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Dressed integrals in F12
This commit is contained in:
parent
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commit
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307
CI/F12CI.ml
307
CI/F12CI.ml
@ -1,314 +1,83 @@
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open Lacaml.D
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module Ds = DeterminantSpace
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type t =
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{
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mo_basis : MOBasis.t ;
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aux_basis : MOBasis.t ;
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det_space : DeterminantSpace.t ;
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ci : CI.t ;
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hf12_integrals : HF12.t ;
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eigensystem : (Mat.t * Vec.t) lazy_t;
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}
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let ci t = t.ci
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let mo_basis t = t.mo_basis
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let det_space t = t.det_space
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let mo_class t = DeterminantSpace.mo_class @@ det_space t
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let mo_class t = Ds.mo_class @@ det_space t
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let eigensystem t = Lazy.force t.eigensystem
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let f12_integrals mo_basis =
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let two_e_ints = MOBasis.f12_ints mo_basis in
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( (fun _ _ _ -> 0.),
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(fun i j k l s s' ->
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if (i=k && j<>l) || (j=l && i<>k) then
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0.
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else
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begin
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let ijkl = F12.get_phys two_e_ints i j k l
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in
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(*
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let hf_ij_non_zero hf12_integrals deg_a deg_b ki kj =
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let integrals = [
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let one_e _ _ _ = 0. in
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let hf12_s, hf12_o = hf12_integrals in
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let two_e i j k l s s' =
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if s' = Spin.other s then
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(* Minus sign because we swap spin variables
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instead of orbital variables *)
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0.375 *. ijkl +. 0.125 *. ijlk
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hf12_o.{i,j,k,l}
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else
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0.25 *. (ijkl -. ijlk)
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*)
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if s' = Spin.other s then
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ijkl
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else
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let ijlk = F12.get_phys two_e_ints i j l k
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hf12_s.{i,j,k,l}
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in
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ijkl -. ijlk
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end
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) )
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let h_ij mo_basis ki kj =
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let integrals =
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List.map (fun f -> f mo_basis)
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[ CI.h_integrals ]
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(one_e, two_e)
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]
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in
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CIMatrixElement.make integrals ki kj
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|> List.hd
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let f_ij mo_basis ki kj =
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let integrals =
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List.map (fun f -> f mo_basis)
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[ f12_integrals ]
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in
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CIMatrixElement.make integrals ki kj
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CIMatrixElement.non_zero integrals deg_a deg_b ki kj
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|> List.hd
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let hf_ij mo_basis ki kj =
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let integrals =
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List.map (fun f -> f mo_basis)
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[ CI.h_integrals ; f12_integrals ]
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in
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CIMatrixElement.make integrals ki kj
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let is_a_double det_space =
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let mo_class = DeterminantSpace.mo_class det_space in
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let mo_num = Array.length @@ MOClass.mo_class_array mo_class in
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let m l =
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List.fold_left (fun accu i ->
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let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)
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) (Bitstring.zero mo_num) l
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in
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let aux_mask = m (MOClass.auxiliary_mos mo_class) in
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fun k ->
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let alfa =
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Determinant.alfa k
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|> Spindeterminant.bitstring
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in
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let beta =
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Determinant.beta k
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|> Spindeterminant.bitstring
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in
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let a = Bitstring.logand aux_mask alfa
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and b = Bitstring.logand aux_mask beta
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in
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match Bitstring.popcount a + Bitstring.popcount b with
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| 2 -> true
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| _ -> false
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let p12 det_space =
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let mo_class = DeterminantSpace.mo_class det_space in
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let mo_num = Array.length @@ MOClass.mo_class_array mo_class in
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let m l =
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List.fold_left (fun accu i ->
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let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)
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) (Bitstring.zero mo_num) l
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in
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let aux_mask = m (MOClass.auxiliary_mos mo_class) in
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let not_aux_mask =
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Bitstring.(shift_left_one mo_num mo_num |> minus_one)
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in
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fun k ->
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let alfa =
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Determinant.alfa k
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|> Spindeterminant.bitstring
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in
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let beta =
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Determinant.beta k
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|> Spindeterminant.bitstring
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in
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let a = Bitstring.logand aux_mask alfa
