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S2 is programmed in CI
This commit is contained in:
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157
CI/CI.ml
157
CI/CI.ml
@ -1,13 +1,12 @@
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open Lacaml.D
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module De = Determinant
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module Ex = Excitation
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module Sp = Spindeterminant
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module Ds = Determinant_space
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type t =
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{
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det_space : Determinant_space.t ;
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det_space : Ds.t ;
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h_matrix : Mat.t lazy_t ;
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s2_matrix : Mat.t lazy_t ;
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eigensystem : (Mat.t * Vec.t) lazy_t;
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}
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@ -15,6 +14,8 @@ let det_space t = t.det_space
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let h_matrix t = Lazy.force t.h_matrix
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let s2_matrix t = Lazy.force t.s2_matrix
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let eigensystem t = Lazy.force t.eigensystem
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let eigenvectors t =
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@ -23,131 +24,49 @@ let eigenvectors t =
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let eigenvalues t =
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let (_,x) = eigensystem t in x
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let h_ij mo_basis ki kj =
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let h_integrals mo_basis =
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let one_e_ints = MOBasis.one_e_ints mo_basis
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and two_e_ints = MOBasis.two_e_ints mo_basis
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and degree_a, degree_b = De.degrees ki kj
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in
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if degree_a+degree_b > 2 then
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0.
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else
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begin
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let kia = De.alfa ki and kib = De.beta ki
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and kja = De.alfa kj and kjb = De.beta kj
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in
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let integral =
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ERI.get_phys two_e_ints
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in
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let anti_integral i j k l =
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integral i j k l -. integral i j l k
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in
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let single h p same opposite =
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let same_spin =
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Sp.to_list same
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|> List.fold_left (fun accu i -> accu +. anti_integral h i p i) 0.
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and opposite_spin =
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Sp.to_list opposite
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|> List.fold_left (fun accu i -> accu +. integral h i p i) 0.
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and one_e =
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one_e_ints.{h,p}
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in one_e +. same_spin +. opposite_spin
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in
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let diag_element () =
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let mo_a = Sp.to_list kia
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and mo_b = Sp.to_list kib
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in
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let one_e =
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List.concat [mo_a ; mo_b]
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|> List.fold_left (fun accu i -> accu +. one_e_ints.{i,i}) 0.
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and two_e =
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let two_index i j = integral i j i j
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and anti_two_index i j = anti_integral i j i j
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in
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let rec aux_same accu = function
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| [] -> accu
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| i :: rest ->
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let new_accu =
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List.fold_left (fun accu j -> accu +. anti_two_index i j) accu rest
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in
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aux_same new_accu rest
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in
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let rec aux_opposite accu other = function
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| [] -> accu
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| i :: rest ->
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let new_accu =
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List.fold_left (fun accu j -> accu +. two_index i j) accu other
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in
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aux_opposite new_accu other rest
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in
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(aux_same 0. mo_a) +. (aux_same 0. mo_b) +. (aux_opposite 0. mo_a mo_b)
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in
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one_e +. two_e
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in
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match degree_a, degree_b with
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| 1, 1 -> (* alpha-beta double *)
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begin
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let ha, pa, phase_a = Ex.single_of_spindet kia kja in
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let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
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match phase_a, phase_b with
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| Phase.Pos, Phase.Pos
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| Phase.Neg, Phase.Neg -> +. integral ha hb pa pb
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| Phase.Neg, Phase.Pos
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| Phase.Pos, Phase.Neg -> -. integral ha hb pa pb
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end
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( (fun i j _ -> one_e_ints.{i,j}),
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(fun i j k l s s' ->
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if s' = Spin.other 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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) )
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| 2, 0 -> (* alpha double *)
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begin
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let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
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match phase with
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| Phase.Pos -> +. anti_integral h1 h2 p1 p2
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| Phase.Neg -> -. anti_integral h1 h2 p1 p2
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end
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| 0, 2 -> (* beta double *)
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begin
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let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
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match phase with
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| Phase.Pos -> +. anti_integral h1 h2 p1 p2
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| Phase.Neg -> -. anti_integral h1 h2 p1 p2
