       "                                      2.94000000e+03   -1.23000000e-04\n",
       "                                      4.41200000e+02   -9.66000000e-04\n",
       "                                      1.00500000e+02   -4.83100000e-03\n",
       "                                      2.84300000e+01   -1.93140000e-02\n",
       "                                      9.16900000e+00   -5.32800000e-02\n",
       "                                      3.19600000e+00   -1.20723000e-01\n",
       "                                      1.15900000e+00   -1.33435000e-01\n",
       "                                      1.81100000e-01    5.30767000e-01\n",
       "                                    \n",
       "                                      5.89000000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  4-9  P   0.0000   0.0000   0.0000   3.61900000e+00    2.91110000e-02\n",
       "                                      7.11000000e-01    1.69365000e-01\n",
       "                                      1.95100000e-01    5.13458000e-01\n",
       "                                    \n",
       "                                      6.01800000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       " 10-15 D   0.0000   0.0000   0.0000   2.38000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis : Basis.t =\n",
       "  \n",
       "                          Atomic Basis set\n",
       "                          ----------------\n",
       "\n",
       "-----------------------------------------------------------------------\n",
       " #   Angular   Coordinates (Bohr)       Exponents       Coefficients\n",
       "    Momentum  X        Y        Z\n",
       "-----------------------------------------------------------------------\n",
       "  1-7  S   0.0000   0.0000   0.0000   2.94000000e+03    6.80000000e-04\n",
       "                                      4.41200000e+02    5.23600000e-03\n",
       "                                      1.00500000e+02    2.66060000e-02\n",
       "                                      2.84300000e+01    9.99930000e-02\n",
       "                                      9.16900000e+00    2.69702000e-01\n",
       "                                      3.19600000e+00    4.51469000e-01\n",
       "                                      1.15900000e+00    2.95074000e-01\n",
       "                                      1.81100000e-01    1.25870000e-02\n",
       "                                    \n",
       "                                      2.94000000e+03   -1.23000000e-04\n",
       "                                      4.41200000e+02   -9.66000000e-04\n",
       "                                      1.00500000e+02   -4.83100000e-03\n",
       "                                      2.84300000e+01   -1.93140000e-02\n",
       "                                      9.16900000e+00   -5.32800000e-02\n",
       "                                      3.19600000e+00   -1.20723000e-01\n",
       "                                      1.15900000e+00   -1.33435000e-01\n",
       "                                      1.81100000e-01    5.30767000e-01\n",
       "                                    \n",
       "                                      5.89000000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                      6.86300000e+03    2.36000000e-04\n",
       "                                      1.03000000e+03    1.82600000e-03\n",
       "                                      2.34700000e+02    9.45200000e-03\n",
       "                                      6.65600000e+01    3.79570000e-02\n",
       "                                      2.16900000e+01    1.19965000e-01\n",
       "                                      7.73400000e+00    2.82162000e-01\n",
       "                                      2.91600000e+00    4.27404000e-01\n",
       "                                      1.13000000e+00    2.66278000e-01\n",
       "                                      1.10100000e-01   -7.27500000e-03\n",
       "                                    \n",
       "                                      6.86300000e+03   -4.30000000e-05\n",
       "                                      1.03000000e+03   -3.33000000e-04\n",
       "                                      2.34700000e+02   -1.73600000e-03\n",
       "                                      6.65600000e+01   -7.01200000e-03\n",
       "                                      2.16900000e+01   -2.31260000e-02\n",
       "                                      7.73400000e+00   -5.81380000e-02\n",
       "                                      2.91600000e+00   -1.14556000e-01\n",
       "                                      1.13000000e+00   -1.35908000e-01\n",
       "                                      1.10100000e-01    5.77441000e-01\n",
       "                                    \n",
       "                                      2.57700000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      4.40900000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  4-18 P   0.0000   0.0000   0.0000   3.61900000e+00    2.91110000e-02\n",
       "                                      7.11000000e-01    1.69365000e-01\n",
       "                                      1.95100000e-01    5.13458000e-01\n",
       "                                    \n",
       "                                      6.01800000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                      7.43600000e+00    1.07360000e-02\n",
       "                                      1.57700000e+00    6.28540000e-02\n",
       "                                      4.35200000e-01    2.48180000e-01\n",
       "                                    \n",
       "                                      1.43800000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      4.99400000e-02    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       " 10-27 D   0.0000   0.0000   0.0000   2.38000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      3.48000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      1.80300000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       " 41-50 F   0.0000   0.0000   0.0000   3.25000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f12 : F12factor.t =\n",
       "  {F12factor.expo_s = 1.;\n",
       "   gaussian =\n",
       "    {GaussianOperator.coef_g =\n",
       "      [  -0.314400  -0.303700  -0.168100  -0.098110  -0.060240  -0.037260 ];\n",
