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QCaml/Notebooks/F12_matrix.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test of F12 matrix elements"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initialization"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"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 \"Spindeterminant.cmo\";;\n",
"#load_rec \"Determinant.cmo\";;\n",
"#load_rec \"HartreeFock.cmo\";;\n",
"#load_rec \"MOBasis.cmo\";;\n",
"#load_rec \"F12CI.cmo\";;\n",
"\n",
"open Lacaml.D;;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Printers"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val pp_mo : Format.formatter -> MOBasis.t -> unit = <fun>\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"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",
"#install_printer MOClass.pp ;;\n",
"let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n",
"#install_printer pp_mo;;\n",
"#install_printer DeterminantSpace.pp;;\n",
"#install_printer SpindeterminantSpace.pp;;\n",
"#install_printer Bitstring.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/6-31g\"\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\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 frozen_core : bool = false\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 state : int = 1\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 1.26458570e+03 1.94480000e-03\n",
" 1.89936810e+02 1.48351000e-02\n",
" 4.31590890e+01 7.20906000e-02\n",
" 1.20986630e+01 2.37154200e-01\n",
" 3.80632320e+00 4.69198700e-01\n",
" 1.27289030e+00 3.56520200e-01\n",
" \n",
" 3.19646310e+00 -1.12648700e-01\n",
" 7.47813300e-01 -2.29506400e-01\n",
" 2.19966300e-01 1.18691670e+00\n",
" \n",
" 8.23099000e-02 1.00000000e+00\n",
" \n",
" \n",
"-----------------------------------------------------------------------\n",
" 3-8 P 0.0000 0.0000 0.0000 3.19646310e+00 5.59802000e-02\n",
" 7.47813300e-01 2.61550600e-01\n",
" 2.19966300e-01 7.93972300e-01\n",
" \n",
" 8.23099000e-02 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",
" 1-6 S 0.0000 0.0000 0.0000 1.26458570e+03 1.94480000e-03\n",
" 1.89936810e+02 1.48351000e-02\n",
" 4.31590890e+01 7.20906000e-02\n",
" 1.20986630e+01 2.37154200e-01\n",
" 3.80632320e+00 4.69198700e-01\n",
" 1.27289030e+00 3.56520200e-01\n",
" \n",
" 3.19646310e+00 -1.12648700e-01\n",
" 7.47813300e-01 -2.29506400e-01\n",
" 2.19966300e-01 1.18691670e+00\n",
" \n",
" 8.23099000e-02 1.00000000e+00\n",
" \n",
" 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",
" 3-14 P 0.0000 0.0000 0.0000 3.19646310e+00 5.59802000e-02\n",
" 7.47813300e-01 2.61550600e-01\n",
" 2.19966300e-01 7.93972300e-01\n",
" \n",
" 8.23099000e-02 1.00000000e+00\n",
" \n",
" 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",
" 19-24 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 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 simulation : Simulation.t = <abstr>\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n",
"let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
"let nuclei = Nuclei.of_zmt_string \"be\" \n",
"let frozen_core = false\n",
"let multiplicity = 1\n",
"let state = 1\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",
"\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": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15 significant shell pairs computed in 0.004974 seconds\n",
"1\n",
"2\n",
"5\n",
"6\n",
"Computed ERIs in 0.026928 seconds\n",
"MOs =\n",
"\n",
"\n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.997996 -0.22266 0 0 -0\n",
" 2 0.0161427 0.288767 2.2404E-15 0 -7.73804E-16\n",
" 3 0 3.58344E-16 0.258415 0.037609 0.0381979\n",
" ... ... ... ... ...\n",
" 7 0 0 0.78727 0.114442 0.116234\n",
" 8 0 0 -0.128237 0.0798944 0.789475\n",
" 9 0 0 -0.100874 0.791587 -0.0964853\n",
" \n",
"\n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 0.00338551 0 -0 0\n",
" 2 2.01724 -3.80748E-15 4.70544E-15 -6.99768E-16\n",
" 3 1.56069E-15 1.292 0.249105 0.0981672\n",
" ... ... ... ...\n",
" 7 -2.3622E-15 -1.05652 -0.20374 -0.0802898\n",
" 8 1.64398E-15 0.172096 -0.528064 -0.92522\n",
" 9 2.61906E-15 0.135375 -0.918775 0.549573\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 -14.35428398 3.4264e-01 0.3789\n",
" 2 -14.52767889 1.8460e-01 0.3848\n",
" 3 -14.56058094 7.7052e-02 0.3856\n",
" 4 -14.56582672 3.0375e-02 0.3848\n",
" 5 -14.56662378 1.1794e-02 0.3842\n",
" 6 -14.56676403 1.7857e-06 0.3837\n",
" 7 -14.56676404 1.7598e-08 0.3837\n",
" 8 -14.56676403 1.3644e-09 0.3837\n",
" ------------------------------------------------------------\n",
"\n",
"\n",
" ============================================================\n",