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end
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| 1, 0 -> (* alpha single *)
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begin
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let h, p, phase = Ex.single_of_spindet kia kja in
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match phase with
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| Phase.Pos -> +. single h p kia kib
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| Phase.Neg -> -. single h p kia kib
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end
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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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[ h_integrals ]
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in
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CIMatrixElement.make integrals ki kj
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|> List.hd
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| 0, 1 -> (* beta single *)
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begin
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let h, p, phase = Ex.single_of_spindet kib kjb in
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match phase with
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| Phase.Pos -> +. single h p kib kia
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| Phase.Neg -> -. single h p kib kia
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end
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| 0, 0 -> (* diagonal element *)
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diag_element ()
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| _ -> assert false
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end
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let make det_space =
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let ndet = Determinant_space.size det_space in
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let det = Determinant_space.determinants det_space in
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let mo_basis = Determinant_space.mo_basis det_space in
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let ndet = Ds.size det_space in
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let det = Ds.determinants det_space in
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let mo_basis = Ds.mo_basis det_space in
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let h_matrix = lazy (
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Array.init ndet (fun i ->
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let ki = det.(i) in
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Array.init ndet (fun j ->
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let kj = det.(j) in
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h_ij mo_basis ki kj
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)
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)
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|> Mat.of_array
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Array.init ndet (fun i -> let ki = det.(i) in
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Array.init ndet (fun j -> let kj = det.(j) in
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h_ij mo_basis ki kj
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))
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|> Mat.of_array
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)
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in
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let s2_matrix = lazy (
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Array.init ndet (fun i -> let ki = det.(i) in
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Array.init ndet (fun j -> let kj = det.(j) in
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CIMatrixElement.make_s2 ki kj
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))
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|> Mat.of_array
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)
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in
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let eigensystem = lazy (
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@ -155,5 +74,5 @@ let make det_space =
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|> Util.diagonalize_symm
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)
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in
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{ det_space ; h_matrix ; eigensystem }
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{ det_space ; h_matrix ; s2_matrix ; eigensystem }
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159
CI/CIMatrixElement.ml
Normal file
159
CI/CIMatrixElement.ml
Normal file
@ -0,0 +1,159 @@
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open Lacaml.D
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module De = Determinant
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module Ex = Excitation
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module Sp = Spindeterminant
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type t = float list
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let non_zero integrals degree_a degree_b ki kj =
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let kia = De.alfa ki and kib = De.beta ki
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and kja = De.alfa kj and kjb = De.beta kj
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in
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let single h p spin same opposite =
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let same_spin_mo_list =
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Sp.to_list same
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and opposite_spin_mo_list =
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Sp.to_list opposite
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in
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fun one_e two_e ->
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let same_spin =
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List.fold_left (fun accu i -> accu +. two_e h i p i spin spin) 0. same_spin_mo_list
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and opposite_spin =
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List.fold_left (fun accu i -> accu +. two_e h i p i spin (Spin.other spin) ) 0. opposite_spin_mo_list
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in (one_e h p spin) +. same_spin +. opposite_spin
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in
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let diag_element =
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let mo_a = Sp.to_list kia
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and mo_b = Sp.to_list kib
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in
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fun one_e two_e ->
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let one =
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(List.fold_left (fun accu i -> accu +. one_e i i Spin.Alfa) 0. mo_a)
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+.
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(List.fold_left (fun accu i -> accu +. one_e i i Spin.Beta) 0. mo_b)
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in
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let two =
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let rec aux_same spin accu = function
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| [] -> accu
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| i :: rest ->
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let new_accu =
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List.fold_left (fun accu j -> accu +. two_e i j i j spin spin) accu rest
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in
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aux_same spin new_accu rest
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in
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let rec aux_opposite accu other = function
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| [] -> accu
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| i :: rest ->
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let new_accu =
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List.fold_left (fun accu j -> accu +. two_e i j i j Spin.Alfa Spin.Beta) accu other
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in
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aux_opposite new_accu other rest
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in
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(aux_same Spin.Alfa 0. mo_a) +. (aux_same Spin.Beta 0. mo_b) +.
