{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Test of F12 matrix elements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val png_image : string -> unit = \n" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Raised at file \"stdlib.ml\", line 34, characters 25-45\n", "Called from file \"toplevel/toploop.ml\", line 468, characters 4-128\n", "Called from file \"toplevel/topdirs.ml\", line 144, characters 10-51\n", "\n", "- : 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" ] }, { "data": { "text/plain": [ "val png_image : string -> Jupyter_notebook.display_id = \n" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let png_image = print_endline ;;\n", "\n", "(* --------- *)\n", "\n", "#cd \"/home/scemama/QCaml\";;\n", "#use \"topfind\";;\n", "#require \"jupyter.notebook\";;\n", "\n", "let png_image name = \n", " Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n", ";;\n", "\n", "#require \"lacaml.top\";;\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" ] }, { "cell_type": "code", "execution_count": 66, "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\";;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Printers" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val pp_mo : Format.formatter -> MOBasis.t -> unit = \n" ] }, "execution_count": 67, "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", "(*\n", "#install_printer DeterminantSpace.pp;;\n", "*)\n", "#install_printer SpindeterminantSpace.pp;;\n", "#install_printer Bitstring.pp;;\n", "\n", "(* --------- *)\n", "\n", "open Lacaml.D\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation\n" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val nuclei : Nuclei.t = [|(Element.C, 0.0000 0.0000 0.0000)|]\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val frozen_core : bool = false\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val multiplicity : int = 1\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val state : int = 1\n" ] }, "execution_count": 68, "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 3.04752490e+03 1.83470000e-03\n", " 4.57369510e+02 1.40373000e-02\n", " 1.03948690e+02 6.88426000e-02\n", " 2.92101550e+01 2.32184400e-01\n", " 9.28666300e+00 4.67941300e-01\n", " 3.16392700e+00 3.62312000e-01\n", " \n", " 7.86827240e+00 -1.19332400e-01\n", " 1.88128850e+00 -1.60854200e-01\n", " 5.44249300e-01 1.14345640e+00\n", " \n", " 1.68714400e-01 1.00000000e+00\n", " \n", " \n", "-----------------------------------------------------------------------\n", " 3-8 P 0.0000 0.0000 0.0000 7.86827240e+00 6.89991000e-02\n", " 1.88128850e+00 3.16424000e-01\n", " 5.44249300e-01 7.44308300e-01\n", " \n", " 1.68714400e-01 1.00000000e+00\n", " \n", " \n", "-----------------------------------------------------------------------\n", "\n" ] }, "execution_count": 68, "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 3.04752490e+03 1.83470000e-03\n", " 4.57369510e+02 1.40373000e-02\n", " 1.03948690e+02 6.88426000e-02\n", " 2.92101550e+01 2.32184400e-01\n", " 9.28666300e+00 4.67941300e-01\n", " 3.16392700e+00 3.62312000e-01\n", " \n", " 7.86827240e+00 -1.19332400e-01\n", " 1.88128850e+00 -1.60854200e-01\n", " 5.44249300e-01 1.14345640e+00\n", " \n", " 1.68714400e-01 1.00000000e+00\n", " \n", " 6.66500000e+03 6.92000000e-04\n", " 1.00000000e+03 5.32900000e-03\n", " 2.28000000e+02 2.70770000e-02\n", " 6.47100000e+01 1.01718000e-01\n", " 2.10600000e+01 2.74740000e-01\n", " 7.49500000e+00 4.48564000e-01\n", " 2.79700000e+00 2.85074000e-01\n", " 5.21500000e-01 1.52040000e-02\n", " \n", " 6.66500000e+03 -1.46000000e-04\n", " 1.00000000e+03 -1.15400000e-03\n", " 2.28000000e+02 -5.72500000e-03\n", " 6.47100000e+01 -2.33120000e-02\n", " 2.10600000e+01 -6.39550000e-02\n", " 7.49500000e+00 -1.49981000e-01\n", " 2.79700000e+00 -1.27262000e-01\n", " 5.21500000e-01 5.44529000e-01\n", " \n", " 1.59600000e-01 1.00000000e+00\n", " \n", " \n", "-----------------------------------------------------------------------\n", " 3-14 P 0.0000 0.0000 0.0000 7.86827240e+00 6.89991000e-02\n", " 1.88128850e+00 3.16424000e-01\n", " 5.44249300e-01 7.44308300e-01\n", " \n", " 1.68714400e-01 1.00000000e+00\n", " \n", " 9.43900000e+00 3.81090000e-02\n", " 2.00200000e+00 2.09480000e-01\n", " 5.45600000e-01 5.08557000e-01\n", " \n", " 1.51700000e-01 1.00000000e+00\n", " \n", " \n", "-----------------------------------------------------------------------\n", " 19-24 D 0.0000 0.0000 0.0000 5.50000000e-01 1.00000000e+00\n", " \n", " \n", "-----------------------------------------------------------------------\n", "\n" ] }, "execution_count": 68, "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": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val charge : int = 0\n" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val simulation : Simulation.t = \n" ] }, "execution_count": 68, "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 \"c\" \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": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val n_elec_alfa : int = 3\n", "val n_elec_beta : int = 3\n", "val n_elec : int = 6\n" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let n_elec_alfa, n_elec_beta, n_elec = \n", " let e = Simulation.electrons simulation in\n", " Electrons.(n_alfa e, n_beta e, n_elec e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hartree-Fock" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "15 significant shell pairs computed in 0.016332 seconds\n", "1\n", "2\n", "5\n", "6\n", "Computed ERIs in 0.046598 seconds\n", "MOs =\n", "\n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0.996612 -0.227167 -0 -0 0\n", " 2 0.0192375 0.476116 -0 -0 2.6158E-15\n", " 3 0 2.03898E-15 -0.311528 0.112708 0.385089\n", " ... ... ... ... ...\n", " 7 0 -1.27056E-15 -0.2512 0.160842 0.549548\n", " 8 0 -3.86977E-16 0.0682945 0.640967 -0.133725\n", " 9 0 -2.94182E-16 0.430493 -0.00783052 0.341885\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 -0 0.0754634 -4.03636E-15 -5.48678E-15\n", " 2 2.47356E-15 -1.66012 9.26322E-14 1.31026E-13\n", " 3 0.521643 9.10799E-14 0.273858 0.935677\n", " ... ... ... ...\n", " 7 -0.553226 -8.12878E-14 -0.248658 -0.849577\n", " 8 0.150407 -3.91558E-14 -0.990908 0.206736\n", " 9 0.948091 -3.91643E-14 0.0121041 -0.52854\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 -36.54848161 7.4861e-01 0.2723\n", " 2 -37.55037352 1.9776e-01 0.4104\n", " 3 -37.58727938 3.0130e-02 0.4115\n", " 4 -37.58813705 7.2124e-03 0.4099\n", " 5 -37.58819378 2.3539e-03 0.4094\n", " 6 -37.58820226 1.0327e-03 0.4092\n", " 7 -37.58820371 4.5157e-04 0.4091\n", " 8 -37.58820396 1.9102e-04 0.4091\n", " 9 -37.58820401 8.0044e-05 0.4091\n", " 10 -37.58820402 3.3447e-05 0.4091\n", " ------------------------------------------------------------\n", "\n", "\n", " ============================================================\n", " One-electron energy -50.3759860187\n", " Kinetic 37.5972073815\n", " Potential -87.9731934002\n", " -------------------------------------------------------- \n", " Two-electron energy 12.7877820020\n", " Coulomb 17.8173369652\n", " Exchange -5.0295549632\n", " -------------------------------------------------------- \n", " HF HOMO -9.3108539820\n", " HF LUMO 1.8212205669\n", " HF LUMO-LUMO 11.1320745489\n", " -------------------------------------------------------- \n", " Electronic energy -37.5882040167\n", " Nuclear repulsion 0.0000000000\n", " Hartree-Fock energy -37.5882040167\n", " ============================================================\n", " \n", "\n" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mo_basis : MOBasis.t =\n", " Eigenvalues: -11.348496 -0.709564 -0.342166 0.066926 0.066926 \n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0.996612 -0.227167 -0 -0 0\n", " 2 0.0192375 0.476116 -0 -0 2.6158E-15\n", " 3 0 2.03898E-15 -0.311528 0.112708 0.385089\n", " ... ... ... ... ...\n", " 7 0 -1.27056E-15 -0.2512 0.160842 0.549548\n", " 8 0 -3.86977E-16 0.0682945 0.640967 -0.133725\n", " 9 0 -2.94182E-16 0.430493 -0.00783052 0.341885\n", " \n", " Eigenvalues: 0.758670 0.787535 0.789515 0.789515 \n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 -0 0.0754634 -4.03636E-15 -5.48678E-15\n", " 2 2.47356E-15 -1.66012 9.26322E-14 1.31026E-13\n", " 3 0.521643 9.10799E-14 0.273858 0.935677\n", " ... ... ... ...\n", " 7 -0.553226 -8.12878E-14 -0.248658 -0.849577\n", " 8 0.150407 -3.91558E-14 -0.990908 0.206736\n", " 9 0.948091 -3.91643E-14 0.0121041 -0.52854\n", " \n", " \n" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let hf = HartreeFock.make ~guess:`Hcore ~max_scf:10 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": 70, "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": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mo_num : int = 9\n" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = \n" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val pp_det : Format.formatter -> Determinant.t -> unit = \n" ] }, "execution_count": 70, "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": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val simulation_aux : Simulation.t = \n" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "66 significant shell pairs computed in 0.062429 seconds\n", "1\n", "2\n", "5\n", "6\n", "9\n", "10\n", "11\n", "12\n", "15\n", "18\n", "Computed ERIs in 0.799183 seconds\n" ] }, { "data": { "text/plain": [ "val aux_basis : MOBasis.t =\n", " Eigenvalues: -11.348496 -0.709564 -0.342166 0.066926 0.066926 \n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0.996612 -0.227167 -1.55889E-11 -6.35567E-12 -1.34954E-12\n", " 2 0.0192375 0.476116 -3.63701E-12 2.3503E-12 -1.30322E-12\n", " 3 -1.94978E-12 1.78028E-12 -0.311528 0.112708 0.385089\n", " ... ... ... ... ...\n", " 22 0 0 -0 0 -0\n", " 23 0 0 -0 0 -0\n", " 24 0 0 -0 0 -0\n", " \n", " Eigenvalues: 0.758670 0.787535 0.789515 0.789515 1.401263 \n", " -- 6 -- -- 7 -- -- 8 -- -- 9 -- -- 10 --\n", " 1 1.68715E-11 0.0754634 -3.20267E-12 -2.55841E-12 5.89356E-13\n", " 2 2.50504E-12 -1.66012 5.42225E-13 5.5698E-12 4.15278E-13\n", " 3 0.521643 9.98939E-13 0.273858 0.935677 -1.60551E-12\n", " ... ... ... ... ...\n", " 22 0 0 0 -0 0.866025\n", " 23 0 0 0 -0 -0\n", " 24 5.34208E-16 0 -5.0103E-16 -5.16533E-16 -0\n", " \n", " Eigenvalues: 1.041443 1.042290 1.054347 1.485261 25.739829 \n", " -- 11 -- -- 12 -- -- 13 -- -- 14 -- -- 15 --\n", " 1 -5.48487E-10 -1.11498E-09 6.09785E-10 5.77229 1.19123E-08\n", " 2 -1.94824E-10 3.47045E-11 4.11571E-12 -21.703 -1.7907E-09\n", " 3 -9.41452 3.69747 -0.652915 2.28355E-11 -103.655\n", " ... ... ... ... ...\n", " 22 0 2.26934E-14 3.81775E-14 0 4.22204E-13\n", " 23 0 -0 -0 0 0\n", " 24 1.19652E-14 -4.56971E-14 -7.36206E-14 0 -8.2604E-13\n", " \n", " Eigenvalues: 25.783000 25.748833 17.771759 378.085285 1.415838 \n", " -- 16 -- -- 17 -- -- 18 -- -- 19 -- -- 20 --\n", " 1 -1.21774E-08 -2.0721E-08 20.5865 436.893 -8.50365E-11\n", " 2 -3.08075E-09 -3.38443E-10 -125.907 -12.7961 3.11494E-12\n", " 3 -138.626 11.0904 3.97511E-09 -1.32873E-09 -7.82399E-11\n", " ... ... ... ... ...\n", " 22 -5.42356E-13 5.36689E-13 -0 0 0.499656\n", " 23 0 0 -0 0 3.09005E-06\n", " 24 1.06385E-12 -1.07453E-12 -0 0 -0.999313\n", " \n", " Eigenvalues: 1.404881 1.410962 1.410166 \n", " -- 21 -- -- 22 -- -- 23 --\n", " 1 3.87235E-12 -1.73871E-12 3.46244E-11\n", " 2 -1.41864E-13 6.38182E-14 -1.23539E-12\n", " 3 -2.83484E-12 -3.14844E-12 0\n", " ... ... ...