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911 lines
25 KiB
OCaml
911 lines
25 KiB
OCaml
(** %{ $ \langle ij | H F | kl \rangle $ %} integrals. *)
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open Lacaml.D
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module Fis = FourIdxStorage
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type t = {
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simulation : Simulation.t ;
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aux_basis : MOBasis.t ;
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f_0 : Determinant.t -> float ;
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f_1 : Determinant.t -> Determinant.t -> float ;
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f_2 : Determinant.t -> Determinant.t -> float ;
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f_3 : Determinant.t -> Determinant.t -> float ;
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}
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let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l
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let array_3_init d1 d2 d3 fx =
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let f k =
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let x =
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Bigarray.(Array2.create Float64 fortran_layout d1 d2)
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in
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for j=1 to d2 do
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for i=1 to d1 do
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x.{i,j} <- fx i j k
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done
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done;
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(k,x)
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in
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let result =
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SharedMemory.create Bigarray.Float64 [| d1 ; d2 ; d3 |]
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|> Bigarray.array3_of_genarray
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in
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Util.list_range 1 d3
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|> Stream.of_list
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|> Farm.run ~f
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|> Stream.iter (fun (k,x) ->
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for j=1 to d2 do
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for i=1 to d1 do
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result.{i,j,k} <- x.{i,j}
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done
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done)
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;
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Parallel.broadcast (lazy result)
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let array_4_init d1 d2 d3 d4 fx =
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let f l =
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let x =
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Bigarray.(Array3.create Float64 fortran_layout d1 d2 d3)
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in
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for k=1 to d3 do
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for j=1 to d2 do
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for i=1 to d1 do
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x.{i,j,k} <- fx i j k l
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done
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done
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done;
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(l,x)
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in
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let result =
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SharedMemory.create Bigarray.Float64 [| d1;d2;d3;d4 |]
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in
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Util.list_range 1 d4
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|> Stream.of_list
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|> Farm.run ~f
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|> Stream.iter (fun (l,x) ->
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for k=1 to d3 do
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for j=1 to d2 do
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for i=1 to d1 do
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result.{i,j,k,l} <- x.{i,j,k}
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done
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done
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done)
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;
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Parallel.broadcast (lazy result)
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let array_5_init d1 d2 d3 d4 d5 fx =
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let f m =
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let x =
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Bigarray.(Genarray.create Float64 fortran_layout [| d1; d2; d3; d4 |])
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in
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for l=1 to d4 do
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for k=1 to d3 do
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for j=1 to d2 do
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for i=1 to d1 do
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x.{i,j,k,l} <- fx i j k l m
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done
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done
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done
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done;
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(m,x)
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in
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let result =
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SharedMemory.create Bigarray.Float64 [| d1;d2;d3;d4;d5 |]
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in
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Util.list_range 1 d5
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|> Stream.of_list
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|> Farm.run ~f
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|> Stream.iter (fun (m,x) ->
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for l=1 to d4 do
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for k=1 to d3 do
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for j=1 to d2 do
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for i=1 to d1 do
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result.{i,j,k,l,m} <- x.{i,j,k,l}
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done
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done
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done
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done)
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;
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Parallel.broadcast (lazy result)
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let make ~simulation ~mo_basis ~aux_basis_filename () =
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let f12 = Util.of_some @@ Simulation.f12 simulation in
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let mo_num = MOBasis.size mo_basis in
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(* Add auxiliary basis set *)
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let simulation =
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let charge = Charge.to_int @@ Simulation.charge simulation
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and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation
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and nuclei = Simulation.nuclei simulation
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in
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let general_basis =
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Basis.general_basis @@ Simulation.basis simulation
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in
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GeneralBasis.combine [
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general_basis ; GeneralBasis.read aux_basis_filename
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]
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|> Basis.of_nuclei_and_general_basis nuclei
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|> Simulation.make ~f12 ~charge ~multiplicity ~nuclei
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in
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let aux_basis =
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MOBasis.of_mo_basis simulation mo_basis
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in
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let aux_num = MOBasis.size aux_basis in
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(* Fire calculation of F12 and ERI *)
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ignore @@ MOBasis.f12_ints aux_basis ;
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ignore @@ MOBasis.two_e_ints aux_basis ;
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(* Compute the <ij|QHF|kl> integrals *)
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if Parallel.master then Printf.eprintf "Computing HF12 integrals\n%!";
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let mos_cabs =
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Util.list_range (mo_num+1) aux_num
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in
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let mos_in =
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Util.list_range 1 mo_num
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in
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let mos_a k =
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Determinant.alfa k
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|> Spindeterminant.to_list
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in
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let mos_b k =
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Determinant.beta k
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|> Spindeterminant.to_list
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in
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let h_one =
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let h =
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MOBasis.one_e_ints aux_basis
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in fun i j _ -> h.{i,j}
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in
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let h_two =
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let two_e_ints = MOBasis.two_e_ints aux_basis in
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let h2 i j k l (s:Spin.t) (s':Spin.t) =
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if s' <> s then
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ERI.get_phys two_e_ints i j k l
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else
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(ERI.get_phys two_e_ints i j k l) -.