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and b = Bitstring.logand aux_mask beta
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in
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match Bitstring.popcount a, Bitstring.popcount b with
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| 2, 0
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| 0, 2 -> Some (Determinant.negate_phase k)
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| 1, 1 -> Some (Determinant.of_spindeterminants
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(Spindeterminant.of_bitstring @@
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Bitstring.(logor b (logand not_aux_mask alfa)) )
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(Spindeterminant.of_bitstring @@
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Bitstring.(logor a (logand not_aux_mask beta))
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) )
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(*
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| 1, 0
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| 0, 1 -> Some (Determinant.negate_phase k)
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| 0, 1 -> Some (Determinant.vac 1)
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*)
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| _ -> None
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let dressing_vector ~frozen_core aux_basis f12_amplitudes ci =
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let dressing_vector ~frozen_core hf12_integrals f12_amplitudes ci =
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if Parallel.master then
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Printf.printf "Building matrix\n%!";
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(* Determinants of the FCI space as a list *)
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let in_dets =
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DeterminantSpace.determinant_stream ci.CI.det_space
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|> Util.stream_to_list
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let det_space =
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ci.CI.det_space
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in
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(* Stream that generates only singly and doubly excited determinants
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wrt FCI space *)
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let out_dets_stream =
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(* Stream that generates all determinants of FCI space *)
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let s =
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DeterminantSpace.fci_of_mo_basis ~frozen_core aux_basis
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|> DeterminantSpace.determinant_stream
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in
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(* Select only doubly excited determinants wrt FCI space *)
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Stream.from (fun _ ->
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try
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let p12 = p12 ci.CI.det_space in
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let rec result () =
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let ki = Stream.next s in
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match p12 ki with
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| Some ki' -> Some (ki, ki')
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| None -> result ()
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in
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result ()
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with Stream.Failure -> None
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)
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in
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let make_h_and_f alpha_list =
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let rec col_vecs_list accu_H accu_F = function
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| [] ->
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List.rev accu_H,
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List.rev accu_F
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| (ki, ki') :: rest ->
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begin
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let h, f =
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List.map (fun kj ->
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match hf_ij aux_basis kj ki with
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| [ a ; b ] -> a, b
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| _ -> assert false ) in_dets
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|> List.split
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in
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let f' =
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List.map (fun kj -> f_ij aux_basis kj ki') in_dets
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in
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let h = Vec.of_list h in
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let f = Vec.of_list f in
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let f' = Vec.of_list f' in
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scal 0.375 f;
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scal 0.125 f';
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let f = Vec.add f f' in
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col_vecs_list (h::accu_H) (f::accu_F) rest
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end
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in
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let h, f =
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col_vecs_list [] [] alpha_list
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in
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Mat.of_col_vecs_list h,
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Mat.of_col_vecs_list f
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in
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let m_HF =
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let batch_size = 1 + 1_000_000 / (Mat.dim1 f12_amplitudes) in
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let input_stream =
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Stream.from (fun i ->
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let rec make_batch accu = function
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| 0 -> accu
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| n -> try
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let alpha = Stream.next out_dets_stream in
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let accu = alpha :: accu in
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make_batch accu (n-1)
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with Stream.Failure -> accu
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let f =
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match Ds.determinants det_space with
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| Ds.Arbitrary _ -> CI.create_matrix_arbitrary
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| Ds.Spin _ -> CI.create_matrix_spin_computed
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in
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let result = make_batch [] batch_size in
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if result = [] then None else Some result
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)
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f (fun deg_a deg_b ki kj ->
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hf_ij_non_zero hf12_integrals deg_a deg_b ki kj
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) det_space
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in
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let iteration input =
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Printf.printf ".%!";
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let m_H_aux, m_F_aux = make_h_and_f input in
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let m_HF =
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gemm m_H_aux m_F_aux ~transb:`T
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in
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gemm m_HF f12_amplitudes
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in
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let result =
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let x =
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try [ Stream.next out_dets_stream ]
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with Stream.Failure -> failwith "Auxiliary basis set does not produce any excited determinant"
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in
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iteration x
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in
