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mirror of https://gitlab.com/scemama/QCaml.git synced 2024-07-15 15:44:34 +02:00

S2 is programmed in CI

This commit is contained in:
Anthony Scemama 2019-02-22 19:19:11 +01:00
parent f2794fa54e
commit ecf61058f9
10 changed files with 265 additions and 131 deletions

157
CI/CI.ml
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@ -1,13 +1,12 @@
open Lacaml.D
module De = Determinant
module Ex = Excitation
module Sp = Spindeterminant
module Ds = Determinant_space
type t =
{
det_space : Determinant_space.t ;
det_space : Ds.t ;
h_matrix : Mat.t lazy_t ;
s2_matrix : Mat.t lazy_t ;
eigensystem : (Mat.t * Vec.t) lazy_t;
}
@ -15,6 +14,8 @@ let det_space t = t.det_space
let h_matrix t = Lazy.force t.h_matrix
let s2_matrix t = Lazy.force t.s2_matrix
let eigensystem t = Lazy.force t.eigensystem
let eigenvectors t =
@ -23,131 +24,49 @@ let eigenvectors t =
let eigenvalues t =
let (_,x) = eigensystem t in x
let h_ij mo_basis ki kj =
let h_integrals mo_basis =
let one_e_ints = MOBasis.one_e_ints mo_basis
and two_e_ints = MOBasis.two_e_ints mo_basis
and degree_a, degree_b = De.degrees ki kj
in
if degree_a+degree_b > 2 then
0.
else
begin
let kia = De.alfa ki and kib = De.beta ki
and kja = De.alfa kj and kjb = De.beta kj
in
let integral =
ERI.get_phys two_e_ints
in
let anti_integral i j k l =
integral i j k l -. integral i j l k
in
let single h p same opposite =
let same_spin =
Sp.to_list same
|> List.fold_left (fun accu i -> accu +. anti_integral h i p i) 0.
and opposite_spin =
Sp.to_list opposite
|> List.fold_left (fun accu i -> accu +. integral h i p i) 0.
and one_e =
one_e_ints.{h,p}
in one_e +. same_spin +. opposite_spin
in
let diag_element () =
let mo_a = Sp.to_list kia
and mo_b = Sp.to_list kib
in
let one_e =
List.concat [mo_a ; mo_b]
|> List.fold_left (fun accu i -> accu +. one_e_ints.{i,i}) 0.
and two_e =
let two_index i j = integral i j i j
and anti_two_index i j = anti_integral i j i j
in
let rec aux_same accu = function
| [] -> accu
| i :: rest ->
let new_accu =
List.fold_left (fun accu j -> accu +. anti_two_index i j) accu rest
in
aux_same new_accu rest
in
let rec aux_opposite accu other = function
| [] -> accu
| i :: rest ->
let new_accu =
List.fold_left (fun accu j -> accu +. two_index i j) accu other
in
aux_opposite new_accu other rest
in
(aux_same 0. mo_a) +. (aux_same 0. mo_b) +. (aux_opposite 0. mo_a mo_b)
in
one_e +. two_e
in
match degree_a, degree_b with
| 1, 1 -> (* alpha-beta double *)
begin
let ha, pa, phase_a = Ex.single_of_spindet kia kja in
let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
match phase_a, phase_b with
| Phase.Pos, Phase.Pos
| Phase.Neg, Phase.Neg -> +. integral ha hb pa pb
| Phase.Neg, Phase.Pos
| Phase.Pos, Phase.Neg -> -. integral ha hb pa pb
end
( (fun i j _ -> one_e_ints.{i,j}),
(fun i j k l s s' ->
if s' = Spin.other s then
ERI.get_phys two_e_ints i j k l
else
(ERI.get_phys two_e_ints i j k l) -.
(ERI.get_phys two_e_ints i j l k)
) )
| 2, 0 -> (* alpha double *)
begin
let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
match phase with
| Phase.Pos -> +. anti_integral h1 h2 p1 p2
| Phase.Neg -> -. anti_integral h1 h2 p1 p2
end
| 0, 2 -> (* beta double *)
begin
let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
match phase with
| Phase.Pos -> +. anti_integral h1 h2 p1 p2
| Phase.Neg -> -. anti_integral h1 h2 p1 p2
end
| 1, 0 -> (* alpha single *)
begin
let h, p, phase = Ex.single_of_spindet kia kja in
match phase with
| Phase.Pos -> +. single h p kia kib
| Phase.Neg -> -. single h p kia kib
end
let h_ij mo_basis ki kj =
let integrals =
List.map (fun f -> f mo_basis)
[ h_integrals ]
in
CIMatrixElement.make integrals ki kj
|> List.hd
| 0, 1 -> (* beta single *)
begin
let h, p, phase = Ex.single_of_spindet kib kjb in
match phase with
| Phase.Pos -> +. single h p kib kia
| Phase.Neg -> -. single h p kib kia
end
| 0, 0 -> (* diagonal element *)
diag_element ()
| _ -> assert false
end
let make det_space =
let ndet = Determinant_space.size det_space in
let det = Determinant_space.determinants det_space in
let mo_basis = Determinant_space.mo_basis det_space in
let ndet = Ds.size det_space in
let det = Ds.determinants det_space in
let mo_basis = Ds.mo_basis det_space in
let h_matrix = lazy (
Array.init ndet (fun i ->
let ki = det.(i) in
Array.init ndet (fun j ->
let kj = det.(j) in
h_ij mo_basis ki kj
)
)
|> Mat.of_array
Array.init ndet (fun i -> let ki = det.(i) in
Array.init ndet (fun j -> let kj = det.(j) in
h_ij mo_basis ki kj
))
|> Mat.of_array
)
in
let s2_matrix = lazy (
Array.init ndet (fun i -> let ki = det.(i) in
Array.init ndet (fun j -> let kj = det.(j) in
CIMatrixElement.make_s2 ki kj
))
|> Mat.of_array
)
in
let eigensystem = lazy (
@ -155,5 +74,5 @@ let make det_space =
|> Util.diagonalize_symm
)
in
{ det_space ; h_matrix ; eigensystem }
{ det_space ; h_matrix ; s2_matrix ; eigensystem }