\n", " 22 -0.0166614 0.0081182 -1.77664E-05\n", " 23 0.000220122 0.00245004 0.999997\n", " 24 0.0333229 -0.0162364 3.55327E-05\n", " \n", " \n" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val aux_num : int = 23\n" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "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 aux_num = \n", " MOBasis.size aux_basis\n" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "66 significant shell pairs computed in 1.000310 seconds\n", "1\n", "2\n", "5\n", "6\n", "9\n", "10\n", "11\n", "12\n", "15\n", "18\n", "Computed ERIs in 18.798852 seconds\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "4-idx transformation \n", "23 / 23\n", "4-idx transformation \n", "23 / 23\n" ] } ], "source": [ "let () = ignore @@ MOBasis.f12_ints aux_basis\n", "let () = ignore @@ MOBasis.two_e_ints aux_basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integral-based functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{equation}\n", "\\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", "\\end{equation}\n", "\n", "\n", "\\begin{equation}\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}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val cancel_singles : bool = false\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mos_cabs : int list =\n", " [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mos_abs : int list =\n", " [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21;\n", " 22; 23]\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mos_in : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mos_a : Determinant.t -> int list = \n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val mos_b : Determinant.t -> int list = \n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let cancel_singles = false \n", "\n", "let mos_cabs = \n", " Util.list_range (mo_num+1) aux_num\n", " \n", "let mos_abs = \n", " Util.list_range 1 aux_num\n", " \n", "let mos_in = \n", " Util.list_range 1 mo_num\n", "\n", "let mos_a k =\n", " Determinant.alfa k\n", " |> Spindeterminant.to_list\n", " \n", "let mos_b k =\n", " Determinant.beta k\n", " |> Spindeterminant.to_list\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### H integrals" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val h_one : int -> int -> '_weak1 -> float = \n" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let h_one =\n", " let h = \n", " MOBasis.one_e_ints aux_basis\n", " in fun i j _ -> h.{i,j}\n", " \n", "let h_two = \n", " let two_e_ints = MOBasis.two_e_ints aux_basis in\n", " let h2 i j k l (s:Spin.t) (s':Spin.t) =\n", " if s' <> s then\n", " ERI.get_phys two_e_ints i j k l\n", " else\n", " (ERI.get_phys two_e_ints i j k l) -. \n", " (ERI.get_phys two_e_ints i j l k)\n", " in\n", " h2\n", "\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### F12 integrals" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val f_one : 'a -> 'b -> 'c -> float = \n" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let f_two = \n", " let two_e_ints = MOBasis.f12_ints aux_basis in\n", " let f2 i j k l (s:Spin.t) (s':Spin.t) =\n", " if s' <> s then\n", " 0.5 *. F12.get_phys two_e_ints i j k l\n", " else\n", " 0.5 *. (\n", " (F12.get_phys two_e_ints i j k l) -. \n", " (F12.get_phys two_e_ints i j l k) )\n", " in\n", " let f3 i j k l (s:Spin.t) (s':Spin.t) = \n", " if (i=k && j<>l) || (j=l && i<>k) then\n", " 0.\n", " else\n", " f2 i j k l s s'\n", " in\n", " if cancel_singles then f3 else f2\n", "\n", "let f_one = fun _ _ _ -> 0.\n", "\n", "(*\n", "let f_two = h_two\n", "\n", "let f_one = h_one\n", "*)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Determinant-based functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Integrals" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val f12_integrals :\n", " 'a ->\n", " ('b -> 'c -> 'd -> float) *\n", " (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'e option = \n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", " \n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", " \n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val hf_ij :\n", " MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n", " \n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let f12_integrals mo_basis =\n", " ( f_one, f_two, None )\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": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = \n" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "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": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of determinants : 84 84 7056\n" ] }, { "data": { "text/plain": [ "val in_space : DeterminantSpace.t = \n" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Number of determinants : 1771 1771 3136441\n" ] }, { "data": { "text/plain": [ "val aux_space : DeterminantSpace.t = \n" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val det_space_in : unit -> Determinant.t Stream.t = \n" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = \n" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let in_space = \n", " DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n", " \n", "let aux_space = \n", " DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core \n", "\n", "let det_space_in () =\n", " DeterminantSpace.determinant_stream in_space\n", "\n", "let det_space_out () =\n", " let s = \n", " DeterminantSpace.determinant_stream aux_space\n", " in\n", " Stream.from (fun _ ->\n", " try\n", " let is_a_double = is_a_double in_space in\n", " let rec result () =\n", " let ki = Stream.next s in\n", " if is_a_double ki then\n", " Some (ki,ki)\n", " else\n", " result ()\n", " in\n", " result ()\n", " with Stream.Failure -> None\n", " )\n", " " ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val ci : CI.t =\n", " {CI.e_shift = -37.5503735182818161; det_space = ; m_H = ;\n", " m_S2 = ; eigensystem = ; n_states = 1}\n" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ " 1 0.0000000000 4.27876360e-01\n", " 2 -0.0892428570 1.30475542e-01\n", " 3 -0.0992140799 8.74622675e-02\n", " 4 -0.1022422032 2.82063712e-02\n", " 5 -0.1043598763 3.75067204e-02\n", " 6 -0.1065557047 4.71900892e-02\n", " 7 -0.1080257392 1.17050936e-02\n", " 8 -0.1082438239 4.19578866e-03\n", " 0 -0.1082636731 1.74312968e-03\n", " 1 -0.1082673304 7.12907991e-04\n", " 2 -0.1082677273 3.29773895e-04\n", " 3 -0.1082677955 1.62017305e-04\n", " 4 -0.1082678250 1.97376527e-04\n", " 5 -0.1082678653 1.65667298e-04\n", " 6 -0.1082678853 1.24231373e-04\n", " 7 -0.1082678901 1.06697885e-05\n", " 8 -0.1082678902 5.05286976e-06\n", " 0 -0.1082678902 2.52891309e-06\n" ] }, { "data": { "text/plain": [ "val ci_coef : Lacaml.D.Mat.t =\n", " \n", "\n", " -- 1 --\n", " 1 -0.780949\n", " 2 -0\n", " 3 -0\n", " ...\n", " 7054 -0\n", " 7055 -0\n", " 7056 -3.12865E-06\n", " \n", "val ci_energy : Lacaml.D.Vec.t =\n", " R1 R2 R3\n", " -37.6586 -36.7238 -36.2286\n" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ " 1 -0.1082678902 4.37908381e-07\n", "\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let ci = CI.make ~n_states:state in_space\n", "\n", "let ci_coef, ci_energy = Lazy.force ci.eigensystem \n", "\n", "let _ = print_newline () \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": [ "## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "let randomize = false\n", "\n", "let out_list =\n", " Util.stream_to_list (det_space_out ())\n", " \n", "let in_list =\n", " Util.stream_to_list (det_space_in ())\n", " \n", "let det_a = Array.of_list out_list\n", " |> Array.map (fun (i,_) -> i)\n", "\n", "let det_I =\n", " if randomize then\n", " let n = 123456789 in\n", " in_list\n", " |> List.map (fun k -> (Random.int n, k))\n", " |> List.sort compare\n", " |> List.map (fun (_,k) -> k)\n", " |> Array.of_list\n", " else\n", " Array.of_list in_list\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/markdown" }, "source": [ "let m_H_aux, m_F_aux = \n", " \n", " let rec col_vecs_list accu_H accu_F = function\n", " | [] -> \n", " List.rev accu_H, \n", " List.rev accu_F \n", " | (ki, ki') :: rest when ki = ki' ->\n", " begin\n", " let h, f = \n", " List.map (fun kj ->\n", " match hf_ij aux_basis kj ki with\n", " | [ a ; b ] -> a, b\n", " | _ -> assert false ) in_list\n", " |> List.split\n", " in\n", " let h = Vec.of_list h in\n", " let f = Vec.of_list f in\n", " scal 0.5 f; (* Specific to He singlet *)\n", " col_vecs_list (h::accu_H) (f::accu_F) rest\n", " end\n", " | (ki, ki') :: rest ->\n", " begin\n", " assert false;\n", " end\n", " in\n", " let h, f = \n", " col_vecs_list [] [] out_list\n", " in\n", " Mat.of_col_vecs_list h,\n", " Mat.of_col_vecs_list f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n", "\n", "* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$\n", "* `cabs` is the number of electrons in the CABS\n", "* `l` is the degree of excitation between $|I\\rangle$ and $|\\alpha \\rangle$\n", "* `r` is the degree of excitation between $|\\alpha \\rangle$ and $|J\\rangle$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val generate_alphas :\n", " Determinant.t ->\n", " Determinant.t -> int -> int -> int -> int -> Determinant.t list = \n" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val compute_HaaF :\n", " CIMatrixElement.De.t ->\n", " CIMatrixElement.De.t list -> CIMatrixElement.De.t -> float = \n" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let generate_alphas ki kj exc cabs l r =\n", " (* Check input excitation degree *)\n", " let d = Determinant.degree ki kj in\n", " if d <> exc then\n", " Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n", " |> failwith;\n", " \n", " (* Generate single excitations *)\n", " let all_singles ki =\n", " let mos_a, mos_b = Determinant.to_lists ki in\n", " [ List.map (fun hole -> \n", " List.map (fun particle ->\n", " if hole = particle then None else\n", " Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n", " ) mos_abs\n", " ) mos_a\n", " ;\n", " List.map (fun hole -> \n", " List.map (fun particle ->\n", " if hole = particle then None else\n", " Some (Determinant.single_excitation Spin.Beta hole particle ki)\n", " ) mos_abs\n", " ) mos_b \n", " ]\n", " |> List.concat\n", " |> List.concat\n", " |> Util.list_some\n", " |> List.filter (fun x -> Determinant.is_none x = false)\n", " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", " in\n", " \n", " (* Generate double excitations *)\n", " let all_doubles ki =\n", " let mos_a, mos_b = Determinant.to_lists ki in\n", " [ List.map (fun hole -> (* Alpha-Alpha *)\n", " List.map (fun particle ->\n", " List.map (fun hole' -> \n", " List.map (fun particle' ->\n", " if hole = particle || hole' = particle' then None else\n", " if hole' > hole && particle' < particle then\n", " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n", " else None\n", " ) mos_abs\n", " ) mos_a \n", " ) mos_abs\n", " ) mos_a\n", " ; \n", " List.map (fun hole -> (* Beta-Beta *)\n", " List.map (fun particle ->\n", " List.map (fun hole' -> \n", " List.map (fun particle' ->\n", " if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n", " Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n", " else None\n", " ) mos_abs\n", " ) mos_b \n", " ) mos_abs\n", " ) mos_b\n", " ;\n", " List.map (fun hole -> (* Alpha-Beta *)\n", " List.map (fun particle ->\n", " List.map (fun hole' -> \n", " List.map (fun particle' ->\n", " if hole = particle || hole' = particle' then None else\n", " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n", " ) mos_abs\n", " ) mos_b \n", " ) mos_abs\n", " ) mos_a\n", " ]\n", " |> List.concat\n", " |> List.concat\n", " |> List.concat\n", " |> List.concat\n", " |> Util.list_some\n", " |> List.filter (fun x -> Determinant.is_none x = false)\n", " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", " in\n", "\n", " (* Generate left and right excitations *)\n", " let al = \n", " match l with\n", " | 1 -> all_singles ki\n", " | 2 -> all_doubles ki\n", " | _ -> assert false\n", " in\n", " let ar = \n", " match r with\n", " | 1 -> all_singles kj\n", " | 2 -> all_doubles kj\n", " | _ -> assert false\n", " in\n", " \n", " let mo_class = DeterminantSpace.mo_class in_space 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 good_cabs 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", " Bitstring.popcount a + Bitstring.popcount b = cabs\n", " in\n", " let good_lr k =\n", " Determinant.degree ki k = l &&\n", " Determinant.degree k kj = r \n", " in\n", "\n", "\n", " \n", " (* Merge lists in a set of unique determinants *)\n", " List.concat [ al; ar ]\n", " |> List.sort_uniq compare\n", " \n", " (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n", " |> List.filter good_cabs \n", " \n", " (* Filter out all determinants with incorrect excitation numbers *)\n", " |> List.filter good_lr \n", " \n", " \n", "let compute_HaaF ki alphas kj =\n", " List.fold_left (fun accu alpha -> accu\n", " +. h_ij aux_basis ki alpha\n", " *. f_ij aux_basis alpha kj\n", " ) 0. alphas\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val check :\n", " int ->\n", " (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) ->\n", " int -> int -> int -> int -> unit = \n" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val sum : 'a list -> ('a -> float) -> float = \n" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let check n integral_value exc cabs lexc rexc =\n", " let cpudet, cpuint = ref 0., ref 0. in\n", " let det_list =\n", " match n with\n", " | 0 -> det_I\n", " | n -> Array.sub det_I 0 n\n", " in\n", " let result =\n", " Printf.printf \"Checking ... \\n%!