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(ERI.get_phys two_e_ints i j l k)
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in
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h2
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in
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let f_two =
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let f12_ints = MOBasis.f12_ints aux_basis in
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let f2 i j k l (s:Spin.t) (s':Spin.t) =
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if s' <> s then
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0.375 *. F12.get_phys f12_ints i j k l +.
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0.125 *. F12.get_phys f12_ints i j l k
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else
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0.25 *. (
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(F12.get_phys f12_ints i j k l) -.
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(F12.get_phys f12_ints i j l k) )
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in
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f2
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in
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let f_one = fun _ _ _ -> 0. in
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(* Pre-compute dressed integrals *)
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let m_0111_1H_1F =
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Vec.init mo_num (fun i ->
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sum mos_cabs (fun a ->
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h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))
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in
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let m_0111_1H_2Fa, m_0111_2Ha_2Fa =
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let m_0122_Haa =
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array_3_init mo_num mo_num mo_num (fun i j k ->
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sum mos_cabs (fun a ->
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h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa
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) )
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in
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let m_0111_1H_2Fa =
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Mat.init_cols mo_num mo_num (fun i j ->
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sum mos_cabs (fun a ->
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h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa +.
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h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa
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) +.
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if i < j then 0. else
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begin
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sum mos_cabs (fun a ->
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sum mos_cabs (fun b -> if b >= a then 0. else
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h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa
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)
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) +.
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sum mos_in (fun k -> m_0122_Haa.{i,j,k})
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end
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)
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in
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let m_0111_2Ha_2Fa =
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array_3_init mo_num mo_num mo_num (fun i j k ->
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Alfa *.
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f_two a k i k Spin.Alfa Spin.Alfa
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) -. if i < j then 0. else m_0122_Haa.{i,j,k}
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)
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in m_0111_1H_2Fa, m_0111_2Ha_2Fa
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in
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let m_0111_1H_2Fb, m_0111_2Hb_2Fb =
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let m_0122_Hab =
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array_3_init mo_num mo_num mo_num (fun i j k ->
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sum mos_cabs (fun a ->
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h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta
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) )
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in
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let m_0111_1H_2Fb =
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Mat.init_cols mo_num mo_num (fun i j ->
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sum mos_cabs (fun a ->
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h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta +.
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h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa +.
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h_one j a Spin.Alfa *. f_two a i j i Spin.Alfa Spin.Beta +.
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h_two j i a i Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa
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) +.
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sum mos_in (fun k -> m_0122_Hab.{i,j,k} +. m_0122_Hab.{j,i,k} ) +.
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sum mos_cabs (fun a ->
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sum mos_cabs (fun b ->
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h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta
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)
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)
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)
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in
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let m_0111_2Hb_2Fb =
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array_3_init mo_num mo_num mo_num (fun i j k ->
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sum mos_cabs (fun a ->
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h_two k i a i Spin.Alfa Spin.Beta *.
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f_two a j k j Spin.Alfa Spin.Beta +.
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h_two i k a k Spin.Alfa Spin.Beta *.
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f_two a j i j Spin.Alfa Spin.Alfa
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) -. m_0122_Hab.{k,i,j}
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)
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in
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m_0111_1H_2Fb, m_0111_2Hb_2Fb
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in
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let m_0111_2Ha_2Fb =
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array_3_init mo_num mo_num mo_num (fun i j k ->
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Alfa *.