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(aux_opposite 0. mo_a mo_b)
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in
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one +. two
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in
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let result =
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match degree_a, degree_b with
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| 1, 1 -> (* alpha-beta double *)
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begin
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let ha, pa, phase_a = Ex.single_of_spindet kia kja in
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let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
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match phase_a, phase_b with
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| Phase.Pos, Phase.Pos
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| Phase.Neg, Phase.Neg -> fun _ two_e -> two_e ha hb pa pb Spin.Alfa Spin.Beta
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| Phase.Neg, Phase.Pos
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| Phase.Pos, Phase.Neg -> fun _ two_e -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta
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end
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| 2, 0 -> (* alpha double *)
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begin
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let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
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match phase with
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| Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
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| Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
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end
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| 0, 2 -> (* beta double *)
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begin
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let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
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match phase with
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| Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
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| Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
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end
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| 1, 0 -> (* alpha single *)
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begin
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let h, p, phase = Ex.single_of_spindet kia kja in
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match phase with
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| Phase.Pos -> fun one_e two_e -> single h p Spin.Alfa kia kib one_e two_e
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| Phase.Neg -> fun one_e two_e -> -. single h p Spin.Alfa kia kib one_e two_e
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end
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| 0, 1 -> (* beta single *)
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begin
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let h, p, phase = Ex.single_of_spindet kib kjb in
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match phase with
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| Phase.Pos -> fun one_e two_e -> single h p Spin.Beta kib kia one_e two_e
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| Phase.Neg -> fun one_e two_e -> -. single h p Spin.Beta kib kia one_e two_e
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end
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| 0, 0 -> (* diagonal element *)
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diag_element
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| _ -> assert false
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in
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List.map (fun (one_e, two_e) -> result one_e two_e) integrals
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let make integrals ki kj =
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let degree_a, degree_b =
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De.degrees ki kj
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in
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if degree_a+degree_b > 2 then
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List.map (fun _ -> 0.) integrals
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else
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non_zero integrals degree_a degree_b ki kj
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let make_s2 ki kj =
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let degree_a = De.degree_alfa ki kj in
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let kia = De.alfa ki in
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let kja = De.alfa kj in
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if degree_a > 1 then 0.
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else
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let degree_b = De.degree_beta ki kj in
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let kib = De.beta ki in
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let kjb = De.beta kj in
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match degree_a, degree_b with
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| 1, 1 -> (* alpha-beta double *)
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let ha, pa, phase_a = Ex.single_of_spindet kia kja in
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let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
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if ha = pb && hb = pa then
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begin
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match phase_a, phase_b with
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| Phase.Pos, Phase.Pos
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| Phase.Neg, Phase.Neg -> -1.
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| Phase.Neg, Phase.Pos
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| Phase.Pos, Phase.Neg -> 1.
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end
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else 0.
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| 0, 0 ->
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let ba = Sp.bitstring kia and bb = Sp.bitstring kib in
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let tmp = Z.(logxor ba bb) in
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let popcount x =
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if x = Z.zero then 0 else
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Z.popcount x
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in
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let n_a = Z.(logand ba tmp) |> popcount in
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let n_b = Z.(logand bb tmp) |> popcount in
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let s_z = 0.5 *. float_of_int (n_a - n_b) in
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float_of_int n_a +. s_z *. (s_z -. 1.)
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| _ -> 0.
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@ -41,13 +41,18 @@ let negate_phase t =
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{ t with alfa = Spindeterminant.negate_phase t.alfa }
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let degree_alfa t t' =