\";\n", " let percent = ref 0 in\n", " let task (i,ki) =\n", " (let p = (10 * (i+1))/(Array.length det_list) in\n", " if p <> !percent then\n", " ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n", " Array.mapi (fun j kj -> \n", " if i > j || Determinant.degree ki kj <> exc then\n", " (0,0,0.,0.)\n", " else\n", " begin\n", " let alphas = generate_alphas ki kj exc cabs lexc rexc in\n", " let det_value =\n", " let t0 = Unix.gettimeofday () in\n", " let result = compute_HaaF ki alphas kj in\n", " cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n", " result\n", " in\n", " let int_value = \n", " let t0 = Unix.gettimeofday () in\n", " let result = integral_value ki kj in\n", " cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n", " result\n", " in\n", "(* Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value; *)\n", " (i,j,det_value,int_value)\n", " end\n", " ) det_list\n", " in\n", " det_list\n", " |> Array.mapi (fun i ki -> (i,ki))\n", " |> Array.to_list\n", " |> Stream.of_list\n", " |> Farm.run ~f:task\n", " |> Util.stream_to_list\n", " |> Array.concat\n", " in\n", " let i,j,d,v = \n", " let rec aux k imax jmax emax dmax vmax = \n", " if k = -1 then\n", " imax, jmax, dmax, vmax\n", " else\n", " let i, j, d, v = result.(k) in\n", " let e = abs_float (d -. v) in\n", " if e >= emax then\n", " aux (k-1) i j e d v\n", " else\n", " aux (k-1) imax jmax emax dmax vmax\n", " in\n", " aux (Array.length result - 1) 0 0 0. 0. 0.\n", " in\n", " let error = abs_float (d -. v) in\n", " if error < epsilon_float then\n", " (*\n", " Printf.printf \"OK: %e\\n%!\" error\n", " *)\n", " Printf.printf \"OK: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", " else\n", " Printf.printf \"Failed: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", "\n", " \n", "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val array_3_init :\n", " int ->\n", " int ->\n", " int ->\n", " (int -> int -> int -> float) ->\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val array_4_init :\n", " int ->\n", " int ->\n", " int ->\n", " int ->\n", " (int -> int -> int -> int -> float) ->\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val array_5_init :\n", " int ->\n", " int ->\n", " int ->\n", " int ->\n", " int ->\n", " (int -> int -> int -> int -> int -> float) ->\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let array_3_init d1 d2 d3 f =\n", " let result = \n", " Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3\n", " in\n", " for k=1 to d3 do\n", " for j=1 to d2 do\n", " for i=1 to d1 do\n", " result.{i,j,k} <- f i j k\n", " done\n", " done\n", " done;\n", " result\n", "\n", "\n", "let array_4_init d1 d2 d3 d4 f =\n", " let result = \n", " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n", " in\n", " for l=1 to d4 do\n", " for k=1 to d3 do\n", " for j=1 to d2 do\n", " for i=1 to d1 do\n", " result.{i,j,k,l} <- f i j k l\n", " done\n", " done\n", " done\n", " done;\n", " result\n", "\n", "\n", "let array_5_init d1 d2 d3 d4 d5 f =\n", " let result = \n", " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n", " in\n", " for m=1 to d5 do\n", " for l=1 to d4 do\n", " for k=1 to d3 do\n", " for j=1 to d2 do\n", " for i=1 to d1 do\n", " result.{i,j,k,l,m} <- f i j k l m\n", " done\n", " done\n", " done\n", " done\n", " done;\n", " result\n", "\n", "(* ----- *)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "******" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1. 0 1 11" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : Jupyter_notebook.display_id = \n" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let _ = png_image \"0_1_11.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", "\n", "$\\sum_i \\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{i}$\n", "\n", "\\begin{align}\n", "\\sum_{a} \\sum_{i}\n", " \\left( h_{ia} +\n", " \\sum_{j} \\langle i j || a j \\rangle +\n", " \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n", " \\left( f_{ai} +\n", " \\sum_{j} \\left[ a j || i j \\right] + \n", " \\sum_{\\bar{j}} \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) + \\\\\n", "\\sum_{\\bar{a}} \\sum_{\\bar{i}}\n", " \\left( h_{ia} +\n", " \\sum_{j} \\langle \\bar{i} j | \\bar{a} j \\rangle +\n", " \\sum_{\\bar{j}} \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n", " \\left( f_{ai} +\n", " \\sum_{j} \\left[ \\bar{a} j | \\bar{i} j \\right] + \n", " \\sum_{\\bar{j}} \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right) \n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val integral_value : Determinant.t -> 'a -> float = \n" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (2725, 2725) | -3.638004e-01 -3.638004e-01 | 1.665335e-16 | cpu : 7.381801 1.597322\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " (* Alpha-Beta *)\n", " let s, s' = Spin.(Alfa, Beta) in \n", " let mos_a, mos_b = mos_a ki, mos_b ki in\n", " \n", " sum mos_cabs (fun a ->\n", " sum mos_a (fun i -> \n", " (h_one i a s +.\n", " sum mos_a (fun j -> h_two i j a j s s ) +.\n", " sum mos_b (fun j -> h_two i j a j s s') ) *. \n", " (f_one a i s +.\n", " sum mos_a (fun j -> f_two a j i j s s ) +.\n", " sum mos_b (fun j -> f_two a j i j s s') )\n", " )\n", " +.\n", " sum mos_b (fun i -> \n", " (h_one i a s +.\n", " sum mos_b (fun j -> h_two i j a j s' s') +.\n", " sum mos_a (fun j -> h_two i j a j s' s ) ) *. \n", " (f_one a i s +.\n", " sum mos_a (fun j -> f_two a j i j s' s ) +.\n", " sum mos_b (fun j -> f_two a j i j s' s') )\n", " ) \n", " ) \n", " \n", "let _ =\n", " check 0 integral_value 0 1 1 1\n", " " ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val m_0111_1H_1F : Lacaml.D.vec = R1 R2 R3 R7 R8 R9\n", " 0 0 0 ... 0 0 0\n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_1H_2Fa : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0 4.14739E-05 0.000191942 5.82024E-05 3.17097E-05\n", " 2 0.00441404 0 0.00130171 0.000700762 0.000516783\n", " 3 0.00947473 0.00340706 0 0.00113769 0.000719119\n", " ... ... ... ... ...\n", " 7 0.00330602 0.00100192 0.00129118 0.000663876 0.000505817\n", " 8 0.0342633 0.0165417 0.0159678 0.00914699 0.00756616\n", " 9 0.0351294 0.0167331 0.0160539 0.00925644 0.00811228\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 0.000201052 -1.30724E-06 0.000334792 0.000361285\n", " 2 0.000232155 -0.00168232 0.000833107 0.00101709\n", " 3 -0.00387499 0.000450358 0.00302133 0.0034399\n", " ... ... ... ...\n", " 7 0.000755987 0 0.00138329 0.00154135\n", " 8 0.00932835 0.00680096 0 0.01773\n", " 9 0.00932584 0.00668845 0.0161232 0\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_1H_2Fb : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0.00240706 0.000203061 0.000204496 6.9114E-05 3.98705E-05\n", " 2 0.00453599 0.000921371 0.00101171 0.00018998 6.05419E-06\n", " 3 0.010046 0.00215252 0.00186996 0.000735619 0.00032706\n", " ... ... ... ... ...\n", " 7 0.00333148 0.00134734 0.00136183 0.000678955 0.000509352\n", " 8 0.03544 0.0162787 0.0160193 0.00909405 0.00750383\n", " 9 0.0363843 0.016229 0.0160429 0.00913626 0.00685374\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 0.000172239 0.000122518 0.000307621 0.000336864\n", " 2 0.000706018 0.000468703 0.00152775 0.00171167\n", " 3 0.00115063 0.000924145 0.0033018 0.00371036\n", " ... ... ... ...\n", " 7 0.000821248 0.000738693 0.00150412 0.00167373\n", " 8 0.00938437 0.0089191 0.0164475 0.0178998\n", " 9 0.00941992 0.00884667 0.0163266 0.018548\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Ha_1F : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0 0 0 0 0\n", " 2 0 0 0 0 0\n", " 3 0 0 0 0 0\n", " ... ... ... ... ...\n", " 7 0 0 0 0 0\n", " 8 0 0 0 0 0\n", " 9 0 0 0 0 0\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 0 0 0 0\n", " 2 0 0 0 0\n", " 3 0 0 0 0\n", " ... ... ... ...\n", " 7 0 0 0 0\n", " 8 0 0 0 0\n", " 9 0 0 0 0\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Hb_1F : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0 0 0 0 0\n", " 2 0 0 0 0 0\n", " 3 0 0 0 0 0\n", " ... ... ... ... ...\n", " 7 0 0 0 0 0\n", " 8 0 0 0 0 0\n", " 9 0 0 0 0 0\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 0 0 0 0\n", " 2 0 0 0 0\n", " 3 0 0 0 0\n", " ... ... ... ...\n", " 7 0 0 0 0\n", " 8 0 0 0 0\n", " 9 0 0 0 0\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0111_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value : Determinant.t -> 'a -> float = \n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (416, 416) | -1.497602e-01 -1.497602e-01 | 1.110223e-16 | cpu : 7.418296 0.113910\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_0111_1H_1F = \n", " Vec.init mo_num (fun i -> \n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))\n", "\n", " \n", "let m_0111_1H_2Fa = \n", " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa ))\n", "\n", " \n", "let m_0111_1H_2Fb = \n", " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta ))\n", "\n", "\n", "let m_0111_2Ha_1F = \n", " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa ))\n", "\n", " \n", "let m_0111_2Hb_1F = \n", " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa ))\n", "\n", "\n", "let m_0111_2Ha_2Fa =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *.\n", " f_two a k i k Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_0111_2Hb_2Fa =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *.\n", " f_two a k i k Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_0111_2Ha_2Fb =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *.\n", " f_two a k i k Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let m_0111_2Hb_2Fb =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *.\n", " f_two a k i k Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "\n", "let integral_value ki kj = \n", "\n", " let mos_a, mos_b = mos_a ki, mos_b ki in\n", " \n", " sum mos_a (fun i ->\n", " m_0111_1H_1F.{i} +. \n", " sum mos_a (fun j ->\n", " m_0111_1H_2Fa.{i,j} +. m_0111_2Ha_1F.{i,j} +.\n", " sum mos_a (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n", " sum mos_b (fun k -> m_0111_2Ha_2Fb.