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f_two a k i k Spin.Alfa Spin.Beta
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)
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)
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in
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let f_0 ki =
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let mos_i, mos_i' = mos_a ki, mos_b ki in
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let same = (mos_i = mos_i') in
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(* Alpha *)
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let a =
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sum mos_i (fun i -> m_0111_1H_1F.{i})
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in
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let b =
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if same then a else
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sum mos_i' (fun i -> m_0111_1H_1F.{i})
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in
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let aa =
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sum mos_i (fun j ->
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sum mos_i (fun i -> m_0111_1H_2Fa.{i,j} ))
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in
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let bb =
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if same then aa else
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sum mos_i' (fun j ->
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sum mos_i' (fun i -> m_0111_1H_2Fa.{i,j} ))
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in
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let ab =
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sum mos_i' (fun j ->
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sum mos_i (fun i -> m_0111_1H_2Fb.{i,j} ))
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in
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let aaa =
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sum mos_i (fun k ->
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sum mos_i (fun j ->
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sum mos_i (fun i -> m_0111_2Ha_2Fa.{i,j,k} )))
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in
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let bbb =
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if same then aaa else
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sum mos_i' (fun k ->
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sum mos_i' (fun j ->
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sum mos_i' (fun i -> m_0111_2Ha_2Fa.{i,j,k} )))
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in
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let baa =
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sum mos_i' (fun k ->
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sum mos_i (fun j ->
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sum mos_i (fun i ->
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m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{i,j,k}
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)))
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in
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let bba =
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sum mos_i (fun k ->
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sum mos_i' (fun j ->
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sum mos_i' (fun i ->
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m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{j,i,k}
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)))
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in
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a +. b +. aa +. bb +. ab +. aaa +. baa +. bba +. bbb
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in
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let m_1111_1H_1F =
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Mat.init_cols mo_num mo_num (fun i k ->
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sum mos_cabs (fun a -> h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))
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in
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let m_1111_2Ha_2Fa =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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if l=i then
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sum mos_cabs (fun a ->
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h_two j l a l Spin.Alfa Spin.Alfa *.
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f_two a i j k Spin.Alfa Spin.Alfa
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)
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else
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Alfa *.
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f_two a l k l Spin.Alfa Spin.Alfa +.
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h_two j l a l Spin.Alfa Spin.Alfa *.
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f_two a i j k Spin.Alfa Spin.Alfa )
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)
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in
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let m_1111_2Hb_2Fa =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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if l=i then
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sum mos_cabs (fun a ->
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h_two j l a l Spin.Alfa Spin.Beta *.
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f_two a i j k Spin.Alfa Spin.Beta
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)
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else
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Beta *.
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f_two a l k l Spin.Alfa Spin.Alfa +.
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h_two j l a l Spin.Alfa Spin.Beta *.
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f_two a i j k Spin.Alfa Spin.Beta
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)
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)
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in
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let m_1111_2Ha_2Fb =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Alfa *.
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f_two a l k l Spin.Alfa Spin.Beta +.
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h_two j l a l Spin.Alfa Spin.Beta *.
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f_two a i j k Spin.Alfa Spin.Alfa
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)
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)
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in
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let m_1111_2Hb_2Fb =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j a j Spin.Alfa Spin.Beta *.
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f_two a l k l Spin.Alfa Spin.Beta +.
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h_two j l a l Spin.Alfa Spin.Alfa *.
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f_two a i j k Spin.Alfa Spin.Beta
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)
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)
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in
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let m_1121_2Ha_2Fa =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j k a Spin.Alfa Spin.Alfa *.
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f_two l a l j Spin.Alfa Spin.Alfa
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)
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)
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in
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let m_1121_2Hb_2Fa =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j k a Spin.Alfa Spin.Beta *.
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f_two l a l j Spin.Alfa Spin.Alfa
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)
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)
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in
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let m_1121_2Ha_2Fb =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j k a Spin.Alfa Spin.Alfa *.
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f_two l a l j Spin.Alfa Spin.Beta
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)
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)
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in
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let m_1121_2Hb_2Fb =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j k a Spin.Alfa Spin.Beta *.
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f_two l a l j Spin.Alfa Spin.Beta
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)
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)
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in
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let m_1122_va =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two j i a l Spin.Alfa Spin.Alfa *.
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f_two l a k j Spin.Alfa Spin.Alfa
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)
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)
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in
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let m_1111_1H_2Fa =
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array_3_init mo_num mo_num mo_num (fun j i k ->
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sum mos_in (fun l -> m_1122_va.{l,j,i,k}) +.
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sum mos_cabs (fun a ->
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h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa +.
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h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.
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h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa +.
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h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa +.