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input_stream
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|> Farm.run ~ordered:false ~f:iteration
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|> Stream.iter (fun hf ->
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ignore @@ Mat.add result hf ~c:result );
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Printf.printf "\n";
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Parallel.broadcast (lazy result)
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in
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if Parallel.master then Printf.printf "Done\n%!";
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Matrix.dense_of_mat m_HF
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Matrix.mm (Lazy.force m_HF) (Matrix.dense_of_mat f12_amplitudes)
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let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename ?(state=1) () =
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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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Printf.printf "Add aux basis\n%!";
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(* Add auxiliary basis set *)
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let s =
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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 s mo_basis
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in
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let () =
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ignore @@ MOBasis.f12_ints aux_basis
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in
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let () =
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ignore @@ MOBasis.two_e_ints aux_basis
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in
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let det_space =
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DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num
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DeterminantSpace.fci_of_mo_basis mo_basis ~frozen_core
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in
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let ci = CI.make ~n_states:state det_space in
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let hf12_integrals =
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HF12.make ~simulation ~mo_basis ~aux_basis_filename ()
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in
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let ci_coef, ci_energy =
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let x = Lazy.force ci.eigensystem in
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Parallel.broadcast (lazy x)
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in
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let e_shift =
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let det =
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DeterminantSpace.determinant_stream det_space
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|> Stream.next
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in
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h_ij aux_basis det det
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in
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let eigensystem = lazy (
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let m_H =
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Lazy.force ci.CI.m_H
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@ -320,7 +89,7 @@ Printf.printf "Add aux basis\n%!";
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let delta =
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(* delta_i = {% $\sum_j c_j H_{ij}$ %} *)
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dressing_vector ~frozen_core aux_basis psi ci
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dressing_vector ~frozen_core hf12_integrals psi ci
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|> Matrix.to_mat
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in
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@ -449,14 +218,14 @@ Printf.printf "Add aux basis\n%!";
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(Mat.to_col_vecs eigenvectors).(0) )
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in
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if Parallel.master then
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Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{state} +. e_shift
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Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{state}
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+. Simulation.nuclear_repulsion simulation);
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if conv > threshold then
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iteration ~state eigenvectors
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else
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let eigenvalues =
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Vec.map (fun x -> x +. e_shift) eigenvalues
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Vec.map (fun x -> x +. ci.CI.e_shift) eigenvalues
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in
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eigenvectors, eigenvalues
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in
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@ -464,6 +233,8 @@ Printf.printf "Add aux basis\n%!";
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)
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in
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{ mo_basis ; aux_basis ; det_space ; ci ; eigensystem }
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{ mo_basis ; det_space ; ci ; hf12_integrals ; eigensystem }
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186
MOBasis/HF12.ml
Normal file
186
MOBasis/HF12.ml
Normal file
@ -0,0 +1,186 @@
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(** %{ $ \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 = (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t
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* (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t
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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 aux_basis =
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let s =
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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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MOBasis.of_mo_basis s 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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let f12 =
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MOBasis.f12_ints aux_basis
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in
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let eri =
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MOBasis.two_e_ints aux_basis
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in
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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 result_s, result_o =
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Bigarray.Genarray.create Float64 Bigarray.fortran_layout [| mo_num ; mo_num ; mo_num ; mo_num |] ,
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Bigarray.Genarray.create Float64 Bigarray.fortran_layout [| mo_num ; mo_num ; mo_num ; mo_num |]
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in
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let h_s = Bigarray.Array3.create Float64 Bigarray.fortran_layout mo_num aux_num aux_num in
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let f_s = Bigarray.Array3.create Float64 Bigarray.fortran_layout aux_num aux_num mo_num in
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let h_o = Bigarray.Array3.create Float64 Bigarray.fortran_layout mo_num aux_num aux_num in
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let f_o = Bigarray.Array3.create Float64 Bigarray.fortran_layout aux_num aux_num mo_num in
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let hf_s = Mat.create mo_num mo_num in
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let hf_o = Mat.create mo_num mo_num in
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for a=1 to mo_num do
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for b=1 to mo_num do
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for i=1 to mo_num do
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h_s.{i, a, b} <- 0. ;
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h_o.{i, a, b} <- 0.
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done
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done
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done;
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for k=1 to mo_num do
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for b=1 to mo_num do
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for a=1 to mo_num do
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f_s.{a, b, k} <- 0. ;
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f_o.{a, b, k} <- 0.