{i,j,k})) +.\n", " sum mos_b (fun j ->\n", " m_0111_1H_2Fb.{i,j} +. m_0111_2Hb_1F.{i,j} +.\n", " sum mos_a (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n", " sum mos_b (fun k -> m_0111_2Hb_2Fb.{i,j,k}))\n", " )\n", " +.\n", " sum mos_b (fun i ->\n", " m_0111_1H_1F.{i} +. \n", " sum mos_b (fun j ->\n", " m_0111_1H_2Fa.{i,j} +. m_0111_2Ha_1F.{i,j} +.\n", " sum mos_b (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n", " sum mos_a (fun k -> m_0111_2Ha_2Fb.{i,j,k})) +.\n", " sum mos_a (fun j ->\n", " m_0111_1H_2Fb.{i,j} +. m_0111_2Hb_1F.{i,j} +.\n", " sum mos_b (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n", " sum mos_a (fun k -> m_0111_2Hb_2Fb.{i,j,k}))\n", " )\n", " \n", "let _ =\n", " check 0 integral_value 0 1 1 1\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. 0 1 22" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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}, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : Jupyter_notebook.display_id = \n" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let _ = png_image \"0_1_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", "\n", "$k$ : orbital indices of MOs unoccupied in $|I\\rangle$.\n", "\n", "$\\sum_i \\sum_a \\sum_j \\sum_k \\hat{T}_{ij}^{ak} \\hat{T}_{ak}^{ij}$\n", "\n", "\n", "\\begin{align}\n", "\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j Determinant.t -> float = \n" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (96, 96) | -3.551300e-02 -3.551300e-02 | 4.163336e-17 | cpu : 1.998001 0.120893\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " (* mos unoccupied in both I and J *)\n", " let mos_virt_a, mos_virt_b = \n", " Array.init mo_num (fun i -> Some (i+1)) , \n", " Array.init mo_num (fun i -> Some (i+1)) \n", " in\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", " \n", " let mos_virt_a, mos_virt_b = \n", " Array.to_list mos_virt_a |> Util.list_some,\n", " Array.to_list mos_virt_b |> Util.list_some\n", " in\n", " \n", " (* Alpha-Beta *)\n", " let s, s' = Spin.(Alfa, Beta) in\n", " sum mos_cabs (fun a ->\n", " sum (mos_b ki) (fun j -> \n", " sum (mos_a ki) (fun i -> \n", " sum mos_virt_b (fun k -> \n", " h_two i j a k s s' *. f_two a k i j s s'\n", " )))\n", " +.\n", " sum (mos_a ki) (fun j -> \n", " sum (mos_b ki) (fun i -> \n", " sum mos_virt_a (fun k -> \n", " h_two i j a k s s' *. f_two a k i j s s'\n", " )))) \n", " +.\n", " (* Alpha-Alpha / Beta-Beta *)\n", " List.fold_left (fun accu (mos_virt,mos,s) -> \n", " let s' = s in accu +.\n", " sum mos (fun j -> \n", " sum mos (fun i -> if i < j then 0. else\n", " sum mos_virt (fun k -> \n", " sum mos_cabs (fun a -> \n", " h_two i j a k s s' *. f_two a k i j s s'\n", " )))) \n", " ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n", " \n", "let _ =\n", " check 100 integral_value 0 1 2 2\n", " " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val m_0122_Haa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0122_Hab :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (96, 96) | -3.551300e-02 -3.551300e-02 | 4.163336e-17 | cpu : 1.975414 0.002633\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_0122_Haa = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n", " ) )\n", " \n", "let m_0122_Hab = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n", " ) )\n", "\n", "\n", "let integral_value ki kj = \n", " (* mos unoccupied in both I and J *)\n", " let mos_virt_a, mos_virt_b = \n", " Array.init mo_num (fun i -> Some (i+1)) , \n", " Array.init mo_num (fun i -> Some (i+1)) \n", " in\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", " \n", " let mos_virt_a, mos_virt_b = \n", " Array.to_list mos_virt_a |> Util.list_some,\n", " Array.to_list mos_virt_b |> Util.list_some\n", " in\n", " \n", " let result = \n", " sum (mos_a ki) (fun i -> \n", " sum (mos_b ki) (fun j -> \n", " sum mos_virt_b (fun k -> m_0122_Hab.{i,j,k} )))\n", " +.\n", " sum (mos_b ki) (fun i -> \n", " sum (mos_a ki) (fun j -> \n", " sum mos_virt_a (fun k -> m_0122_Hab.{i,j,k} )))\n", " +.\n", " (* Alpha-Alpha / Beta-Beta *)\n", " List.fold_left (fun accu (mos_virt,mos) -> \n", " accu +.\n", " sum mos (fun j -> \n", " sum mos (fun i -> if i <= j then 0. else\n", " sum mos_virt (fun k -> m_0122_Haa.{i,j,k} )))\n", " ) 0. [ (mos_virt_a,mos_a ki) ; (mos_virt_b,mos_b ki)]\n", " in \n", " result\n", " \n", "let _ =\n", " check 100 integral_value 0 1 2 2\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. 0 2 22" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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}, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : Jupyter_notebook.display_id = \n" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let _ = png_image \"0_2_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", "\n", "$\\sum_i \\sum_a \\sum_j \\sum_b \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{ij}$\n", "\n", "\\begin{align}\n", "\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n", " \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n", " \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val integral_value : Determinant.t -> 'a -> float = \n" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (6, 6) | -5.846493e-03 -5.846493e-03 | 1.821460e-17 | cpu : 2.262464 0.188633\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " (* Alpha-Beta *)\n", " let s, s' = Spin.(Alfa, Beta) in\n", " sum mos_cabs (fun a -> \n", " sum mos_cabs (fun b -> \n", " sum (mos_a ki) (fun i -> \n", " sum (mos_b ki) (fun j -> \n", " h_two i j a b s s' *. f_two a b i j s s'\n", " ))))\n", " +.\n", " (* Alpha-Alpha / Beta-Beta *)\n", " List.fold_left (fun accu (mos,s) -> \n", " let s' = s in accu +.\n", " sum mos_cabs (fun b -> \n", " sum mos_cabs (fun a -> if b > a then 0. else\n", " sum mos (fun j -> \n", " sum mos (fun i -> if i < j then 0. else\n", " h_two i j a b s s' *. f_two a b i j s s'\n", " ))))\n", " ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n", " \n", "let _ =\n", " check 100 integral_value 0 2 2 2\n", " " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val m_0222_Haa : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0 -6.71384E-07 -9.968E-05 -6.45073E-05 -5.27031E-05\n", " 2 -6.71384E-07 0 -4.68481E-05 -2.57378E-05 -2.05896E-05\n", " 3 -9.968E-05 -4.68481E-05 0 -0.00237038 -0.00210405\n", " ... ... ... ... ...\n", " 7 3.23766E-08 -1.08041E-05 -0.000287197 -0.000198078 -0.00017547\n", " 8 -5.45331E-05 -5.28682E-05 -0.000600588 -1.92121E-05 -0.000295033\n", " 9 -6.63373E-05 -5.80165E-05 -0.000866918 -0.000558093 -1.92121E-05\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 -1.93604E-05 3.23766E-08 -5.45331E-05 -6.63373E-05\n", " 2 -3.17579E-05 -1.08041E-05 -5.28682E-05 -5.80165E-05\n", " 3 -1.92121E-05 -0.000287197 -0.000600588 -0.000866918\n", " ... ... ... ...\n", " 7 -0.000208547 0 -0.000297666 -0.000320273\n", " 8 -0.000500592 -0.000297666 0 -0.000806147\n", " 9 -0.000497322 -0.000320273 -0.000806147 0\n", " \n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_0222_Hab : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 -0.000169963 -1.53492E-05 -0.000103698 -6.51009E-05 -5.22436E-05\n", " 2 -1.53492E-05 -0.0025733 -0.00022554 -0.000225645 -0.00021764\n", " 3 -0.000103698 -0.00022554 -0.00532837 -0.00229291 -0.00204143\n", " ... ... ... ... ...\n", " 7 -2.92509E-05 -5.57267E-05 -0.000425167 -0.000318692 -0.00029493\n", " 8 -5.57988E-05 -8.81786E-05 -0.000592839 -0.000542726 -0.00025893\n", " 9 -6.8656E-05 -9.61834E-05 -0.000844322 -0.000504532 -0.000746806\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 -1.72021E-05 -2.92509E-05 -5.57988E-05 -6.8656E-05\n", " 2 -8.82835E-05 -5.57267E-05 -8.81786E-05 -9.61834E-05\n", " 3 -0.000139913 -0.000425167 -0.000592839 -0.000844322\n", " ... ... ... ...\n", " 7 -0.000386756 -0.00048578 -0.000493231 -0.000516994\n", " 8 -0.000633297 -0.000493231 -0.00140435 -0.000967207\n", " 9 -0.000627417 -0.000516994 -0.000967207 -0.00165712\n", " \n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value : Determinant.t -> 'a -> float = \n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (6, 6) | -5.846493e-03 -5.846493e-03 | 1.908196e-17 | cpu : 2.250297 0.000800\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_0222_Haa = \n", " Mat.init_cols mo_num mo_num (fun i j ->\n", " sum mos_cabs (fun a ->\n", " sum mos_cabs (fun b -> if b >= a then 0. else\n", " h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n", " ) )\n", " )\n", " \n", "let m_0222_Hab = \n", " Mat.init_cols mo_num mo_num (fun i j ->\n", " sum mos_cabs (fun a ->\n", " sum mos_cabs (fun b ->\n", " h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n", " ) )\n", " )\n", " \n", "let integral_value ki kj = \n", " (* Alpha-Beta *)\n", " sum (mos_a ki) (fun i -> \n", " sum (mos_b ki) (fun j -> \n", " m_0222_Hab.{i,j} \n", " ))\n", " +.\n", " (* Alpha-Alpha / Beta-Beta *)\n", " List.fold_left (fun accu (mos) -> \n", " accu +.\n", " sum mos (fun j -> \n", " sum mos (fun i -> if i < j then 0. else\n", " m_0222_Haa.{i,j} \n", " ))\n", " ) 0. [ (mos_a ki) ; (mos_b ki)]\n", " \n", "let _ =\n", " check 100 integral_value 0 2 2 2\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. 1 1 11" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": "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}, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "- : Jupyter_notebook.display_id = \n" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let _ = png_image \"1_1_11.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", "\n", "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$\\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{k}$\n", "\n", "\\begin{align}\n", " \\sum_{a} \n", " \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n", " \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right)\n", " \\left( f_{ak} +\\sum_{j} \\left[ a j || k j \\right] + \n", " \\sum_{\\bar{j}} \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \\\\\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (0, 0) | 0.000000e+00 0.000000e+00 | 0.000000e+00 | cpu : 22.881818 5.474353\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos_i, mos_i' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", " let mos_j, mos_j' =\n", " match s with\n", " | Spin.Alfa -> mos_a kj, mos_b kj\n", " | Spin.Beta -> mos_b kj, mos_a kj\n", " in\n", "\n", " let result = \n", " let s' = Spin.other s in\n", " \n", " sum mos_cabs (fun a -> \n", " (h_one i a s +. \n", " sum mos_i (fun j -> h_two i j a j s s ) +.\n", " sum mos_i' (fun j -> h_two i j a j s s') ) *.\n", " (f_one a k s +. \n", " sum mos_j (fun j -> f_two a j k j s s ) +.\n", " sum mos_j' (fun j -> f_two a j k j s s') ) \n", " )\n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 0 integral_value 1 1 1 1" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val ki : Determinant.t =\n", " phase:+1\n", " a:+1 +------++-------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val kj : Determinant.t =\n", " phase:+1\n", " a:+1 ------+++-------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.0173816203798749\n" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let ki = det_I.(77)\n", "let kj = det_I.(83)\n", "\n", "let _ = integral_value ki kj" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val m_1111_1H_1F : Lacaml.D.mat =\n", " \n", "\n", " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", " 1 0 0 0 0 0\n", " 2 0 0 0 0 0\n", " 3 0 0 0 0 0\n", " ... ... ... ... ...\n", " 7 0 0 0 0 0\n", " 8 0 0 0 0 0\n", " 9 0 0 0 0 0\n", " \n", "\n", " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", " 1 0 0 0 0\n", " 2 0 0 0 0\n", " 3 0 0 0 0\n", " ... ... ... ...