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sum mos_cabs (fun b -> if b > a then 0. else
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h_two i j a b Spin.Alfa Spin.Alfa *.
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f_two a b k j Spin.Alfa Spin.Alfa )
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)
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)
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in
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let m_1122_v2 =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j l a Spin.Alfa Spin.Beta *.
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f_two l a k j Spin.Alfa Spin.Beta
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)
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)
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in
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let m_1122_v3 =
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array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
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sum mos_cabs (fun a ->
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h_two i j a l Spin.Alfa Spin.Beta *.
|
|
f_two a l k j Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_1111_1H_2Fb =
|
|
array_3_init mo_num mo_num mo_num (fun j i k ->
|
|
sum mos_in (fun l -> m_1122_v2.{l,j,i,k} +. m_1122_v3.{l,j,i,k}) +.
|
|
sum mos_cabs (fun a ->
|
|
h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta +.
|
|
h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.
|
|
h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta +.
|
|
h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta +.
|
|
sum mos_cabs (fun b ->
|
|
h_two i j a b Spin.Alfa Spin.Beta *.
|
|
f_two a b k j Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_1122_oa =
|
|
array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
|
|
if l > j then
|
|
sum mos_cabs (fun a ->
|
|
h_two j l a k Spin.Alfa Spin.Alfa *.
|
|
f_two i a l j Spin.Alfa Spin.Alfa
|
|
)
|
|
else 0.
|
|
)
|
|
in
|
|
|
|
let m_1122_o =
|
|
array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->
|
|
sum mos_cabs (fun a ->
|
|
h_two l j k a Spin.Alfa Spin.Beta *.
|
|
f_two i a l j Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
in
|
|
|
|
let f_1 ki kj =
|
|
let i, k, s, phase =
|
|
match Excitation.of_det ki kj with
|
|
| Excitation.(Single (phase, { hole ; particle ; spin })) ->
|
|
hole, particle, spin, phase
|
|
| _ -> assert false
|
|
in
|
|
|
|
let mos_novirt, mos_novirt' =
|
|
let alfa =
|
|
let i = Spindeterminant.bitstring @@ Determinant.alfa ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.alfa kj in
|
|
Bitstring.to_list (Bitstring.logor i j)
|
|
in
|
|
let beta =
|
|
let i = Spindeterminant.bitstring @@ Determinant.beta ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.beta kj in
|
|
Bitstring.to_list (Bitstring.logor i j)
|
|
in
|
|
match s with
|
|
| Spin.Alfa -> alfa, beta
|
|
| Spin.Beta -> beta, alfa
|
|
in
|
|
|
|
let mos_ij, mos_ij' =
|
|
let alfa =
|
|
let i = Spindeterminant.bitstring @@ Determinant.alfa ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.alfa kj in
|
|
Bitstring.to_list (Bitstring.logand i j)
|
|
in
|
|
let beta =
|
|
let i = Spindeterminant.bitstring @@ Determinant.beta ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.beta kj in
|
|
Bitstring.to_list (Bitstring.logand i j)
|
|
in
|
|
match s with
|
|
| Spin.Alfa -> alfa, beta
|
|
| Spin.Beta -> beta, alfa
|
|
in
|
|
|
|
let mos_i, mos_i' =
|
|
match s with
|
|
| Spin.Alfa -> mos_a ki, mos_b ki
|
|
| Spin.Beta -> mos_b ki, mos_a ki
|
|
in
|
|
|
|
let mos_j, mos_j' =
|
|
match s with
|
|
| Spin.Alfa -> mos_a kj, mos_b kj
|
|
| Spin.Beta -> mos_b kj, mos_a kj
|
|
in
|
|
|
|
let result =
|
|
m_1111_1H_1F.{i,k} +.
|
|
sum mos_ij (fun j ->
|
|
m_1111_1H_2Fa.{j,i,k}
|
|
+. sum mos_i (fun l -> m_1111_2Ha_2Fa.{l,j,i,k})
|
|
+. sum mos_i' (fun l -> m_1111_2Ha_2Fb.{l,j,i,k})
|
|
+. sum mos_j (fun l -> m_1121_2Ha_2Fa.{l,j,i,k})
|
|
+. sum mos_j' (fun l -> m_1121_2Ha_2Fb.{l,j,i,k})
|
|
-. sum mos_novirt (fun l -> m_1122_va.{l,j,i,k})
|
|
-. sum mos_ij (fun l -> m_1122_oa.{l,j,i,k} )
|
|
) +.