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done
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done
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done;
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let task (j,l) =
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let h i a b =
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h_s.{i, a, b} <- ERI.get_phys eri i j a b -. ERI.get_phys eri i j b a ;
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h_o.{i, a, b} <- ERI.get_phys eri i j a b
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and f a b k =
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f_s.{a, b, k} <- 0.25 *. (F12.get_phys f12 a b k l -. F12.get_phys f12 a b l k) ;
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f_o.{a, b, k} <- 0.375 *. F12.get_phys f12 a b k l +. 0.125 *. F12.get_phys f12 b a k l
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in
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for a=mo_num+1 to aux_num do
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for b=mo_num+1 to aux_num do
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for i=1 to mo_num do
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h i a b
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done
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done
|
||||
done;
|
||||
|
||||
for k=1 to mo_num do
|
||||
for b=mo_num+1 to aux_num do
|
||||
for a=mo_num+1 to aux_num do
|
||||
f a b k
|
||||
done
|
||||
done
|
||||
done;
|
||||
|
||||
(*
|
||||
for a=1 to mo_num do
|
||||
for b=mo_num+1 to aux_num do
|
||||
for i=1 to mo_num do
|
||||
if i <> a then
|
||||
h i a b
|
||||
done
|
||||
done
|
||||
done;
|
||||
|
||||
for k=1 to mo_num do
|
||||
for b=mo_num+1 to aux_num do
|
||||
for a=1 to mo_num do
|
||||
if k <> a then
|
||||
f a b k
|
||||
done
|
||||
done
|
||||
done;
|
||||
*)
|
||||
let h_o =
|
||||
Bigarray.(reshape (genarray_of_array3 h_o)) [| mo_num ; aux_num*aux_num |]
|
||||
|> Bigarray.array2_of_genarray
|
||||
in
|
||||
let f_o =
|
||||
Bigarray.(reshape (genarray_of_array3 f_o)) [| aux_num*aux_num ; mo_num |]
|
||||
|> Bigarray.array2_of_genarray
|
||||
in
|
||||
let h_s =
|
||||
Bigarray.(reshape (genarray_of_array3 h_s)) [| mo_num ; aux_num*aux_num |]
|
||||
|> Bigarray.array2_of_genarray
|
||||
in
|
||||
let f_s =
|
||||
Bigarray.(reshape (genarray_of_array3 f_s)) [| aux_num*aux_num ; mo_num |]
|
||||
|> Bigarray.array2_of_genarray
|
||||
in
|
||||
let hf_s = gemm ~alpha:1.0 ~c:hf_s h_s f_s in
|
||||
let hf_o = gemm ~alpha:1.0 ~c:hf_o h_o f_o in
|
||||
hf_s, hf_o, j, l
|
||||
in
|
||||
|
||||
let tasks =
|
||||
let rec next accu = function
|
||||
| _, 0 -> accu
|
||||
| 0, l -> next accu (mo_num, l-1)
|
||||
| j, l -> next ((j,l) :: accu) ((j-1), l)
|
||||
in
|
||||
next [] (mo_num, mo_num)
|
||||
|> Stream.of_list
|
||||
in
|
||||
|
||||
|
||||
Farm.run ~f:task ~ordered:true tasks
|
||||
|> Stream.iter (fun (hf_s, hf_o, j, l) ->
|
||||
(*
|
||||
Printf.printf "%d %d\n" j l ;
|
||||
*)
|
||||
for k=1 to mo_num do
|
||||
for i=1 to mo_num do
|
||||
result_s.{i,k,j,l} <- hf_s.{i,k} ;
|
||||
result_o.{i,k,j,l} <- hf_o.{i,k}
|
||||
done
|
||||
done );
|
||||
|
||||
|
||||
|
||||
(*
|
||||
for l=1 to mo_num do
|
||||
for k=1 to mo_num do
|
||||
for j=1 to mo_num do
|
||||
for i=1 to mo_num do
|
||||
Printf.printf "%d %d %d %d %e\n" i j k l result.{i,j,k,l}
|
||||
done
|
||||
done
|
||||
done
|
||||
done;
|
||||
Printf.printf "%!";
|
||||
*)
|
||||
|
||||
Parallel.broadcast (lazy (result_s, result_o) )
|
||||
|
||||
|
||||
|
@ -258,6 +258,9 @@ let get_phys t i j k l = get ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l
|
||||
let set_chem t i j k l value = set ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t
|
||||
let set_phys t i j k l value = set ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t
|
||||
|
||||
let increment_chem t i j k l value = increment ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t
|
||||
let increment_phys t i j k l value = increment ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t
|
||||
|
||||
|
||||
|
||||
type element = (** Element for the stream *)
|
||||
|
@ -38,6 +38,12 @@ val set_chem : t -> int -> int -> int -> int -> float -> unit
|
||||
val set_phys : t -> int -> int -> int -> int -> float -> unit
|
||||
(** Set an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
|
||||
|
||||
val increment_chem : t -> int -> int -> int -> int -> float -> unit
|
||||
(** Increments an integral using the Chemist's convention {% $(ij|kl)$ %}. *)
|
||||
|
||||
val increment_phys : t -> int -> int -> int -> int -> float -> unit
|
||||
(** Increments an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
|
||||
|
||||
val get_chem_all_i : t -> j:int -> k:int -> l:int -> Vec.t
|
||||
(** Get all integrals in an array [a.{i} =] {% $(\cdot j|kl)$ %} . *)
|
||||
|
||||
|
@ -87,6 +87,7 @@ let () =
|
||||
MOBasis.of_hartree_fock hf
|
||||
in
|
||||
|
||||
|
||||
let fcif12 =
|
||||
F12CI.make ~simulation ~frozen_core:false ~mo_basis ~aux_basis_filename ~state ()
|
||||
in
|
||||
|
Loading…
Reference in New Issue
Block a user