" One-electron energy -19.1171562840\n",
" Kinetic 14.6787428206\n",
" Potential -33.7958991046\n",
" -------------------------------------------------------- \n",
" Two-electron energy 4.5503922505\n",
" Coulomb 7.2329463384\n",
" Exchange -2.6825540879\n",
" -------------------------------------------------------- \n",
" HF HOMO -8.1986650549\n",
" HF LUMO 2.2431802579\n",
" HF LUMO-LUMO 10.4418453128\n",
" -------------------------------------------------------- \n",
" Electronic energy -14.5667640335\n",
" Nuclear repulsion 0.0000000000\n",
" Hartree-Fock energy -14.5667640335\n",
" ============================================================\n",
" \n",
"\n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mo_basis : MOBasis.t =\n",
" Eigenvalues: -4.706891 -0.301295 0.082435 0.082435 0.082435 \n",
" -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
" 1 0.997996 -0.22266 0 0 -0\n",
" 2 0.0161427 0.288767 2.2404E-15 0 -7.73804E-16\n",
" 3 0 3.58344E-16 0.258415 0.037609 0.0381979\n",
" ... ... ... ... ...\n",
" 7 0 0 0.78727 0.114442 0.116234\n",
" 8 0 0 -0.128237 0.0798944 0.789475\n",
" 9 0 0 -0.100874 0.791587 -0.0964853\n",
" \n",
" Eigenvalues: 0.439754 0.464931 0.464931 0.464931 \n",
" -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
" 1 0.00338551 0 -0 0\n",
" 2 2.01724 -3.80748E-15 4.70544E-15 -6.99768E-16\n",
" 3 1.56069E-15 1.292 0.249105 0.0981672\n",
" ... ... ... ...\n",
" 7 -2.3622E-15 -1.05652 -0.20374 -0.0802898\n",
" 8 1.64398E-15 0.172096 -0.528064 -0.92522\n",
" 9 2.61906E-15 0.135375 -0.918775 0.549573\n",
" \n",
" \n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let hf = HartreeFock.make ~guess:`Hcore simulation ;;\n",
"\n",
"let mo_basis = MOBasis.of_hartree_fock hf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# FCI-F12"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notations:\n",
"\n",
"* $\\langle ij || kl \\rangle = \\int \\phi_i(r_1) \\phi_j(r_2) \\frac{1}{r_{12}} \\phi_k(r1) \\phi_l(r2) $ \n",
"* $\\left[ ij || kl \\right] = \\int \\phi_i(r_1) \\phi_j(r_2) f_{12} \\phi_k(r1) \\phi_l(r2) $ \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Common functions"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"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": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mo_num : int = 9\n"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = <fun>\n"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val pp_det : Format.formatter -> Determinant.t -> unit = <fun>\n"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let f12 = Util.of_some @@ Simulation.f12 simulation \n",
"\n",
"let mo_num = MOBasis.size mo_basis \n",
"\n",
"let pp_spindet = Spindeterminant.pp mo_num\n",
"\n",
"let pp_det = Determinant.pp mo_num\n",
"\n",
";;\n",
"\n",
"#install_printer pp_spindet ;;\n",
"#install_printer pp_det ;;\n",
"\n"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let simulation_aux = \n",
" let charge = Charge.to_int @@ Simulation.charge simulation \n",
" and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation\n",
" and nuclei = Simulation.nuclei simulation\n",
" in\n",
" let general_basis = \n",
" Basis.general_basis @@ Simulation.basis simulation\n",
" in\n",
" GeneralBasis.combine [\n",
" general_basis ; GeneralBasis.read aux_basis_filename\n",
" ]\n",
" |> Basis.of_nuclei_and_general_basis nuclei\n",
" |> Simulation.make ~f12 ~charge ~multiplicity ~nuclei \n",
"\n",
"\n",
"let aux_basis = \n",
" MOBasis.of_mo_basis simulation_aux mo_basis\n",
" \n",
"let () = ignore @@ MOBasis.f12_ints aux_basis\n",
"let () = ignore @@ MOBasis.two_e_ints aux_basis\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Determinant-based functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Integrals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\langle I | \\hat{H} | J \\rangle = \\begin{cases}\n",
"\\sum_i h_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
"h_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
"\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
"\\end{cases}$\n",
"\n",
"\n",
"$\\langle I | \\hat{F} | J \\rangle = \\begin{cases}\n",
"\\sum_i f_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
"f_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
"\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
"\\end{cases}$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val cancel_singles : bool = false\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f12_integrals :\n",
" MOBasis.t ->\n",
" ('a -> 'b -> 'c -> float) *\n",
" (int -> int -> int -> int -> 'd -> 'd -> float) * 'e option = <fun>\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