|
|
sum mos_ij' (fun j ->
|
|
m_1111_1H_2Fb.{j,i,k}
|
|
+. sum mos_i (fun l -> m_1111_2Hb_2Fa.{l,j,i,k})
|
|
+. sum mos_i' (fun l -> m_1111_2Hb_2Fb.{l,j,i,k})
|
|
+. sum mos_j (fun l -> m_1121_2Hb_2Fb.{l,j,i,k})
|
|
+. sum mos_j' (fun l -> m_1121_2Hb_2Fa.{l,j,i,k})
|
|
-. sum mos_novirt (fun l -> m_1122_v2.{l,j,i,k})
|
|
-. sum mos_novirt' (fun l -> m_1122_v3.{l,j,i,k})
|
|
-. sum mos_ij (fun l -> m_1122_o.{l,j,i,k})
|
|
)
|
|
in
|
|
match phase with
|
|
| Phase.Pos -> result
|
|
| Phase.Neg -> -. result
|
|
in
|
|
|
|
let m_2112_1H_2Fa =
|
|
array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.
|
|
h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa +.
|
|
h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.
|
|
h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa +.
|
|
sum mos_in (fun m -> -. h_two i j a m Spin.Alfa Spin.Alfa *.
|
|
f_two m a k l Spin.Alfa Spin.Alfa) +.
|
|
sum mos_cabs (fun b -> if b >= a then 0. else
|
|
h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b k l Spin.Alfa Spin.Alfa
|
|
)
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2112_1H_2Fb =
|
|
array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.
|
|
h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta +.
|
|
h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.
|
|
h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa +.
|
|
sum mos_in (fun m ->
|
|
h_two i j a m Spin.Alfa Spin.Beta *. f_two a m k l Spin.Alfa Spin.Beta +.
|
|
h_two i j m a Spin.Alfa Spin.Beta *. f_two m a k l Spin.Alfa Spin.Beta ) +.
|
|
sum mos_cabs (fun b ->
|
|
h_two i j a b Spin.Alfa Spin.Beta *. f_two a b k l Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2112_2Ha_2Fa =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.
|
|
h_two j n a n Spin.Alfa Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Alfa
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2112_2Hb_2Fa =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i n a n Spin.Alfa Spin.Beta *. f_two a j k l Spin.Alfa Spin.Alfa +.
|
|
h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Alfa
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2112_2Ha_2Fb =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.
|
|
h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Beta )
|
|
)
|
|
in
|
|
|
|
let m_2121_2Ha_2Fa =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Alfa +.
|
|
h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Alfa
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2121_2Hb_2Fa =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a l Spin.Alfa Spin.Beta *. f_two a n k n Spin.Alfa Spin.Alfa +.
|
|
h_two j i a k Spin.Alfa Spin.Beta *. f_two a n l n Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2121_2Ha_2Fb =
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Beta +.
|
|
h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Beta
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2122_2Ha_2Fa_ij =
|
|
let s = Spin.Alfa in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i n a k s s *. f_two j a n l s s
|
|
+. h_two i n a l s s *. f_two j a k n s s
|
|
-. h_two j n a k s s *. f_two i a n l s s
|
|
-. h_two j n a l s s *. f_two i a k n s s
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2122_2Hb_2Fb_ij =
|
|
let s, s' = Spin.(Alfa, Beta) in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two n i a k s s *. f_two a j n l s s'
|
|
+. h_two n j a l s s' *. f_two i a k n s s
|
|
-. h_two n j k a s s' *. f_two i a n l s s'
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2122_2Hb_2Fb_ij2 =
|
|
let s, s' = Spin.(Alfa, Beta) in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
-. h_two i n a l s s' *. f_two a j k n s s' +.