\n", " 7 0 0 0 0\n", " 8 0 0 0 0\n", " 9 0 0 0 0\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_1H_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_1H_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Ha_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Hb_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1111_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value_11 : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_1111_1H_1F = \n", " Mat.init_cols mo_num mo_num (fun i k -> \n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n", "\n", "\n", "let m_1111_1H_2Fa = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa ))\n", "\n", " \n", "let m_1111_1H_2Fb = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta ))\n", "\n", "\n", "let m_1111_2Ha_1F = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa ))\n", "\n", " \n", "let m_1111_2Hb_1F = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa ))\n", "\n", "\n", "let m_1111_2Ha_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *.\n", " f_two a l k l Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_1111_2Hb_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *.\n", " f_two a l k l Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_1111_2Ha_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Alfa *.\n", " f_two a l k l Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let m_1111_2Hb_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a j Spin.Alfa Spin.Beta *.\n", " f_two a l k l Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let integral_value_11 ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " let mos_a, mos_b =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in \n", " \n", " let result = \n", " m_1111_1H_1F.{i,k} +. \n", " sum mos_a (fun j -> if j = i then 0. else\n", " m_1111_1H_2Fa.{i,j,k} +. m_1111_2Ha_1F.{i,j,k} +.\n", " sum mos_a (fun l -> if l = i then 0. else m_1111_2Ha_2Fa.{i,j,k,l}) +.\n", " sum mos_b (fun l -> m_1111_2Ha_2Fb.{i,j,k,l})) +.\n", " sum mos_b (fun j ->\n", " m_1111_1H_2Fb.{i,j,k} +. m_1111_2Hb_1F.{i,j,k} +.\n", " sum mos_a (fun l -> if l = i then 0. else m_1111_2Hb_2Fa.{i,j,k,l}) +.\n", " sum mos_b (fun l -> m_1111_2Hb_2Fb.{i,j,k,l}))\n", " in\n", " \n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "(*\n", "let _ =\n", " check 0 integral_value_11 1 1 1 1\n", "*) \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 5. 1 1 12" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"1_1_12.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", "\n", "$\\sum_{j} \\sum_a \\hat{T}_{j}^{a} \\hat{T}_{ai}^{jk}$\n", "\n", "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "\\begin{align}\n", " \\sum_{a} \\sum_{j} \n", " \\left( h_{ja} +\\sum_{m} \\langle j m || a m \\rangle +\n", " \\sum_{\\bar{m}} \\langle j \\bar{m} | a \\bar{m} \\rangle \\right)\n", " \\left[ a i || j k \\right] + \\\\\n", " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n", " \\left( h_{\\bar{j}\\bar{a}} +\\sum_{m} \\langle \\bar{j} m | \\bar{a} m \\rangle +\n", " \\sum_{\\bar{m}} \\langle \\bar{j} \\bar{m} || \\bar{a} \\bar{m} \\rangle \\right)\n", " \\left[ \\bar{a} i | \\bar{j} k \\right] \n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let integral_value ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " \n", " let mos_i, mos_i' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", "\n", " let result = \n", " let s' = Spin.other s in\n", " sum mos_cabs (fun a -> \n", " sum mos_j (fun j -> \n", " (h_one j a s +. \n", " sum mos_i (fun m -> h_two j m a m s s ) +.\n", " sum mos_i' (fun m -> h_two j m a m s s') ) *.\n", " (f_two a i j k s s )\n", " ) \n", " +.\n", " sum mos_j' (fun j -> \n", " (h_one j a s +. \n", " sum mos_i (fun m -> h_two j m a m s' s ) +.\n", " sum mos_i' (fun m -> h_two j m a m s' s') ) *.\n", " (f_two a i j k s' s )\n", " ) \n", " ) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 1 1 1 2" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val m_1112_1H_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1112_1H_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1112_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1112_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1112_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1112_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value_12 : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_1112_1H_2Fa = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa ))\n", "\n", " \n", "let m_1112_1H_2Fb = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta ))\n", "\n", "\n", "let m_1112_2Ha_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two j m a m Spin.Alfa Spin.Alfa *.\n", " f_two a i j k Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_1112_2Hb_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two j m a m Spin.Alfa Spin.Beta *.\n", " f_two a i j k Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "let m_1112_2Ha_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two j m a m Spin.Alfa Spin.Alfa *.\n", " f_two a i j k Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let m_1112_2Hb_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two j m a m Spin.Alfa Spin.Beta *.\n", " f_two a i j k Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let integral_value_12 ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " \n", " let mos_i, mos_i' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", " \n", " let result = \n", " sum mos_j (fun j -> \n", " m_1112_1H_2Fa.{i,j,k} +. \n", " sum mos_i (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +.\n", " sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +.\n", " sum mos_j' (fun j ->\n", " m_1112_1H_2Fb.{i,j,k} +. \n", " sum mos_i (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +.\n", " sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m}))\n", " in\n", " \n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", " \n", "\n", "(*\n", "let _ = check 100 integral_value_12 1 1 1 2\n", "*)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 6. 1 1 21" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "let _ = png_image \"1_1_21.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", "\n", "$\\sum_{j} \\sum_a \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{j}$\n", "\n", "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "\\begin{align}\n", " \\sum_{a} \\sum_{j} \n", " \\langle i j || k a \\rangle \n", " \\left( f_{aj} +\\sum_{m} \\left[ m a || m j \\right] +\n", " \\sum_{\\bar{m}} \\left[ \\bar{m} a | \\bar{m} j \\right] \\right) + \\\\\n", " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n", " \\langle i \\bar{j} | k \\bar{a} \\rangle\n", " \\left( f_{\\bar{a}\\bar{j}} +\\sum_{m} \\left[ m \\bar{a} | m \\bar{j} \\right] +\n", " \\sum_{\\bar{m}} \\left[ \\bar{m} \\bar{a} || \\bar{m} \\bar{j} \\right] \\right)\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let integral_value ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " \n", " let mos_i, mos_i' =\n", " match s with\n", " | Spin.Alfa -> mos_a kj, mos_b kj\n", " | Spin.Beta -> mos_b kj, mos_a kj\n", " in\n", "\n", " let result = \n", " let s' = Spin.other s in\n", " sum mos_cabs (fun a -> \n", " sum mos_j (fun j -> \n", " (h_two i j k a s s ) *.\n", " (f_one a j s +. \n", " sum mos_i (fun m -> f_two m a m j s s) +.\n", " sum mos_i' (fun m -> f_two m a m j s' s) ) \n", " ) \n", " +.\n", " sum mos_j' (fun j -> \n", " (h_two i j k a s s') *.\n", " (f_one a j s' +. \n", " sum mos_i (fun m -> f_two m a m j s s') +.\n", " sum mos_i' (fun m -> f_two m a m j s' s') ) \n", " )) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 1 1 2 1" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val m_1121_2Ha_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1121_2Hb_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1121_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1121_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1121_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1121_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value_21 : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_1121_2Ha_1F = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa))\n", "\n", " \n", "let m_1121_2Hb_1F = \n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta))\n", "\n", "\n", "let m_1121_2Ha_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Alfa *.\n", " f_two m a m j Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "\n", "let m_1121_2Hb_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Beta *.\n", " f_two m a m j Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "let m_1121_2Ha_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Alfa *.\n", " f_two m a m j Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let m_1121_2Hb_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j k a Spin.Alfa Spin.Beta *.\n", " f_two m a m j Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let integral_value_21 ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " \n", " let mos_i, mos_i' =\n", " match s with\n", " | Spin.Alfa -> mos_a kj, mos_b kj\n", " | Spin.Beta -> mos_b kj, mos_a kj\n", " in\n", " \n", " let result = \n", " sum mos_j (fun j -> \n", " m_1121_2Ha_1F.{i,j,k} +. \n", " sum mos_i (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +.\n", " sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +.\n", " sum mos_j' (fun j ->\n", " m_1121_2Hb_1F.{i,j,k} +. \n", " sum mos_i (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +.\n", " sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m}))\n", " in\n", " \n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", " \n", "\n", "(*\n", "let _ = check 100 integral_value_21 1 1 2 1\n", "*)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 7. 1 1 22" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"1_1_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", "\n", "$\\sum_{j} \\sum_{a} \\sum_{m}\n", " \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} - \n", " \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} + \\\\\n", "\\sum_{\\bar{j}} \\sum_{\\bar{a}} \\sum_{m}\n", " \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} - \n", " \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}} +\n", "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{m}}\n", " \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} \n", "$\n", "\n", "$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$m$ : orbital indices of virtual MOs, unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$a$ : orbital indices of CABS MOs\n", "\n", "\\begin{align}\n", " \\sum_{a} \\sum_{j} \\sum_{m}\n", " \\langle i j || m a \\rangle \\left[ m a || k j \\right] - \\\\\n", " \\sum_{a} \\sum_{j} \\sum_{l}\n", " \\langle l j || k a \\rangle \\left[ i a || l j \\right] + \\\\\n", " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m}\n", " \\langle i \\bar{j} | m \\bar{a} \\rangle \\left[ m \\bar{a} | k \\bar{j} \\right] + \\\\\n", " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l}\n", " \\langle l \\bar{j} | k \\bar{a} \\rangle \\left[ i \\bar{a} | l \\bar{j} \\right] - \\\\\n", " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{\\bar{m}}\n", " \\langle i \\bar{j} | a \\bar{m} \\rangle \\left[ a \\bar{m} | k \\bar{j} \\right] \n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "(*\n", "let ki = det_I.(6)\n", "let kj = det_I.