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Spindeterminant.degree t.alfa t'.alfa
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let degree_beta t t' =
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Spindeterminant.degree t.beta t'.beta
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let degrees t t' =
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Spindeterminant.degree t.alfa t'.alfa,
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Spindeterminant.degree t.beta t'.beta
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degree_alfa t t', degree_beta t t'
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let degree t t' =
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let a, b = degrees t t' in a+b
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(degree_alfa t t') + (degree_beta t t')
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let of_lists a b =
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@ -44,6 +44,12 @@ val single_excitation : Spin.t -> hole -> particle -> t -> t
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val double_excitation : Spin.t -> hole -> particle -> Spin.t -> hole -> particle -> t -> t
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(** Double excitation operator {% $T_{hh'}^{pp'} = a^\dagger_p a^\dagger_{p'} a_{h'} a_h$ %}. *)
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val degree_alfa : t -> t -> int
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(** Returns degree of excitation between two determinants in the {% $\alpha$ %} spin. *)
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val degree_beta : t -> t -> int
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(** Returns degree of excitation between two determinants in the {% $\beta$ %} spin. *)
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val degrees : t -> t -> int*int
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(** Returns degrees of excitation between two determinants in {% $\alpha$ %} and
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{% $\beta$ %} spins as a pair. *)
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@ -21,6 +21,7 @@ type t =
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eN_ints : NucInt.t lazy_t; (* Electron-nucleus potential integrals *)
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ee_ints : ERI.t lazy_t; (* Electron-electron potential integrals *)
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kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *)
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one_e_ints : Mat.t lazy_t; (* Kinetic energy integrals *)
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}
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@ -36,9 +37,7 @@ let eN_ints t = Lazy.force t.eN_ints
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let ee_ints t = Lazy.force t.ee_ints
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let kin_ints t = Lazy.force t.kin_ints
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let two_e_ints t = Lazy.force t.ee_ints
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let one_e_ints t =
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Mat.add (NucInt.matrix @@ Lazy.force t.eN_ints)
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(KinInt.matrix @@ Lazy.force t.kin_ints)
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let one_e_ints t = Lazy.force t.one_e_ints
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let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
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xt_o_x ~x:mo_coef ~o:ao_matrix
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@ -150,8 +149,12 @@ let make ~simulation ~mo_type ~mo_occupation ~mo_coef () =
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|> four_index_transform ~mo_coef
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)
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in
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{ simulation ; mo_type ; mo_occupation ; mo_coef ;
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eN_ints ; ee_ints ; kin_ints }
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let one_e_ints = lazy (
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Mat.add (NucInt.matrix @@ Lazy.force eN_ints)
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(KinInt.matrix @@ Lazy.force kin_ints) )
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in
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{ simulation ; mo_type ; mo_occupation ; mo_coef ;
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eN_ints ; ee_ints ; kin_ints ; one_e_ints }
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let of_rhf hf =
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@ -1,6 +1,47 @@
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(** Electron spin *)
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type t = Alfa | Beta
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type t = (* m_s *)
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| Alfa (* {% $m_s = +1/2$ %} *)
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| Beta (* {% $m_s = -1/2$ %} *)
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let other = function
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| Alfa -> Beta
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| Beta -> Alfa
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(*
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let half = 1. /. 2.
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(** {% $\alpha(m_s)$ %} *)
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let alfa = function
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| n, Alfa -> n
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||||
| _, Beta -> 0.
|
||||
|
||||
|
||||
(** {% $\beta(m_s)$ %} *)
|
||||
let beta = function
|
||||
| _, Alfa -> 0.
|
||||
| n, Beta -> n
|
||||
|
||||
|
||||
(** {% $S_z(m_s)$ %} *)
|
||||
let s_z = function
|
||||
| n, Alfa -> half *. n, Alfa
|
||||
| n, Beta -> -. half *. n, Beta
|
||||
|
||||
let s_plus = function
|
||||
| n, Beta -> n , Alfa
|
||||
| _, Alfa -> 0., Alfa
|
||||
|
||||
let s_minus = function
|
||||
| n, Alfa -> n , Beta
|
||||
| _, Beta -> 0., Beta
|
||||
|
||||
let ( ++ ) (n, t) (m,t) =
|
||||
(m. +n.)
|
||||
|
||||
let s2 s =
|
||||
s_minus @@ s_plus s +.
|
||||
s_z s +.
|
||||
s_z @@ s_z s
|
||||
*)
|
||||
|
||||
@ -8,5 +8,6 @@ letters as [Beta], so the alignment of the code is nicer.
|
||||
|
||||
type t = Alfa | Beta
|
||||
|
||||
val other : t -> t
|
||||
|
||||
|
||||
|
||||
@ -29,7 +29,7 @@ let run ~out =
|
||||
| Some x -> x
|
||||
and nuclei_file =
|
||||
match !nuclei_file with
|
||||
| None -> raise (Invalid_argument "Basis set file should be specified with -c")
|
||||
| None -> raise (Invalid_argument "Coordinate file should be specified with -c")
|
||||
| Some x -> x
|
||||
and charge = !charge
|
||||
and multiplicity = !multiplicity
|
||||
|
||||
@ -29,7 +29,7 @@ let run ~out =
|
||||
| Some x -> x
|
||||
and nuclei_file =
|
||||
match !nuclei_file with
|
||||
| None -> raise (Invalid_argument "Basis set file should be specified with -c")
|
||||
| None -> raise (Invalid_argument "Coordinate file should be specified with -c")
|
||||
| Some x -> x
|
||||
and charge = !charge
|
||||
and multiplicity = !multiplicity
|
||||
|
||||
@ -23,7 +23,7 @@ let run ~out =
|
||||
| Some x -> x
|
||||
and nuclei_file =
|
||||
match !nuclei_file with
|
||||
| None -> raise (Invalid_argument "Basis set file should be specified with -c")
|
||||
| None -> raise (Invalid_argument "Coordinate file should be specified with -c")
|
||||
| Some x -> x
|
||||
in
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user