|
|
(if n < j then
|
|
h_two i n k a s s' *. f_two j a l n s' s'
|
|
+. h_two n j a l s' s' *. f_two i a k n s s'
|
|
else
|
|
-. h_two i n k a s s' *. f_two j a n l s' s'
|
|
-. h_two j n a l s' s' *. f_two i a k n s s'
|
|
)
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2122_2Ha_2Fa_ij2 =
|
|
let s, s' = Spin.(Alfa, Beta) in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i n k a s s' *. f_two j a l n s s'
|
|
+. h_two j n l a s s' *. f_two i a k n s s'
|
|
-. h_two i n l a s s' *. f_two j a k n s s'
|
|
-. h_two j n k a s s' *. f_two i a l n s s'
|
|
)
|
|
)
|
|
in
|
|
|
|
let m_2122_2Ha_2Fa_nv =
|
|
let s = Spin.Alfa in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a -> h_two i j a n s s *. f_two n a k l s s ) )
|
|
in
|
|
|
|
let m_2122_2Hb_2Fb_nv =
|
|
let s, s' = Spin.(Alfa, Beta) in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a -> -. h_two i j a n s s' *. f_two a n k l s s' ) )
|
|
in
|
|
|
|
let m_2122_2Hb_2Fb_nv2 =
|
|
let s, s' = Spin.(Alfa, Beta) in
|
|
array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->
|
|
sum mos_cabs (fun a -> -. h_two i j n a s s' *. f_two n a k l s s' ) )
|
|
in
|
|
|
|
let f_2 ki kj =
|
|
let i, j, k, l, s, s', phase =
|
|
match Excitation.of_det ki kj with
|
|
| Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->
|
|
hole, hole', particle, particle', spin, spin', phase
|
|
| _ -> assert false
|
|
in
|
|
let mos_i, mos_i' =
|
|
match s with
|
|
| Spin.Alfa -> mos_a ki, mos_b ki
|
|
| Spin.Beta -> mos_b ki, mos_a ki
|
|
in
|
|
|
|
let mos_j, mos_j' =
|
|
match s with
|
|
| Spin.Alfa -> mos_a kj, mos_b kj
|
|
| Spin.Beta -> mos_b kj, mos_a kj
|
|
in
|
|
|
|
let mos_ij, mos_ij' =
|
|
let alfa =
|
|
let i = Spindeterminant.bitstring @@ Determinant.alfa ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.alfa kj in
|
|
Bitstring.to_list (Bitstring.logand i j)
|
|
in
|
|
let beta =
|
|
let i = Spindeterminant.bitstring @@ Determinant.beta ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.beta kj in
|
|
Bitstring.to_list (Bitstring.logand i j)
|
|
in
|
|
match s with
|
|
| Spin.Alfa -> alfa, beta
|
|
| Spin.Beta -> beta, alfa
|
|
in
|
|
|
|
let mos_novirt, mos_novirt' =
|
|
let alfa =
|
|
let i = Spindeterminant.bitstring @@ Determinant.alfa ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.alfa kj in
|
|
Bitstring.to_list (Bitstring.logor i j)
|
|
in
|
|
let beta =
|
|
let i = Spindeterminant.bitstring @@ Determinant.beta ki in
|
|
let j = Spindeterminant.bitstring @@ Determinant.beta kj in
|
|
Bitstring.to_list (Bitstring.logor i j)
|
|
in
|
|
match s with
|
|
| Spin.Alfa -> alfa, beta
|
|
| Spin.Beta -> beta, alfa
|
|
in
|
|
|
|
let result =
|
|
if s = s' then
|
|
m_2112_1H_2Fa.{i,j,k,l} +.
|
|
sum mos_i (fun n -> m_2112_2Ha_2Fa.{n,i,j,k,l} ) +.
|
|
sum mos_i' (fun n -> m_2112_2Hb_2Fa.{n,i,j,k,l} ) +.
|
|
sum mos_j (fun n -> m_2121_2Ha_2Fa.{n,i,j,k,l} ) +.
|
|
sum mos_j' (fun n -> m_2121_2Ha_2Fb.{n,i,j,k,l} ) +.
|
|
sum mos_ij (fun n -> m_2122_2Ha_2Fa_ij.{n,i,j,k,l} ) +.
|
|
sum mos_ij' (fun n -> m_2122_2Ha_2Fa_ij2.{n,i,j,k,l} ) +.
|
|
sum mos_novirt (fun n -> m_2122_2Ha_2Fa_nv.{n,i,j,k,l} )
|
|
else
|
|
m_2112_1H_2Fb.{i,j,k,l} +.
|
|
sum mos_i (fun n -> m_2112_2Ha_2Fb.{n,i,j,k,l} ) +.
|
|
sum mos_i' (fun n -> m_2112_2Ha_2Fb.{n,j,i,l,k} ) +.
|
|
sum mos_j (fun n -> m_2121_2Hb_2Fa.{n,i,j,k,l} ) +.