(58)\n", "\n", "let _ = \n", " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", "generate_alphas ki kj 1 1 2 2\n", "|> Array.of_list\n", "|> Array.mapi (fun kk alpha -> \n", "\n", "(*\n", "let _ = Determinant.to_lists ki\n", "let _ = Determinant.to_lists alpha\n", "let _ = Determinant.to_lists kj\n", "\n", " \n", "let _ = \n", " Format.printf \"|I> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det ki kj);\n", " Format.printf \"|I> -> |a> : %a\\n@.\" Excitation.pp (Excitation.of_det ki alpha);\n", " Format.printf \"|a> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det alpha kj)\n", "*)\n", "\n", " let integral_value ki kj = \n", " \n", " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", " let exc1 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n", " let exc2 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n", " \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin } )) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " let spin = function\n", " | Spin.Alfa -> 0\n", " | _ -> 1\n", " in\n", " exc0.(i).(spin s ) <- \"i\" \n", " ; exc0.(k).(spin s ) <- \"k\" \n", " ;\n", " let s0 = s in\n", " \n", " let i, j, k, l, s, s', p1 =\n", " match Excitation.of_det ki alpha with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n", " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n", " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n", " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n", " \n", " let string_h = \n", " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (if s = s0 then \"s \" else \"s'\")\n", " (if s' = s0 then \"s \" else \"s'\")\n", " (*\n", " (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n", " if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \"s''\")\n", " (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n", " if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \"s''\")\n", " *)\n", " in \n", " \n", " let i, j, k, l, s, s', p2 =\n", " match Excitation.of_det alpha kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " let string_f = \n", " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (*\n", " (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n", " if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \n", " if exc0.(i).(spin s ) = \"n\" || exc0.(k).(spin s ) = \"n\" then \"s''\" else\n", " if s = s0 then \"s\" else \"s'\")\n", " (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n", " if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \n", " if exc0.(j).(spin s') = \"n\" || exc0.(l).(spin s') = \"n\" then \"s''\" else\n", " if s' = s0 then \"s\" else \"s'\")\n", " *)\n", " (if s = s0 then \"s \" else \"s'\")\n", " (if s' = s0 then \"s \" else \"s'\")\n", " in\n", " \n", " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", " \n", " let sign = \n", " if Phase.add p1 p2 = phase then \"+. \" else \"-. \"\n", " in\n", "sign ^ string_h ^ string_f\n", "(*\n", " \n", " let mos, mos' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", "\n", " let result = \n", " let k=4 and l=5 in\n", " let i=1 and j=2 in\n", " let n=2 and a=7 in\n", " let s = Spin.Alfa\n", " and s' = Spin.Alfa\n", " and s'' = Spin.Beta\n", " in\n", " (* \n", " h_two j n l a s' s'' *. f_two a i n k s s''\n", " *)\n", " h_two i n k a s s'' *. f_two j a l n s s''\n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " *)\n", "\n", "in\n", "integral_value ki kj\n", "(*\n", "let a = (compute_HaaF ki [alpha] kj)\n", "and b = (integral_value ki kj)\n", "in\n", "if kk = 31 then\n", " Format.printf \"%6d %e %e@.@.\" (kk) a b\n", " *)\n", ")\n", "|> Array.to_list\n", "|> List.sort_uniq compare\n", "\n", "let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj\n", "\n", "let _ = integral_value ki kj\n", "\n", "*)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "let integral_value ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " (* MOs unoccupied in both I and J *)\n", " let mos_virt_a, mos_virt_b = \n", " Array.init mo_num (fun i -> Some (i+1)) , \n", " Array.init mo_num (fun i -> Some (i+1)) \n", " in\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", " \n", " let mos_virt_a, mos_virt_b = \n", " Array.to_list mos_virt_a |> Util.list_some,\n", " Array.to_list mos_virt_b |> Util.list_some\n", " in\n", "\n", " let mos_virt, mos_virt' =\n", " match s with\n", " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", " | Spin.Beta -> mos_virt_b, mos_virt_a\n", " in\n", " \n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " let result = \n", " let s' = Spin.other s in\n", " sum mos_cabs (fun a -> \n", " sum mos_j (fun n -> \n", " sum mos_virt (fun m -> \n", " h_two n i a m s s *. f_two m a k n s s \n", " ))) +.\n", " sum mos_cabs (fun a' -> \n", " sum mos_j' (fun n' -> \n", " sum mos_virt (fun m -> \n", " h_two i n' m a' s s' *. f_two m a' k n' s s'\n", " ))) +.\n", " sum mos_cabs (fun a -> \n", " sum mos_j' (fun n' -> \n", " sum mos_virt' (fun m' -> \n", " h_two i n' a m' s s' *. f_two a m' k n' s s'\n", " ))) -. \n", " sum mos_cabs (fun a -> \n", " sum mos_j (fun n -> \n", " sum mos_j (fun l -> if l <=n then 0. else\n", " h_two n l a k s s *. f_two i a l n s s \n", " ))) -. \n", " sum mos_cabs (fun a' -> \n", " sum mos_j' (fun n' -> \n", " sum mos_j (fun l -> \n", " h_two l n' k a' s s' *. f_two i a' l n' s s'\n", " ))) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "let _ = check 10 integral_value 1 1 2 2\n", "\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val m_1122_va :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1122_v2 :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1122_v3 :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1122_oa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_1122_o :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value_22 : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_1122_va =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two j i a m Spin.Alfa Spin.Alfa *.\n", " f_two m a k j Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "let m_1122_v2 =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j m a Spin.Alfa Spin.Beta *.\n", " f_two m a k j Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "let m_1122_v3 =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a m Spin.Alfa Spin.Beta *.\n", " f_two a m k j Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "let m_1122_oa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two j l a k Spin.Alfa Spin.Alfa *.\n", " f_two i a l j Spin.Alfa Spin.Alfa \n", " )\n", " )\n", "\n", "let m_1122_o =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two l j k a Spin.Alfa Spin.Beta *.\n", " f_two i a l j Spin.Alfa Spin.Beta \n", " )\n", " )\n", "\n", "\n", "let integral_value_22 ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " (* MOs unoccupied in both I and J *)\n", " let mos_virt_a, mos_virt_b = \n", " Array.init mo_num (fun i -> Some (i+1)) , \n", " Array.init mo_num (fun i -> Some (i+1)) \n", " in\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", " \n", " let mos_virt_a, mos_virt_b = \n", " Array.to_list mos_virt_a |> Util.list_some,\n", " Array.to_list mos_virt_b |> Util.list_some\n", " in\n", "\n", " let mos_virt, mos_virt' =\n", " match s with\n", " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", " | Spin.Beta -> mos_virt_b, mos_virt_a\n", " in\n", " \n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", " \n", " let result = \n", " sum mos_j (fun j -> \n", " sum mos_virt (fun m -> \n", " m_1122_va.{i,j,k,m}\n", " )) +.\n", " sum mos_j' (fun j -> \n", " sum mos_virt (fun m -> \n", " m_1122_v2.{i,j,k,m}\n", " )) +.\n", " \n", " sum mos_j' (fun j -> \n", " sum mos_virt' (fun m -> \n", " m_1122_v3.{i,j,k,m}\n", " )) -.\n", " sum mos_j (fun j -> \n", " sum mos_j (fun l -> if l <= j then 0. else\n", " m_1122_oa.{i,j,k,l}\n", " )) -. \n", " sum mos_j' (fun j -> \n", " sum mos_j (fun l -> \n", " m_1122_o.{i,j,k,l}\n", " )) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "(*\n", "let _ = check 100 integral_value_22 1 1 2 2\n", "*)\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val ki : Determinant.t =\n", " phase:+1\n", " a:+1 +------++-------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n", "val kj : Determinant.t =\n", " phase:+1\n", " a:+1 ------+++-------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.029105573460178686\n" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let ki = det_I.(77) and kj = det_I.(83)\n", "\n", "let _ =\n", "integral_value_11 ki kj\n", "+. integral_value_12 ki kj\n", "+. integral_value_21 ki kj\n", "+. integral_value_22 ki kj " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 8. 1 2 22" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"1_2_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", "\n", "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$\\sum_{j} \\sum_{a} \\sum_{b}\n", " \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{kj} +\n", "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{b}}\n", " \\hat{T}_{i\\bar{j}}^{a\\bar{b}} \\hat{T}_{a\\bar{b}}^{k\\bar{j}} \n", "$\n", "\n", "\n", "$$\n", "\\sum_{j} \\sum_{b}\\sum_{a\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos, mos' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", " \n", " \n", "\n", " let result = \n", " (* Alpha-Beta *)\n", " let s' = Spin.other s in\n", " sum mos_cabs (fun b -> \n", " sum mos_cabs (fun a -> \n", " sum mos' (fun j -> h_two h j a b s s' *. f_two a b p j s s')\n", " ))\n", " +.\n", " (* Alpha-Alpha / Beta-Beta *)\n", " sum mos_cabs (fun b -> \n", " sum mos_cabs (fun a -> if b >= a then 0. else\n", " sum mos (fun j -> h_two h j a b s s *. f_two a b p j s s)\n", " )) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 1 2 2 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "let m_1222a =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " sum mos_cabs (fun b -> if b > a then 0. else\n", " h_two i j a b Spin.Alfa Spin.Alfa *.\n", " f_two a b k j Spin.Alfa Spin.Alfa \n", " )\n", " )\n", " )\n", "\n", "let m_1222 =\n", " array_3_init mo_num mo_num mo_num (fun i j k ->\n", " sum mos_cabs (fun a ->\n", " sum mos_cabs (fun b ->\n", " h_two i j a b Spin.Alfa Spin.Beta *.\n", " f_two a b k j Spin.Alfa Spin.Beta \n", " )\n", " )\n", " )\n", " \n", "\n", "let integral_value ki kj = \n", " let i, k, s, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", " hole, particle, spin, phase\n", " | _ -> assert false\n", " in\n", " \n", " (* MOs unoccupied in both I and J *)\n", " let mos_j, mos_j' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", "\n", " let result = \n", " sum mos_j (fun j -> m_1222a.{i,j,k} ) +.\n", " sum mos_j' (fun j -> m_1222.{i,j,k} )\n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 1 2 2 2\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 9. 2 1 12" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"2_1_12.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", "\n", "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n", "\n", "$\\sum_{a} \n", " \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n", " \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n", "$\n", "\n", "\n", "$$\n", "\\sum_{a}\n", " \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n", "\\sum_{a}\n", " \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n", "$$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val ki : Determinant.t =\n", " phase:+1\n", " a:+1 +-++------------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val kj : Determinant.t =\n", " phase:+1\n", " a:+1 ---+-++---------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.00102394452584360905\n" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.00102394452584360926\n" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos, mos' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", " \n", " let mos2, mos2' =\n", " match s' with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", "\n", " let result = \n", " sum mos_cabs (fun a -> \n", " let s'' = Spin.other s in\n", " ( h_one i a s +.