159
CI/CIMatrixElement.ml Normal file
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@ -0,0 +1,159 @@
open Lacaml.D
module De = Determinant
module Ex = Excitation
module Sp = Spindeterminant
type t = float list
let non_zero integrals degree_a degree_b ki kj =
let kia = De.alfa ki and kib = De.beta ki
and kja = De.alfa kj and kjb = De.beta kj
in
let single h p spin same opposite =
let same_spin_mo_list =
Sp.to_list same
and opposite_spin_mo_list =
Sp.to_list opposite
in
fun one_e two_e ->
let same_spin =
List.fold_left (fun accu i -> accu +. two_e h i p i spin spin) 0. same_spin_mo_list
and opposite_spin =
List.fold_left (fun accu i -> accu +. two_e h i p i spin (Spin.other spin) ) 0. opposite_spin_mo_list
in (one_e h p spin) +. same_spin +. opposite_spin
in
let diag_element =
let mo_a = Sp.to_list kia
and mo_b = Sp.to_list kib
in
fun one_e two_e ->
let one =
(List.fold_left (fun accu i -> accu +. one_e i i Spin.Alfa) 0. mo_a)
+.
(List.fold_left (fun accu i -> accu +. one_e i i Spin.Beta) 0. mo_b)
in
let two =
let rec aux_same spin accu = function
| [] -> accu
| i :: rest ->
let new_accu =
List.fold_left (fun accu j -> accu +. two_e i j i j spin spin) accu rest
in
aux_same spin new_accu rest
in
let rec aux_opposite accu other = function
| [] -> accu
| i :: rest ->
let new_accu =
List.fold_left (fun accu j -> accu +. two_e i j i j Spin.Alfa Spin.Beta) accu other
in
aux_opposite new_accu other rest
in
(aux_same Spin.Alfa 0. mo_a) +. (aux_same Spin.Beta 0. mo_b) +.
(aux_opposite 0. mo_a mo_b)
in
one +. two
in
let result =
match degree_a, degree_b with
| 1, 1 -> (* alpha-beta double *)
begin
let ha, pa, phase_a = Ex.single_of_spindet kia kja in
let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
match phase_a, phase_b with
| Phase.Pos, Phase.Pos
| Phase.Neg, Phase.Neg -> fun _ two_e -> two_e ha hb pa pb Spin.Alfa Spin.Beta
| Phase.Neg, Phase.Pos
| Phase.Pos, Phase.Neg -> fun _ two_e -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta
end
| 2, 0 -> (* alpha double *)
begin
let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
match phase with
| Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
| Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
end
| 0, 2 -> (* beta double *)
begin
let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
match phase with
| Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
| Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
end
| 1, 0 -> (* alpha single *)
begin
let h, p, phase = Ex.single_of_spindet kia kja in
match phase with
| Phase.Pos -> fun one_e two_e -> single h p Spin.Alfa kia kib one_e two_e
| Phase.Neg -> fun one_e two_e -> -. single h p Spin.Alfa kia kib one_e two_e
end
| 0, 1 -> (* beta single *)
begin
let h, p, phase = Ex.single_of_spindet kib kjb in
match phase with
| Phase.Pos -> fun one_e two_e -> single h p Spin.Beta kib kia one_e two_e
| Phase.Neg -> fun one_e two_e -> -. single h p Spin.Beta kib kia one_e two_e
end
| 0, 0 -> (* diagonal element *)
diag_element
| _ -> assert false
in
List.map (fun (one_e, two_e) -> result one_e two_e) integrals
let make integrals ki kj =
let degree_a, degree_b =
De.degrees ki kj
in
if degree_a+degree_b > 2 then
List.map (fun _ -> 0.) integrals
else
non_zero integrals degree_a degree_b ki kj
let make_s2 ki kj =
let degree_a = De.degree_alfa ki kj in
let kia = De.alfa ki in
let kja = De.alfa kj in
if degree_a > 1 then 0.
else
let degree_b = De.degree_beta ki kj in
let kib = De.beta ki in
let kjb = De.beta kj in
match degree_a, degree_b with
| 1, 1 -> (* alpha-beta double *)
let ha, pa, phase_a = Ex.single_of_spindet kia kja in
let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
if ha = pb && hb = pa then
begin
match phase_a, phase_b with
| Phase.Pos, Phase.Pos
| Phase.Neg, Phase.Neg -> -1.
| Phase.Neg, Phase.Pos
| Phase.Pos, Phase.Neg -> 1.
end
else 0.
| 0, 0 ->
let ba = Sp.bitstring kia and bb = Sp.bitstring kib in
let tmp = Z.(logxor ba bb) in
let popcount x =
if x = Z.zero then 0 else
Z.popcount x
in
let n_a = Z.(logand ba tmp) |> popcount in
let n_b = Z.(logand bb tmp) |> popcount in
let s_z = 0.5 *. float_of_int (n_a - n_b) in
float_of_int n_a +. s_z *. (s_z -. 1.)
| _ -> 0.

