mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-06-02 11:25:19 +02:00
801 lines
23 KiB
Plaintext
801 lines
23 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Test of F12 matrix elements"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Initialization"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"#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 to load"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"#load \"Constants.cmo\";;\n",
|
|
"#load_rec \"Util.cma\";;\n",
|
|
"#load_rec \"Matrix.cmo\";;\n",
|
|
"#load_rec \"Simulation.cmo\";;\n",
|
|
"#load_rec \"Spindeterminant.cmo\";;\n",
|
|
"#load_rec \"Determinant.cmo\";;\n",
|
|
"#load_rec \"HartreeFock.cmo\";;\n",
|
|
"#load_rec \"MOBasis.cmo\";;\n",
|
|
"#load_rec \"F12CI.cmo\";;\n",
|
|
"\n",
|
|
"open Lacaml.D;;"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Printers"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"#install_printer AngularMomentum.pp_string ;;\n",
|
|
"#install_printer Basis.pp ;;\n",
|
|
"#install_printer Charge.pp ;;\n",
|
|
"#install_printer Coordinate.pp ;;\n",
|
|
"#install_printer Vector.pp;;\n",
|
|
"#install_printer Matrix.pp;;\n",
|
|
"#install_printer Util.pp_float_2darray;;\n",
|
|
"#install_printer Util.pp_float_array;;\n",
|
|
"#install_printer Util.pp_matrix;;\n",
|
|
"#install_printer HartreeFock.pp ;;\n",
|
|
"#install_printer Fock.pp ;;\n",
|
|
"#install_printer MOClass.pp ;;\n",
|
|
"let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n",
|
|
"#install_printer pp_mo;;\n",
|
|
"#install_printer DeterminantSpace.pp;;\n",
|
|
"#install_printer SpindeterminantSpace.pp;;\n",
|
|
"#install_printer Bitstring.pp;;\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Run"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Simulation\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n",
|
|
"let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
|
|
"let nuclei = Nuclei.of_zmt_string \"be\" \n",
|
|
"let frozen_core = false\n",
|
|
"let multiplicity = 1\n",
|
|
"let state = 1\n",
|
|
"\n",
|
|
"let basis = Basis.of_nuclei_and_basis_filenames ~nuclei [basis_filename] \n",
|
|
"let aux_basis = Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n",
|
|
"let f12 = F12factor.gaussian_geminal 1.0 \n",
|
|
"let charge = 0 \n",
|
|
"\n",
|
|
"\n",
|
|
"let simulation =\n",
|
|
" Simulation.make \n",
|
|
" ~f12 ~charge ~multiplicity ~nuclei\n",
|
|
" ~cartesian:true\n",
|
|
" basis\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Hartree-Fock"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let hf = HartreeFock.make ~guess:`Hcore simulation ;;\n",
|
|
"\n",
|
|
"let mo_basis = MOBasis.of_hartree_fock hf"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# FCI-F12"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Notations:\n",
|
|
"\n",
|
|
"* $\\langle ij || kl \\rangle = \\int \\phi_i(r_1) \\phi_j(r_2) \\frac{1}{r_{12}} \\phi_k(r1) \\phi_l(r2) $ \n",
|
|
"* $\\left[ ij || kl \\right] = \\int \\phi_i(r_1) \\phi_j(r_2) f_{12} \\phi_k(r1) \\phi_l(r2) $ \n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Common functions"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"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": "raw",
|
|
"metadata": {},
|
|
"source": [
|
|
"let () = ignore @@ MOBasis.f12_ints aux_basis\n",
|
|
"let () = ignore @@ MOBasis.two_e_ints aux_basis"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Determinant-based functions"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Integrals"
|
|
]
|
|
},
|
|
{
|
|
"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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let cancel_singles = false \n",
|
|
"\n",
|
|
"let f12_integrals mo_basis =\n",
|
|
"\n",
|
|
" \n",
|
|
" let two_e_ints = MOBasis.f12_ints mo_basis in\n",
|
|
" let f2 i j k l s s' =\n",
|
|
" let ijkl = F12.get_phys two_e_ints i j k l in\n",
|
|
" let ijlk = F12.get_phys two_e_ints i j l k in\n",
|
|
" if s' <> s then\n",
|
|
" ijkl \n",
|
|
" else\n",
|
|
" (ijkl -. ijlk) \n",
|
|
" in\n",
|
|
" ( (fun _ _ _ -> 0.),\n",
|
|
" (if cancel_singles then\n",
|
|
" (fun i j k l s s' ->\n",
|
|
" (* Required to cancel out single excitations *)\n",
|
|
" if (i=k && j<>l) || (j=l && i<>k) then\n",
|
|
" 0.\n",
|
|
" else\n",
|
|
" f2 i j k l s s'\n",
|
|
" ) \n",
|
|
" else f2),\n",
|
|
" None\n",
|
|
" )\n",
|
|
"\n",
|
|
"let h_ij mo_basis ki kj =\n",
|
|
" let integrals =\n",
|
|
" List.map (fun f -> f mo_basis)\n",
|
|
" [ CI.h_integrals ]\n",
|
|
" in\n",
|
|
" CIMatrixElement.make integrals ki kj \n",
|
|
" |> List.hd\n",