\n", " sum mos (fun n -> h_two i n a n s s ) +.\n", " sum mos' (fun n -> h_two i n a n s s'') \n", " ) *. f_two a j k l s s'\n", " ) +.\n", " sum mos_cabs (fun a -> \n", " let s'' = Spin.other s' in\n", " ( h_one j a s' +.\n", " sum mos2 (fun n -> h_two j n a n s' s' ) +.\n", " sum mos2' (fun n -> h_two j n a n s' s'') \n", " ) *. f_two i a k l s s'\n", " ) \n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", "\n", "\n", "let _ = check 100 integral_value 2 1 1 2\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", "\n", "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n", "\n", "$\\sum_{a} \n", " \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n", " \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n", "$\n", "\n", "\n", "$$\n", "\\sum_{a}\n", " \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n", "\\sum_{a}\n", " \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n", "$$" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val m_2112_1H_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2112_1H_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2112_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2112_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2112_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2112_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val ki : Determinant.t =\n", " phase:+1\n", " a:+1 +-++------------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val kj : Determinant.t =\n", " phase:+1\n", " a:+1 ---+-++---------------------------------------------------------\n", " b:+1 +++-------------------------------------------------------------\n", "\n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.00102394452584360905\n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "- : float = -0.00102394452584360926\n" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_2112_1H_2Fa =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n", " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa )\n", " )\n", "\n", "let m_2112_1H_2Fb =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n", " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta)\n", " )\n", "\n", "let m_2112_2Ha_2Fa =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i n a n Spin.Alfa Spin.Alfa *.\n", " f_two a j k l Spin.Alfa Spin.Alfa )\n", " )\n", " \n", "let m_2112_2Hb_2Fa =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i n a n Spin.Alfa Spin.Beta *.\n", " f_two a j k l Spin.Alfa Spin.Alfa )\n", " )\n", " \n", "let m_2112_2Ha_2Fb =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i n a n Spin.Alfa Spin.Alfa *.\n", " f_two a j k l Spin.Alfa Spin.Beta )\n", " )\n", " \n", "let m_2112_2Hb_2Fb =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i n a n Spin.Alfa Spin.Beta *.\n", " f_two a j k l Spin.Alfa Spin.Beta )\n", " )\n", " \n", "let integral_value ki kj = \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " let mos, mos' =\n", " match s with\n", " | Spin.Alfa -> mos_a ki, mos_b ki\n", " | Spin.Beta -> mos_b ki, mos_a ki\n", " in\n", " \n", " let result = \n", " if s = s' then\n", " m_2112_1H_2Fa.{i,j,k,l} +. \n", " sum mos (fun n ->\n", " m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n}\n", " ) +.\n", " sum mos' (fun n ->\n", " m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n}\n", " ) \n", " else\n", " m_2112_1H_2Fb.{i,j,k,l} +.\n", " 0. (*\n", " sum mos (fun n ->\n", " m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n}\n", " ) +.\n", " sum mos' (fun n ->\n", " m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n}\n", " ) \n", " *)\n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "let _ = check 100 integral_value 2 1 1 2\n", "\n", "let ki = det_I.(2)\n", "let kj = det_I.(33)\n", "\n", "let _ = integral_value ki kj\n", "let _ = \n", " let alphas = generate_alphas ki kj 2 1 1 2\n", " in compute_HaaF ki alphas kj\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 10. 2 1 21" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"2_1_21.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", "\n", "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$n$ : orbital indices of MOs occupied in $|J\\rangle$\n", "\n", "$\\sum_{a} \n", " \\hat{T}_{ij}^{al} \\hat{T}_{a}^{k} +\n", " \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{l} +\n", " \\hat{T}_{i\\bar{j}}^{a\\bar{l}} \\hat{T}_{a}^{k} +\n", " \\hat{T}_{i\\bar{j}}^{k\\bar{a}} \\hat{T}_{\\bar{a}}^{\\bar{l}}\n", "$\n", "\n", "\n", "$$\n", "\\sum_{a}\n", " \\langle i j || a l \\rangle \\left( f_{ak} + \\sum_{n} \\left[ a n || k n \\right] + \\sum_{\\bar{n}} \\left[ a \\bar{n} | k \\bar{n} \\right] \\right) + \\\\\n", "\\sum_{a}\n", " \\langle i j || k a \\rangle \\left( f_{al} + \\sum_{n} \\left[ n a || n l \\right] + \\sum_{\\bar{n}} \\left[ \\bar{n} a | \\bar{n} l \\right] \\right) \n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let integral_value ki kj = \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", "\n", " let result = \n", " \n", " let mos, mos', s'' =\n", " match s with\n", " | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n", " | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n", " in\n", " sum mos_cabs (fun a -> \n", " h_two i j a l s s' *.\n", " ( f_one a k s +.\n", " sum mos (fun n -> f_two a n k n s s) +.\n", " sum mos' (fun n -> f_two a n k n s s'') \n", " ) ) +.\n", "\n", " let mos, mos', s'' =\n", " match s' with\n", " | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n", " | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n", " in\n", " sum mos_cabs (fun a -> \n", " h_two j i a k s' s *.\n", " ( f_one a l s' +.\n", " sum mos (fun n -> f_two a n l n s' s') +.\n", " sum mos' (fun n -> f_two a n l n s' s'') \n", " ) \n", " ) \n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", "\n", "\n", "let _ = check 100 integral_value 2 1 2 1" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "val m_2121_2Ha_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2121_2Hb_1F :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2121_2Ha_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2121_2Hb_2Fa :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2121_2Ha_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val m_2121_2Hb_2Fb :\n", " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", " \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (25, 59) | 2.096432e-03 2.096432e-03 | 8.673617e-19 | cpu : 0.111770 0.004378\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let m_2121_2Ha_1F =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n", " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa)\n", " )\n", "\n", "let m_2121_2Hb_1F =\n", " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n", " h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa)\n", " )\n", "\n", "let m_2121_2Ha_2Fa =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Alfa *.\n", " f_two a n k n Spin.Alfa Spin.Alfa )\n", " )\n", " \n", "let m_2121_2Hb_2Fa =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Beta *.\n", " f_two a n k n Spin.Alfa Spin.Alfa )\n", " )\n", " \n", "let m_2121_2Ha_2Fb =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Alfa *.\n", " f_two a n k n Spin.Alfa Spin.Beta )\n", " )\n", " \n", "let m_2121_2Hb_2Fb =\n", " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", " sum mos_cabs (fun a ->\n", " h_two i j a l Spin.Alfa Spin.Beta *.\n", " f_two a n k n Spin.Alfa Spin.Beta )\n", " )\n", " \n", "let integral_value ki kj = \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " let mos, mos' =\n", " match s with\n", " | Spin.Alfa -> mos_a kj, mos_b kj\n", " | Spin.Beta -> mos_b kj, mos_a kj\n", " in\n", " \n", " let result = \n", " if s = s' then\n", " m_2121_2Ha_1F.{i,j,k,l} +. \n", " sum mos (fun n ->\n", " m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n}\n", " ) +.\n", " sum mos' (fun n ->\n", " m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n}\n", " ) \n", " else\n", " m_2121_2Hb_1F.{i,j,k,l} +.\n", " sum mos (fun n ->\n", " m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n}\n", " ) +.\n", " sum mos' (fun n ->\n", " m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n}\n", " ) \n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 2 1 2 1\n", "\n", "(*\n", "let ki = det_I.(2)\n", "let kj = det_I.(33)\n", "\n", "let _ = integral_value ki kj\n", "let _ = \n", " let alphas = generate_alphas ki kj 2 1 2 1\n", " in compute_HaaF ki alphas kj\n", "*)\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 11. 2 1 22" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"2_1_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", "\n", "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", "\n", "$n$ : orbital indices of MOs occupied in both $|I\\rangle$ and $|J\\rangle$ .\n", "\n", "$\\sum_{a} \n", " \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kl} +\n", " \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kl} -\n", " \\hat{T}_{in}^{al} \\hat{T}_{aj}^{kn} -\n", " \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} +\n", " \\sum_{n}\n", " \\hat{T}_{i\\bar{n}}^{k\\bar{a}} \\hat{T}_{\\bar{a}j}^{\\bar{n}l}\n", "$\n", "\n", "\n", "$$\n", "\\sum_{a}\n", "\\sum_{m} \\langle i j || a m \\rangle \\left[ a m || k l \\right] + \\langle i j || m a \\rangle \\left[ m a || k l \\right] - \\\\\n", "\\sum_{n} \\langle i n || a l \\rangle \\left[ a j || k n \\right] + \\langle n j || k a \\rangle \\left[ i a || n l \\right] \n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let integral_value ki kj = \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", "\n", " let mos_virt_a, mos_virt_b = \n", " Array.init mo_num (fun i -> Some (i+1)) , \n", " Array.init mo_num (fun i -> Some (i+1)) \n", " in\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", "\n", " let mos_virt_a, mos_virt_b = \n", " Array.to_list mos_virt_a |> Util.list_some,\n", " Array.to_list mos_virt_b |> Util.list_some\n", " in\n", " \n", " let result = \n", " \n", " let mos_virt, mos_virt' =\n", " match s with\n", " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", " | Spin.Beta -> mos_virt_b, mos_virt_a\n", " in\n", " \n", " let mos, mos' =\n", " let alfa = \n", " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " let beta = \n", " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", " Bitstring.to_list (Bitstring.logand i j)\n", " in\n", " match s with\n", " | Spin.Alfa -> alfa, beta\n", " | Spin.Beta -> beta, alfa\n", " in\n", "\n", " if s = s' then \n", " let s'' = Spin.other s' in\n", " sum mos_cabs (fun a -> \n", " sum mos (fun n ->\n", " h_two i n a k s s *. f_two j a n l s s \n", " +. h_two i n a l s s *. f_two j a k n s s \n", " -. h_two j n a k s s *. f_two i a n l s s \n", " -. h_two j n a l s s *. f_two i a k n s s\n", " )\n", " +. sum mos_virt (fun m ->\n", " -. h_two i j a m s s *. f_two m a k l s s )\n", " +. sum mos' (fun n ->\n", " h_two i n k a s s'' *. f_two j a l n s s''\n", " +. h_two j n l a s s'' *. f_two i a k n s s''\n", " -. h_two i n l a s s'' *. f_two j a k n s s''\n", " -. h_two j n k a s s'' *. f_two i a l n s s''\n", " )\n", " )\n", " else\n", " sum mos_cabs (fun a ->\n", " sum mos_virt' (fun m ->\n", " h_two i j a m s s' *. f_two a m k l s s' ) +.\n", " sum mos_virt (fun m ->\n", " h_two i j m a s s' *. f_two m a k l s s' ) +.\n", " sum mos (fun n ->\n", " h_two n i a k s s *. f_two a j n l s s'\n", " +. h_two n j a l s s' *. f_two i a k n s s \n", " -. h_two n j k a s s' *. f_two i a n l s s'\n", " ) +.