" <fun>\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val f_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
" <fun>\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val hf_ij :\n",
" MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n",
" <fun>\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let cancel_singles = false \n",
"\n",
"let f12_integrals mo_basis =\n",
"\n",
" \n",
" let two_e_ints = MOBasis.f12_ints mo_basis in\n",
" let f2 i j k l s s' =\n",
" let ijkl = F12.get_phys two_e_ints i j k l in\n",
" let ijlk = F12.get_phys two_e_ints i j l k in\n",
" if s' <> s then\n",
" ijkl \n",
" else\n",
" (ijkl -. ijlk) \n",
" in\n",
" ( (fun _ _ _ -> 0.),\n",
" (if cancel_singles then\n",
" (fun i j k l s s' ->\n",
" (* Required to cancel out single excitations *)\n",
" if (i=k && j<>l) || (j=l && i<>k) then\n",
" 0.\n",
" else\n",
" f2 i j k l s s'\n",
" ) \n",
" else f2),\n",
" None\n",
" )\n",
"\n",
"let h_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ CI.h_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj \n",
" |> List.hd\n",
"\n",
"\n",
"let f_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ f12_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj \n",
" |> List.hd \n",
"\n",
"\n",
"let hf_ij mo_basis ki kj =\n",
" let integrals =\n",
" List.map (fun f -> f mo_basis)\n",
" [ CI.h_integrals ; f12_integrals ]\n",
" in\n",
" CIMatrixElement.make integrals ki kj\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Determinant space"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"- : Spindeterminant.t =\n",
"+1 +-+-+-+---------------------------------------------------------\n"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Spindeterminant.of_list 10 [1; 3 ; 5; 7]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val det_space : SpindeterminantSpace.t =\n",
" [ 0 +1 ++--------------------------------------------------------------\n",
" 1 +1 --+-------------------------------------------------------------\n",
" 2 +1 ---+------------------------------------------------------------\n",
" 3 +1 ----+-----------------------------------------------------------\n",
" 4 +1 +----+----------------------------------------------------------\n",
" 5 +1 -+---+----------------------------------------------------------\n",
" 6 +1 --+--+----------------------------------------------------------\n",
" 7 +1 ---+-+----------------------------------------------------------\n",
" 8 +1 ----++----------------------------------------------------------\n",
" 9 +1 ------+---------------------------------------------------------\n",
" 10 +1 +++----+--------------------------------------------------------\n",
" 11 +1 ---+---+--------------------------------------------------------\n",
" 12 +1 ----+--+--------------------------------------------------------\n",
" 13 +1 -----+-+--------------------------------------------------------\n",
" 14 +1 ++----++--------------------------------------------------------\n",
" 15 +1 --+---++--------------------------------------------------------\n",
" 16 +1 ---+--++--------------------------------------------------------\n",
" 17 +1 ----+-++--------------------------------------------------------\n",
" 18 +1 +----+++--------------------------------------------------------\n",
" 19 +1 -+---+++--------------------------------------------------------\n",
" 20 +1 --+--+++--------------------------------------------------------\n",
" 21 +1 ---+-+++--------------------------------------------------------\n",
" 22 +1 ----++++--------------------------------------------------------\n",
" 23 +1 +++-----+-------------------------------------------------------\n",
" 24 +1 ---+----+-------------------------------------------------------\n",
" 25 +1 ----+---+-------------------------------------------------------\n",
" 26 +1 +----+--+-------------------------------------------------------\n",
" 27 +1 -+---+--+-------------------------------------------------------\n",
" 28 +1 --+--+--+-------------------------------------------------------\n",
" 29 +1 ---+-+--+-------------------------------------------------------\n",
" 30 +1 ----++--+-------------------------------------------------------\n",
" 31 +1 +-----+-+-------------------------------------------------------\n",
" 32 +1 -+----+-+-------------------------------------------------------\n",
" 33 +1 --+---+-+-------------------------------------------------------\n",
" 34 +1 ---+--+-+-------------------------------------------------------\n",
" 35 +1 ----+-+-+-------------------------------------------------------\n",