|
|
"\n",
|
|
"\n",
|
|
"let f_ij mo_basis ki kj =\n",
|
|
" let integrals =\n",
|
|
" List.map (fun f -> f mo_basis)\n",
|
|
" [ f12_integrals ]\n",
|
|
" in\n",
|
|
" CIMatrixElement.make integrals ki kj \n",
|
|
" |> List.hd \n",
|
|
"\n",
|
|
"\n",
|
|
"let hf_ij mo_basis ki kj =\n",
|
|
" let integrals =\n",
|
|
" List.map (fun f -> f mo_basis)\n",
|
|
" [ CI.h_integrals ; f12_integrals ]\n",
|
|
" in\n",
|
|
" CIMatrixElement.make integrals ki kj\n",
|
|
"\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Determinant space"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let ci = CI.make ~n_states:state in_space\n",
|
|
"\n",
|
|
"let ci_coef, ci_energy = Lazy.force ci.eigensystem \n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"metadata": {},
|
|
"source": [
|
|
"let p12 det_space =\n",
|
|
" let mo_class = DeterminantSpace.mo_class det_space in\n",
|
|
" let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
|
|
" let m l =\n",
|
|
" List.fold_left (fun accu i ->\n",
|
|
" let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
|
|
" ) (Bitstring.zero mo_num) l\n",
|
|
" in\n",
|
|
" let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
|
|
" let not_aux_mask =\n",
|
|
" Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n",
|
|
" in\n",
|
|
" fun k ->\n",
|
|
" let alfa =\n",
|
|
" Determinant.alfa k\n",
|
|
" |> Spindeterminant.bitstring\n",
|
|
" in\n",
|
|
" let beta =\n",
|
|
" Determinant.beta k\n",
|
|
" |> Spindeterminant.bitstring\n",
|
|
" in\n",
|
|
" let a = Bitstring.logand aux_mask alfa\n",
|
|
" and b = Bitstring.logand aux_mask beta\n",
|
|
" in\n",
|
|
" match Bitstring.popcount a, Bitstring.popcount b with\n",
|
|
" | 2, 0 \n",
|
|
" | 0, 2 -> Some (Determinant.negate_phase k)\n",
|
|
" | 1, 1 -> Some (Determinant.of_spindeterminants\n",
|
|
" (Spindeterminant.of_bitstring @@\n",
|
|
" Bitstring.(logor b (logand not_aux_mask alfa)) )\n",
|
|
" (Spindeterminant.of_bitstring @@\n",
|
|
" Bitstring.(logor a (logand not_aux_mask beta))\n",
|
|
" ) )\n",
|
|
" | 1, 0 \n",
|
|
" | 0, 1 -> Some k\n",
|
|
" | _ -> None\n",
|
|
" \n",
|
|
" \n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Integral-based functions"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"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 = Array.of_list in_list\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"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\n",
|
|
" "
|
|
]
|
|
},
|
|
{
|
|
"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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let mos_cabs = \n",
|
|
" Util.list_range (mo_num+1) aux_num\n",
|
|
"\n",
|
|
"\n",
|
|
"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",
|
|
" Determinant.single_excitation Spin.Alfa hole particle ki\n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_a\n",
|
|
" ;\n",
|
|
" List.map (fun hole -> \n",
|
|
" List.map (fun particle ->\n",
|
|
" Determinant.single_excitation Spin.Beta hole particle ki\n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_b \n",
|
|
" ]\n",
|
|
" |> List.concat\n",
|
|
" |> List.concat\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' > hole && particle' < particle then\n",
|
|
" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
|
|
" else None\n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_a \n",
|
|
" ) mos_cabs\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 then\n",
|
|
" Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
|
|
" else None\n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_b \n",
|
|
" ) mos_cabs\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",
|
|
" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_a \n",
|
|
" ) mos_cabs\n",
|
|
" ) mos_a\n",
|
|
" ]\n",
|
|
" |> List.concat\n",
|
|
" |> List.concat\n",
|
|
" |> List.concat\n",
|
|
" |> List.concat\n",
|
|
" |> Util.list_some\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": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"let ki = det_I.(0) \n",
|
|
"let kj = det_I.(0)\n",
|
|
"let alphas =\n",
|
|
" generate_alphas ki kj 0 1 1 1\n",
|
|
"\n",
|
|
"let _ =\n",
|
|
" compute_HaaF ki alphas kj\n",
|
|
"\n",
|
|
" \n",
|
|
"(*\n",
|
|
"|> SetDet.iter (fun x -> Format.printf \"@[%a@]@;\" (Determinant.pp 24) x)\n",
|
|
"*)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"String.concat"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 0 1 11"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"png_image \"0_1_11.png\""
|
|
]
|
|
},
|
|
{
|
|
"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": 2
|
|
}
|