|
|
sum mos_j' (fun n -> m_2121_2Hb_2Fa.{n,j,i,l,k} ) +.
|
|
sum mos_novirt'(fun n -> m_2122_2Hb_2Fb_nv.{n,i,j,k,l} ) +.
|
|
sum mos_novirt (fun n -> m_2122_2Hb_2Fb_nv2.{n,i,j,k,l} )+.
|
|
sum mos_ij (fun n -> m_2122_2Hb_2Fb_ij.{n,i,j,k,l} ) +.
|
|
sum mos_ij' (fun n -> m_2122_2Hb_2Fb_ij2.{n,i,j,k,l} )
|
|
in
|
|
|
|
match phase with
|
|
| Phase.Pos -> result
|
|
| Phase.Neg -> -. result
|
|
|
|
in
|
|
|
|
let f_3 ki kj =
|
|
let i, j, m, k, l, n, s1, s2, s3, phase =
|
|
match Excitation.of_det ki kj with
|
|
| Excitation.(Triple (phase,
|
|
{ hole=h1 ; particle=p1 ; spin=s1 },
|
|
{ hole=h2 ; particle=p2 ; spin=s2 },
|
|
{ hole=h3 ; particle=p3 ; spin=s3 }) ) ->
|
|
h1, h2, h3, p1, p2, p3, s1, s2, s3, phase
|
|
| _ -> assert false
|
|
in
|
|
|
|
let result =
|
|
let open Spin in
|
|
match s1, s2, s3 with
|
|
| Alfa, Alfa, Alfa
|
|
| Beta, Beta, Beta ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a k s1 s2 *. f_two m a l n s3 s3
|
|
+. h_two i j a n s1 s2 *. f_two m a k l s3 s2
|
|
+. h_two i m a l s1 s3 *. f_two j a k n s2 s3
|
|
+. h_two j m a k s2 s3 *. f_two i a l n s1 s3
|
|
+. h_two j m a n s2 s3 *. f_two i a k l s1 s2
|
|
-. h_two i j a l s1 s2 *. f_two m a k n s3 s3
|
|
-. h_two i m a k s1 s3 *. f_two j a l n s2 s3
|
|
-. h_two i m a n s1 s3 *. f_two j a k l s2 s2
|
|
-. h_two j m a l s2 s3 *. f_two i a k n s1 s3 )
|
|
| Alfa, Alfa, Beta
|
|
| Beta, Beta, Alfa ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a l s1 s2 *. f_two a m k n s1 s3
|
|
+. h_two i m k a s1 s3 *. f_two j a l n s2 s3
|
|
+. h_two j m a n s2 s3 *. f_two i a k l s1 s2
|
|
+. h_two j m l a s2 s3 *. f_two i a k n s1 s3
|
|
-. h_two i j a k s1 s2 *. f_two a m l n s1 s3
|
|
-. h_two i m a n s1 s3 *. f_two j a k l s2 s2
|
|
-. h_two i m l a s1 s3 *. f_two j a k n s2 s3
|
|
-. h_two j m k a s2 s3 *. f_two i a l n s1 s3
|
|
)
|
|
| Alfa, Beta, Beta
|
|
| Beta, Alfa, Alfa ->
|
|
sum mos_cabs (fun a ->
|
|
h_two i j a l s1 s2 *. f_two a m k n s1 s3
|
|
+. h_two i m a n s1 s3 *. f_two a j k l s1 s2
|
|
+. h_two i m k a s1 s3 *. f_two j a l n s2 s3
|
|
+. h_two j m a n s2 s3 *. f_two i a k l s1 s2
|
|
-. h_two i j a n s1 s2 *. f_two a m k l s1 s2
|
|
-. h_two i j k a s1 s2 *. f_two m a l n s2 s3
|
|
-. h_two i m a l s1 s3 *. f_two a j k n s1 s3
|
|
-. h_two j m a l s2 s3 *. f_two i a k n s1 s3
|
|
)
|
|
| Beta, Alfa, Beta
|
|
| Alfa, Beta, Alfa -> assert false (*TODO *)
|
|
in
|
|
match phase with
|
|
| Phase.Pos -> result
|
|
| Phase.Neg -> -. result
|
|
in
|
|
|
|
let result =
|
|
{ simulation ; aux_basis ;
|
|
f_0 ; f_1 ; f_2 ; f_3
|
|
}
|
|
in
|
|
Parallel.broadcast (lazy result)
|
|
|
|
|
|
|