" ]\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let det_space = \n",
"(*\n",
" DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n",
" *)\n",
" SpindeterminantSpace.fci_of_mo_basis mo_basis ~frozen_core (Electrons.n_alfa @@ Simulation.electrons simulation)\n"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"unsigned int v; // current permutation of bits \n",
"unsigned int w; // next permutation of bits\n",
"\n",
"unsigned int t = v | (v - 1); // t gets v's least significant 0 bits set to 1\n",
"// Next set to 1 the most significant bit to change, \n",
"// set to 0 the least significant ones, and add the necessary 1 bits.\n",
"w = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1)); "
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"- : int = 31\n"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let _ = \n",
" let open Bitstring in\n",
"(*\n",
"\n",
" let u = Bitstring.of_int 63 in\n",
"\n",
" let t = logor u @@ minus_one u in\n",
" let not_t = lognot t in\n",
" let neg_not_t = neg not_t in\n",
" \n",
" shift_right\n",
" (minus_one @@ logand not_t neg_not_t) \n",
" ( (trailing_zeros u) + 1),\n",
" *)\n",
" popcount (Bitstring.of_int 1)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val elec_num : int = 4\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val alfa_num : int = 2\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val mo_class : MOClass.t =\n",
" [Active 1;Active 2;Active 3;Active 4;Active 5;Active 6;Active 7;Active 8;\n",
" Active 9]\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m : int list -> Bitstring.t = <fun>\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val occ_mask : Bitstring.t =\n",
" ----------------------------------------------------------------\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val active_mask : Bitstring.t =\n",
" +++++++++-------------------------------------------------------\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val neg_active_mask : Bitstring.t =\n",
" ---------+++++++++++++++++++++++++++++++++++++++++++++++++++++++\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val permtutations : int -> int -> Bitstring.t list = <fun>\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val spin_determinants : Bitstring.t list =\n",
" [++--------------------------------------------------------------;\n",
" --+-------------------------------------------------------------;\n",
" ---+------------------------------------------------------------;\n",
" ----+-----------------------------------------------------------;\n",
" -----+----------------------------------------------------------;\n",
" ++----+---------------------------------------------------------;\n",
" --+---+---------------------------------------------------------;\n",
" ---+--+---------------------------------------------------------;\n",
" ----+-+---------------------------------------------------------;\n",
" +----++---------------------------------------------------------;\n",
" -+---++---------------------------------------------------------;\n",
" --+--++---------------------------------------------------------;\n",
" ---+-++---------------------------------------------------------;\n",
" ----+++---------------------------------------------------------;\n",
" +------+--------------------------------------------------------;\n",
" -+-----+--------------------------------------------------------;\n",
" --+----+--------------------------------------------------------;\n",
" ---+---+--------------------------------------------------------;\n",
" ----+--+--------------------------------------------------------;\n",
" +----+-+--------------------------------------------------------;\n",
" -+---+-+--------------------------------------------------------;\n",
" --+--+-+--------------------------------------------------------;\n",
" ---+-+-+--------------------------------------------------------;\n",
" ----++-+--------------------------------------------------------;\n",
" +-----++--------------------------------------------------------;\n",
" -+----++--------------------------------------------------------;\n",
" --+---++--------------------------------------------------------;\n",
" ---+--++--------------------------------------------------------;\n",
" ----+-++--------------------------------------------------------;\n",
" +----+++--------------------------------------------------------;\n",
" -+---+++--------------------------------------------------------;\n",
" --+--+++--------------------------------------------------------;\n",
