mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-12-22 12:23:31 +01:00
283 lines
8.0 KiB
OCaml
283 lines
8.0 KiB
OCaml
open Lacaml.D
|
|
open Util
|
|
open Constants
|
|
|
|
(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *)
|
|
|
|
module HF = HartreeFock
|
|
module Si = Simulation
|
|
|
|
type mo_type =
|
|
| RHF | ROHF | UHF | CASSCF | Projected
|
|
| Natural of string
|
|
| Localized of string
|
|
|
|
type t =
|
|
{
|
|
simulation : Simulation.t; (* Simulation which produced the MOs *)
|
|
mo_type : mo_type; (* Kind of MOs (RHF, CASSCF, Localized...) *)
|
|
mo_occupation : Vec.t; (* Occupation numbers *)
|
|
mo_coef : Mat.t; (* Matrix of the MO coefficients in the AO basis *)
|
|
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 *)
|
|
}
|
|
|
|
|
|
let size t =
|
|
Mat.dim2 t.mo_coef
|
|
|
|
let simulation t = t.simulation
|
|
let mo_type t = t.mo_type
|
|
let ao_basis t = Si.ao_basis t.simulation
|
|
let mo_occupation t = t.mo_occupation
|
|
let mo_coef t = t.mo_coef
|
|
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 = Lazy.force t.one_e_ints
|
|
|
|
let mo_energies t =
|
|
let f =
|
|
let m_C = mo_coef t in
|
|
let m_N = Mat.of_diag @@ mo_occupation t in
|
|
let m_P =
|
|
gemm m_C @@ (gemm m_N m_C ~transb:`T)
|
|
in
|
|
match t.mo_type with
|
|
| RHF -> Fock.make_rhf ~density:m_P (ao_basis t)
|
|
| ROHF -> Fock.make_uhf ~density_same:m_P ~density_other:m_P (ao_basis t)
|
|
| _ -> failwith "Not implemented"
|
|
in
|
|
let m_F = Fock.fock f in
|
|
Vec.init (size t) (fun i -> m_F.{i,i})
|
|
|
|
|
|
let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
|
|
xt_o_x ~x:mo_coef ~o:ao_matrix
|
|
|
|
|
|
let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix =
|
|
let sc = gemm ao_overlap mo_coef in
|
|
x_o_xt ~x:sc ~o:mo_matrix
|
|
|
|
|
|
let four_index_transform ~mo_coef eri_ao =
|
|
|
|
let ao_num = Mat.dim1 mo_coef in
|
|
let mo_num = Mat.dim2 mo_coef in
|
|
let eri_mo =
|
|
ERI.create ~size:mo_num `Dense
|
|
in
|
|
|
|
let mo_num_2 = mo_num * mo_num in
|
|
let ao_num_2 = ao_num * ao_num in
|
|
let ao_mo_num = ao_num * mo_num in
|
|
|
|
let range_mo = list_range 1 mo_num in
|
|
let range_ao = list_range 1 ao_num in
|
|
|
|
let u = Mat.create mo_num_2 mo_num
|
|
and o = Mat.create ao_num ao_num_2
|
|
and p = Mat.create ao_num_2 mo_num
|
|
and q = Mat.create ao_mo_num mo_num
|
|
in
|
|
|
|
if Parallel.master then Printf.eprintf "4-idx transformation \n%!";
|
|
|
|
let task delta =
|
|
Mat.fill u 0.;
|
|
|
|
List.iter (fun l ->
|
|
if abs_float mo_coef.{l,delta} > epsilon then
|
|
begin
|
|
let jk = ref 0 in
|
|
List.iter (fun k ->
|
|
List.iter (fun j ->
|
|
incr jk;
|
|
ERI.get_chem_all_i eri_ao ~j ~k ~l
|
|
|> Array.iteri (fun i x -> o.{i+1,!jk} <- x)
|
|
) range_ao
|
|
) range_ao;
|
|
(* o_i_jk *)
|
|
|
|
let p =
|
|
gemm ~transa:`T ~c:p o mo_coef
|
|
(* p_jk_alpha = \sum_i o_i_jk c_i_alpha *)
|
|
in
|
|
let p' =
|
|
Bigarray.reshape_2 (Bigarray.genarray_of_array2 p) ao_num ao_mo_num
|
|
(* p_j_kalpha *)
|
|
in
|
|
|
|
let q =
|
|
gemm ~transa:`T ~c:q p' mo_coef
|
|
(* q_kalpha_beta = \sum_j p_j_kalpha c_j_beta *)
|
|
in
|
|
let q' =
|
|
Bigarray.reshape_2 (Bigarray.genarray_of_array2 q) ao_num mo_num_2
|
|
(* q_k_alphabeta = \sum_j p_j_kalpha c_j_beta *)
|
|
in
|
|
|
|
ignore @@
|
|
gemm ~transa:`T ~beta:1. ~alpha:mo_coef.{l,delta} ~c:u q' mo_coef ;
|
|