\n", " sum mos' (fun n -> if n >= j then 0. else \n", " h_two i n k a s s' *. f_two j a l n s' s'\n", " +. h_two n j a l s' s' *. f_two i a k n s s' ) +. \n", " sum mos' (fun n -> if n <= j then 0. else \n", " -. h_two i n k a s s' *. f_two j a n l s' s' \n", " -. h_two j n a l s' s' *. f_two i a k n s s' ) +.\n", " sum mos' (fun n -> \n", " -. h_two i n a l s s' *. f_two a j k n s s'\n", " )\n", " )\n", " in\n", "\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", "\n", "\n", "let _ = check 300 integral_value 2 1 2 2" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/markdown", "scrolled": false }, "source": [ "let ki = det_I.(99)\n", "let kj = det_I.(193)\n", "\n", "let alpha_to_string alpha = \n", " \n", " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", " \n", " let i, j, k, l, s, s', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " let spin = function\n", " | Spin.Alfa -> 0\n", " | _ -> 1\n", " in\n", " exc0.(i).(spin s ) <- \"i\" \n", " ; exc0.(j).(spin s') <- \"j\" \n", " ; exc0.(k).(spin s ) <- \"k\" \n", " ; exc0.(l).(spin s') <- \"l\" \n", " ;\n", " let s0, s0' = s, s' in\n", " \n", " let i, j, k, l, s, s', p1 =\n", " match Excitation.of_det ki alpha with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n", " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n", " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n", " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n", " \n", " let string_h = \n", " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (if s = s0 then \"s \" else \"s'\")\n", " (if s' = s0 then \"s \" else \"s'\")\n", " in \n", " \n", " let i, j, k, l, s, s', p2 =\n", " match Excitation.of_det alpha kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " let string_f = \n", " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (if s = s0 then \"s \" else \"s'\")\n", " (if s' = s0 then \"s \" else \"s'\")\n", " in\n", "(*\n", " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", " *)\n", "\n", " \n", " let sign = \n", " if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n", " in\n", " sign ^ string_h ^ string_f\n", " \n", "\n", "let alpha_debug alpha = \n", " \n", " let i, j, k, l, s, s', p1 =\n", " match Excitation.of_det ki alpha with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " Printf.printf \"%d %d %d %d \" i j k l;\n", " \n", " let i, j, k, l, s, s', p2 =\n", " match Excitation.of_det alpha kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " (*\n", " Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n", " Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n", " *)\n", " Printf.printf \"%d %d %d %d \\n%!\" i j k l\n", "\n", " \n", "let strings = \n", " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", " generate_alphas ki kj 2 1 2 2\n", " |> Array.of_list\n", " |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n", " |> Array.to_list\n", " |> List.sort_uniq compare\n", " |> Array.of_list\n", "\n", "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n", "\n", "let _ =\n", " let v =\n", " let alphas =\n", " generate_alphas ki kj 2 1 2 2\n", " (*\n", " |> List.filter (fun alpha ->\n", " let x = alpha_to_string alpha in\n", " x = strings.(6)\n", " )\n", " *)\n", " in\n", " (*\n", " List.iter alpha_debug alphas ;\n", " Printf.printf \"\\n%!\";\n", " *)\n", " compute_HaaF ki alphas kj \n", " in\n", " let x = (integral_value ki kj) in\n", " Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 12. 2 2 22" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"2_2_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", "\n", "$$\n", "\\sum_{b}\\sum_{a h, h', p, p', s, s', phase\n", " | _ -> assert false\n", " in\n", "\n", " let result = \n", " if s <> s' then (* Alpha-Beta *)\n", " sum mos_cabs (fun b -> \n", " sum mos_cabs (fun a -> \n", " h_two h h' a b s s' *. f_two a b p p' s s'\n", " )) \n", " else (* Alpha-Alpha / Beta-Beta *)\n", " sum mos_cabs (fun b -> \n", " sum mos_cabs (fun a -> if b >= a then 0. else\n", " h_two h h' a b s s' *. f_two a b p p' s s'\n", " )) \n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 100 integral_value 2 2 2 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 13. *3 1 2 2*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "let _ = png_image \"3_1_22.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|J\\rangle = \\hat{T}_{ijm}^{kln}|I\\rangle$\n", "\n", "$\\sum_{a}\n", " \\hat{T}_{ij}^{al} \\hat{T}_{am}^{kn} \n", " + \\hat{T}_{ij}^{ka} \\hat{T}_{am}^{ln} \n", " + \\hat{T}_{im}^{ka} \\hat{T}_{ja}^{ln} \n", " + \\hat{T}_{im}^{an} \\hat{T}_{aj}^{kl} \n", " + \\hat{T}_{jm}^{an} \\hat{T}_{ia}^{kl} \n", " + \\hat{T}_{jm}^{la} \\hat{T}_{ia}^{kn} \n", "$\n", "\n", "$$\n", "\\sum_{a} \\langle i j || a l \\rangle \\left[ a m || k n \\right] +\n", " \\langle i j || k a \\rangle \\left[ a m || l n \\right] +\n", " \\langle i m || k a \\rangle \\left[ j a || l n \\right] +\n", " \\langle i m || a n \\rangle \\left[ a j || k l \\right] +\n", " \\langle j m || a n \\rangle \\left[ i a || k l \\right] +\n", " \\langle j m || l a \\rangle \\left[ i a || k n \\right] \n", "$$" ] }, { "cell_type": "code", "execution_count": 419, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "val integral_value : Determinant.t -> Determinant.t -> float = \n" ] }, "execution_count": 419, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Checking ... \n", " - 10 %\n", " - 20 %\n", " - 30 %\n", " - 40 %\n", " - 50 %\n", " - 60 %\n", " - 70 %\n", " - 80 %\n", " - 90 %\n", " - 100 %\n", "OK: (24, 43) | 1.154913e-03 1.154913e-03 | 6.505213e-19 | cpu : 10.122233 0.688825\n" ] }, { "data": { "text/plain": [ "- : unit = ()\n" ] }, "execution_count": 419, "metadata": {}, "output_type": "execute_result" } ], "source": [ "let integral_value ki kj = \n", " let i, j, m, k, l, n, s1, s2, s3, phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Triple (phase,\n", " { hole=h1 ; particle=p1 ; spin=s1 },\n", " { hole=h2 ; particle=p2 ; spin=s2 },\n", " { hole=h3 ; particle=p3 ; spin=s3 }) ) -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n", " | _ -> assert false\n", " in\n", "\n", " let result = \n", " let open Spin in \n", " match s1, s2, s3 with\n", " | Alfa, Alfa, Alfa\n", " | Beta, Beta, Beta -> \n", " sum mos_cabs (fun a -> \n", " h_two i j a k s1 s2 *. f_two m a l n s3 s3 \n", " +. h_two i j a n s1 s2 *. f_two m a k l s3 s2 \n", " +. h_two i m a l s1 s3 *. f_two j a k n s2 s3 \n", " +. h_two j m a k s2 s3 *. f_two i a l n s1 s3 \n", " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", " -. h_two i j a l s1 s2 *. f_two m a k n s3 s3 \n", " -. h_two i m a k s1 s3 *. f_two j a l n s2 s3 \n", " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 )\n", " | Alfa, Alfa, Beta\n", " | Beta, Beta, Alfa -> \n", " sum mos_cabs (fun a -> \n", " h_two i j a l s1 s2 *. f_two a m k n s1 s3\n", " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3\n", " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", " +. h_two j m l a s2 s3 *. f_two i a k n s1 s3\n", " -. h_two i j a k s1 s2 *. f_two a m l n s1 s3\n", " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", " -. h_two i m l a s1 s3 *. f_two j a k n s2 s3\n", " -. h_two j m k a s2 s3 *. f_two i a l n s1 s3\n", " ) \n", " | Alfa, Beta, Beta\n", " | Beta, Alfa, Alfa -> \n", " sum mos_cabs (fun a -> \n", " h_two i j a l s1 s2 *. f_two a m k n s1 s3 \n", " +. h_two i m a n s1 s3 *. f_two a j k l s1 s2 \n", " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 \n", " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", " -. h_two i j a n s1 s2 *. f_two a m k l s1 s2 \n", " -. h_two i j k a s1 s2 *. f_two m a l n s2 s3 \n", " -. h_two i m a l s1 s3 *. f_two a j k n s1 s3 \n", " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 \n", " ) \n", " | Beta, Alfa, Beta\n", " | Alfa, Beta, Alfa -> assert false (*TODO *)\n", " in\n", " match phase with\n", " | Phase.Pos -> result\n", " | Phase.Neg -> -. result\n", " \n", "\n", "let _ = check 200 integral_value 3 1 2 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "let ki = det_I.(129)\n", "let kj = det_I.(349)\n", "\n", "let alpha_to_string alpha = \n", " \n", " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", " \n", " let i, j, m, k, l, n, s, s', s'', phase =\n", " match Excitation.of_det ki kj with\n", " | Excitation.(Triple (phase,\n", " { hole ; particle ; spin },\n", " {hole=hole' ; particle=particle' ; spin=spin' }, \n", " {hole=hole''; particle=particle''; spin=spin''} )) ->\n", " hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase\n", " | _ -> assert false\n", " in\n", " let spin = function\n", " | Spin.Alfa -> 0\n", " | _ -> 1\n", " in\n", " exc0.(i).(spin s ) <- \"i\" \n", " ; exc0.(j).(spin s' ) <- \"j\" \n", " ; exc0.(k).(spin s ) <- \"k\" \n", " ; exc0.(l).(spin s' ) <- \"l\" \n", " ; exc0.(m).(spin s'') <- \"m\" \n", " ; exc0.(n).(spin s'') <- \"n\" \n", " ;\n", " let s0, s0', s0'' = s, s', s'' in\n", " \n", " let i, j, k, l, s, s', p1 =\n", " match Excitation.of_det ki alpha with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"p\";\n", " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"p\";\n", " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"q\";\n", " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"q\";\n", " \n", " let string_h = \n", " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", " in \n", " \n", " let i, j, k, l, s, s', p2 =\n", " match Excitation.of_det alpha kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " \n", " let string_f = \n", " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", " exc0.(i).(spin s )\n", " exc0.(j).(spin s')\n", " exc0.(k).(spin s )\n", " exc0.(l).(spin s')\n", " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", " in\n", " (*\n", " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", " *)\n", "\n", " \n", " let sign = \n", " if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n", " in\n", " sign ^ string_h ^ string_f\n", " \n", "\n", "let alpha_debug alpha = \n", " \n", " let i, j, k, l, s, s', p1 =\n", " match Excitation.of_det ki alpha with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " Printf.printf \"%d %d %d %d \" i j k l;\n", " \n", " let i, j, k, l, s, s', p2 =\n", " match Excitation.of_det alpha kj with\n", " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", " hole, hole', particle, particle', spin, spin', phase\n", " | _ -> assert false\n", " in\n", " (*\n", " Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n", " Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n", " *)\n", " Printf.printf \"%d %d %d %d \\n%!\" i j k l\n", "\n", " \n", "let strings = \n", " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", " generate_alphas ki kj 3 1 2 2\n", " |> Array.of_list\n", " |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n", " |> Array.to_list\n", " |> List.sort_uniq compare\n", " |> Array.of_list\n", "\n", "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n", "\n", "let _ =\n", " let v =\n", " let alphas =\n", " generate_alphas ki kj 3 1 2 2\n", " (*\n", " |> List.filter (fun alpha ->\n", " let x = alpha_to_string alpha in\n", " x = strings.(6)\n", " )\n", " *)\n", " in\n", " (*\n", " List.iter alpha_debug alphas ;\n", " Printf.printf \"\\n%!\";\n", " *)\n", " compute_HaaF ki alphas kj \n", " in\n", " let x = (integral_value ki kj) in\n", " Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "OCaml 4.07.1", "language": "OCaml", "name": "ocaml-jupyter" }, "language_info": { "codemirror_mode": "text/x-ocaml", "file_extension": ".ml", "mimetype": "text/x-ocaml", "name": "OCaml", "nbconverter_exporter": null, "pygments_lexer": "OCaml", "version": "4.07.1" } }, "nbformat": 4, "nbformat_minor": 4 }