" ---+-+++--------------------------------------------------------;\n",
" ----++++--------------------------------------------------------;\n",
" +-------+-------------------------------------------------------;\n",
" -+------+-------------------------------------------------------]\n"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let elec_num = Electrons.n_elec @@ Simulation.electrons simulation\n",
"\n",
"let alfa_num = Electrons.n_alfa @@ Simulation.electrons simulation\n",
"\n",
"let mo_class = MOClass.fci ~frozen_core mo_basis \n",
"\n",
"\n",
"let m l = \n",
" List.fold_left (fun accu i -> let j = i-1 in\n",
" Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" \n",
"let occ_mask = m (MOClass.core_mos mo_class)\n",
"\n",
"let active_mask = m (MOClass.active_mos mo_class)\n",
"\n",
"\n",
"let neg_active_mask = Bitstring.lognot active_mask \n",
"\n",
" (* Here we generate the FCI space and filter out unwanted determinants\n",
" with excitations involving the core electrons. This should be improved. *)\n",
" \n",
"let permtutations m n = \n",
" let open Bitstring in\n",
" let rec aux k u rest =\n",
" if k=1 then\n",
" List.rev (u :: rest)\n",
" else\n",
" let t = (logor u (minus_one u)) in\n",
" let t' = plus_one t in\n",
" let t'' = shift_right (minus_one (logand (lognot t) (neg @@ lognot t))) (trailing_zeros u + 1) in \n",
" (*\n",
" let t'' = shift_right (minus_one (logand (lognot t) t')) (trailing_zeros u + 1) in\n",
" *)\n",
" (aux [@tailcall]) (k-1) (logor t' t'') (u :: rest)\n",
" in\n",
" aux (Util.binom n m) (minus_one (shift_left_one n m)) []\n",
"\n",
" \n",
"let spin_determinants =\n",
" Bitstring.permtutations alfa_num mo_num\n",
" (*\n",
" |> List.filter (fun b -> Bitstring.logand neg_active_mask b = occ_mask)\n",
" |> List.map (fun b -> Spindeterminant.of_bitstring b)\n",
" |> Array.of_list\n",
" *)\n"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let ci = CI.make ~n_states:state det_space\n",
"\n",
"let ci_coef, ci_energy = Lazy.force ci.eigensystem "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Creates a function `f : Determinant.t -> bool` that returns `true` when the determinant has one or two electrons in the CABS."
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let is_a_double det_space =\n",
" let mo_class = DeterminantSpace.mo_class det_space in\n",
" let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
" let m l =\n",
" List.fold_left (fun accu i ->\n",
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" in\n",
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
" fun k -> \n",
" let alfa =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let beta =\n",
" Determinant.beta k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let a = Bitstring.logand aux_mask alfa\n",
" and b = Bitstring.logand aux_mask beta\n",
" in\n",
" match Bitstring.popcount a + Bitstring.popcount b with\n",
" | 2 | 1 -> true\n",
" | 0 | _ -> false\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped."
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let p12 det_space =\n",
" let mo_class = DeterminantSpace.mo_class det_space in\n",
" let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
" let m l =\n",
" List.fold_left (fun accu i ->\n",
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
" ) (Bitstring.zero mo_num) l\n",
" in\n",
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
" let not_aux_mask =\n",
" Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n",
" in\n",
" fun k ->\n",
" let alfa =\n",
" Determinant.alfa k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let beta =\n",
" Determinant.beta k\n",
" |> Spindeterminant.bitstring\n",
" in\n",
" let a = Bitstring.logand aux_mask alfa\n",
" and b = Bitstring.logand aux_mask beta\n",
" in\n",
" match Bitstring.popcount a, Bitstring.popcount b with\n",
" | 2, 0 \n",
" | 0, 2 -> Some (Determinant.negate_phase k)\n",
" | 1, 1 -> Some (Determinant.of_spindeterminants\n",
" (Spindeterminant.of_bitstring @@\n",
" Bitstring.(logor b (logand not_aux_mask alfa)) )\n",
" (Spindeterminant.of_bitstring @@\n",
" Bitstring.(logor a (logand not_aux_mask beta))\n",
" ) )\n",
" | 1, 0 \n",
" | 0, 1 -> Some k\n",
" | _ -> None\n",
" \n",
" \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Determinants of the FCI space"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"let in_dets = \n",
" DeterminantSpace.determinant_stream ci.CI.det_space \n",
" |> Util.stream_to_list\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Integral-based functions"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "OCaml 4.07.1",
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