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@ -41,13 +41,18 @@ let negate_phase t =
{ t with alfa = Spindeterminant.negate_phase t.alfa }
let degree_alfa t t' =
Spindeterminant.degree t.alfa t'.alfa
let degree_beta t t' =
Spindeterminant.degree t.beta t'.beta
let degrees t t' =
Spindeterminant.degree t.alfa t'.alfa,
Spindeterminant.degree t.beta t'.beta
degree_alfa t t', degree_beta t t'
let degree t t' =
let a, b = degrees t t' in a+b
(degree_alfa t t') + (degree_beta t t')
let of_lists a b =

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@ -44,6 +44,12 @@ val single_excitation : Spin.t -> hole -> particle -> t -> t
val double_excitation : Spin.t -> hole -> particle -> Spin.t -> hole -> particle -> t -> t
(** Double excitation operator {% $T_{hh'}^{pp'} = a^\dagger_p a^\dagger_{p'} a_{h'} a_h$ %}. *)
val degree_alfa : t -> t -> int
(** Returns degree of excitation between two determinants in the {% $\alpha$ %} spin. *)
val degree_beta : t -> t -> int
(** Returns degree of excitation between two determinants in the {% $\beta$ %} spin. *)
val degrees : t -> t -> int*int
(** Returns degrees of excitation between two determinants in {% $\alpha$ %} and
{% $\beta$ %} spins as a pair. *)

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@ -21,6 +21,7 @@ type t =
eN_ints : NucInt.t lazy_t; (* Electron-nucleus potential integrals *)
ee_ints : ERI.t lazy_t; (* Electron-electron potential integrals *)
kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *)
one_e_ints : Mat.t lazy_t; (* Kinetic energy integrals *)
}
@ -36,9 +37,7 @@ let eN_ints t = Lazy.force t.eN_ints
let ee_ints t = Lazy.force t.ee_ints
let kin_ints t = Lazy.force t.kin_ints
let two_e_ints t = Lazy.force t.ee_ints
let one_e_ints t =
Mat.add (NucInt.matrix @@ Lazy.force t.eN_ints)
(KinInt.matrix @@ Lazy.force t.kin_ints)
let one_e_ints t = Lazy.force t.one_e_ints
let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
xt_o_x ~x:mo_coef ~o:ao_matrix
@ -150,8 +149,12 @@ let make ~simulation ~mo_type ~mo_occupation ~mo_coef () =
|> four_index_transform ~mo_coef
)
in
{ simulation ; mo_type ; mo_occupation ; mo_coef ;
eN_ints ; ee_ints ; kin_ints }
let one_e_ints = lazy (
Mat.add (NucInt.matrix @@ Lazy.force eN_ints)
(KinInt.matrix @@ Lazy.force kin_ints) )
in
{ simulation ; mo_type ; mo_occupation ; mo_coef ;
eN_ints ; ee_ints ; kin_ints ; one_e_ints }
let of_rhf hf =

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@ -1,6 +1,47 @@
(** Electron spin *)
type t = Alfa | Beta
type t = (* m_s *)
| Alfa (* {% $m_s = +1/2$ %} *)
| Beta (* {% $m_s = -1/2$ %} *)
let other = function
| Alfa -> Beta
| Beta -> Alfa
(*
let half = 1. /. 2.
(** {% $\alpha(m_s)$ %} *)
let alfa = function
| n, Alfa -> n
| _, 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
*)

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@ -8,5 +8,6 @@ letters as [Beta], so the alignment of the code is nicer.
type t = Alfa | Beta
val other : t -> t

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@ -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

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@ -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

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@ -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