       "     expo_sg =\n",
       "      [   0.220900   1.004000   3.622000  12.160000  45.870000 254.400000 ];\n",
       "     expo_sg_inv =\n",
       "      [   4.526935   0.996016   0.276091   0.082237   0.021801   0.003931 ]}}\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val charge : int = 0\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val multiplicity : int = 1\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val simulation : Simulation.t = <abstr>\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let basis_filename  = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
    "let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvtz\" \n",
    "let nuclei = Nuclei.of_zmt_string \"be\" \n",
    "\n",
    "let basis =  Basis.of_nuclei_and_basis_filenames ~nuclei [basis_filename] \n",
    "let aux_basis =  Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n",
    "let f12 = F12factor.gaussian_geminal 1.0 \n",
    "let charge = 0 \n",
    "let multiplicity = 1 \n",
    "\n",
    "\n",
    "let simulation =\n",
    "    Simulation.make \n",
    "        ~f12 ~charge ~multiplicity ~nuclei\n",
    "        ~cartesian:true\n",
    "        basis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hartree-Fock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MOs =\n",
      "\n",
      "\n",
      "             -- 1 --     -- 2 --      -- 3 --      -- 4 -- -- 5 --\n",
      "             1        1.0006  0.00028918           -0           -0       0\n",
      "             2    0.00576322     1.00367 -7.13815E-16           -0       0\n",
      "             3   -0.00181801    0.582215  4.68436E-16 -6.48338E-16       0\n",
      "                         ...         ...          ...          ...     ...\n",
      "            13   -0.00209072 -0.00172308           -0           -0       0\n",
      "            14            -0          -0           -0           -0       0\n",
      "            15   -0.00209072 -0.00172308           -0 -8.65517E-16       0\n",
      "      \n",
      "\n",
      "          -- 6 --      -- 7 -- -- 8 --      -- 9 --     -- 10 --\n",
      "             1   0.549926 -7.88204E-16       0            0 -5.10457E-16\n",
      "             2    2.77214 -4.20928E-15       0 -8.18142E-16 -6.26457E-16\n",
      "             3     -1.826  2.68321E-15       0            0  4.82834E-15\n",
      "                      ...          ...     ...          ...          ...\n",
      "            13   0.224421            0       0            0    -0.995373\n",
      "            14         -0            0       0            0  -0.00304009\n",
      "            15   0.224421            0       0            0     0.534433\n",
      "      \n",
      "\n",
      "             -- 11 --    -- 12 --     -- 13 --    -- 14 -- -- 15 --\n",
      "             1   -8.47272E-16 4.18722E-16            0           0 0.516133\n",
      "             2   -7.29877E-15 3.26085E-15 -5.13582E-16           0  4.52711\n",
      "             3   -1.53999E-15           0            0           0  1.08073\n",
      "                          ...         ...          ...         ...      ...\n",
      "            13      0.0741226   0.0584492     -0.01795 0.000120624 -1.45115\n",
      "            14     0.00668622    0.201298     0.848372   -0.489582        0\n",
      "            15       0.750441   -0.380516    0.0792247  -0.0122393 -1.45115\n",
      "      \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val hf : HartreeFock.t = \n",
       "======================================================================\n",
       "                        Restricted Hartree-Fock                      \n",
       "======================================================================\n",
       "\n",
       "    ------------------------------------------------------------\n",
       "        #     HF energy       Convergence  HOMO-LUMO\n",
       "    ------------------------------------------------------------\n",
       "        1    -14.05142130      8.0958e-01     0.2991\n",
       "        2    -14.51982122      2.7933e-01     0.3600\n",
       "        3    -14.56519147      8.3990e-02     0.3674\n",
       "        4    -14.57117146      2.6217e-02     0.3679\n",
       "        5    -14.57214606      1.0744e-02     0.3676\n",
       "        6    -14.57232209      5.0392e-03     0.3675\n",
       "        7    -14.57235521      2.2956e-03     0.3674\n",
       "        8    -14.57236154      1.0293e-03     0.3673\n",
       "        9    -14.57236304      4.1738e-08     0.3673\n",
       "       10    -14.57236304      4.9181e-09     0.3673\n",
       "    ------------------------------------------------------------\n",
       "\n",
       "\n",
       "    ============================================================\n",
       "               One-electron energy  -19.0610711155\n",
       "                           Kinetic   14.5598880887\n",
       "                         Potential  -33.6209592042\n",
       "      --------------------------------------------------------  \n",
       "               Two-electron energy    4.4887080772\n",
       "                           Coulomb    7.1543328046\n",
       "                          Exchange   -2.6656247274\n",
       "      --------------------------------------------------------  \n",
       "                           HF HOMO   -8.4100296422\n",
       "                           HF LUMO    1.5842692336\n",
       "                      HF LUMO-LUMO    9.9942988758\n",
       "      --------------------------------------------------------  \n",
       "               Electronic   energy  -14.5723630383\n",
       "               Nuclear   repulsion    0.0000000000\n",
       "               Hartree-Fock energy  -14.5723630383\n",
       "    ============================================================\n",
       "    \n",
       "\n"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let hf = \n",
    "    HartreeFock.make ~guess:`Hcore  simulation \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ints : ERI.t = <abstr>\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : float = 0.\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ints = Simulation.ao_basis simulation\n",
    "|> AOBasis.ee_ints ;;\n",
    "ERI.get_phys ints 1 1 1 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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