(* u_alphabeta_gamma = \sum_k q_k_alphabeta c_k_gamma *)
|
|
end
|
|
) range_ao;
|
|
let u =
|
|
Bigarray.reshape
|
|
(Bigarray.genarray_of_array2 u)
|
|
[| mo_num ; mo_num ; mo_num |]
|
|
|> Bigarray.array3_of_genarray
|
|
in
|
|
let result = ref [] in
|
|
List.iter (fun gamma ->
|
|
List.iter (fun beta ->
|
|
List.iter (fun alpha ->
|
|
let x = u.{alpha,beta,gamma} in
|
|
if x <> 0. then
|
|
result := (alpha, beta, gamma, delta, x) :: !result;
|
|
) (list_range 1 beta)
|
|
) range_mo
|
|
) (list_range 1 delta);
|
|
Array.of_list !result
|
|
in
|
|
|
|
let n = ref 0 in
|
|
Stream.of_list range_mo
|
|
|> Farm.run ~f:task ~ordered:false
|
|
|> Stream.iter (fun l ->
|
|
if Parallel.master then (Printf.eprintf "\r%d / %d%!" !n mo_num; incr n);
|
|
Array.iter (fun (alpha, beta, gamma, delta, x) ->
|
|
ERI.set_chem eri_mo alpha beta gamma delta x) l);
|
|
|
|
if Parallel.master then Printf.eprintf "\n";
|
|
Parallel.broadcast (lazy eri_mo)
|
|
|
|
|
|
let make ~simulation ~mo_type ~mo_occupation ~mo_coef () =
|
|
let ao_basis =
|
|
Si.ao_basis simulation
|
|
in
|
|
let eN_ints = lazy (
|
|
AOBasis.eN_ints ao_basis
|
|
|> NucInt.matrix
|
|
|> mo_matrix_of_ao_matrix ~mo_coef
|
|
|> NucInt.of_matrix
|
|
)
|
|
and kin_ints = lazy (
|
|
AOBasis.kin_ints ao_basis
|
|
|> KinInt.matrix
|
|
|> mo_matrix_of_ao_matrix ~mo_coef
|
|
|> KinInt.of_matrix
|
|
)
|
|
and ee_ints = lazy (
|
|
AOBasis.ee_ints ao_basis
|
|
|> four_index_transform ~mo_coef
|
|
)
|
|
in
|
|
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_hartree_fock hf =
|
|
let mo_coef = HF.eigenvectors hf in
|
|
let simulation = HF.simulation hf in
|
|
let mo_occupation = HF.occupation hf in
|
|
let mo_type =
|
|
match HF.kind hf with
|
|
| HartreeFock.RHF -> RHF
|
|
| HartreeFock.ROHF -> ROHF
|
|
| HartreeFock.UHF -> UHF
|
|
in
|
|
make ~simulation ~mo_type ~mo_occupation ~mo_coef ()
|
|
|
|
|
|
let of_mo_basis simulation other =
|
|
|
|
let mo_coef =
|
|
let basis = Simulation.ao_basis simulation in
|
|
let basis_other = ao_basis other in
|
|
let m_S =
|
|
Overlap.(matrix @@ of_basis_pair
|
|
(AOBasis.basis basis)
|
|
(AOBasis.basis basis_other) )
|
|
in
|
|
let m_X = AOBasis.ortho basis in
|
|
(* Project other vectors in the current basis *)
|
|
let m_C =
|
|
gemm m_S @@ mo_coef other
|
|
in
|
|
(* Append dummy vectors to the input vectors *)
|
|
let result =
|
|
let vecs = Mat.to_col_vecs m_X in
|
|
Array.iteri (fun i v -> if (i < Array.length vecs) then vecs.(i) <- v)
|
|
(Mat.to_col_vecs m_C) ;
|
|
Mat.of_col_vecs vecs
|
|
in
|
|
(* Gram-Schmidt Orthonormalization *)
|
|
gemm m_X @@ (Util.qr_ortho @@ gemm ~transa:`T m_X result)
|
|
in
|
|
|
|
let mo_occupation =
|
|
let occ = mo_occupation other in
|
|
Vec.init (Mat.dim2 mo_coef) (fun i ->
|
|
if (i <= Vec.dim occ) then occ.{i}
|
|
else 0.)
|
|
in
|
|
make ~simulation ~mo_type:Projected ~mo_occupation ~mo_coef ()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
let pp_mo ?(start=1) ?finish ppf t =
|
|
let open Lacaml.Io in
|
|
let rows = Mat.dim1 t.mo_coef
|
|
and cols = Mat.dim2 t.mo_coef
|
|
in
|
|
let finish =
|
|
match finish with
|
|
| None -> cols
|
|
| Some x -> x
|
|
in
|
|
|
|
let rec aux first =
|
|
|
|
if (first > finish) then ()
|
|
else
|
|
begin
|
|
Format.fprintf ppf "@[<v>@[<v4>@[<h>%s@;" "Eigenvalues:";
|
|
|
|
Array.iteri (fun i x ->
|
|
if (i+1 >= first) && (i+1 <= first+4 ) then
|
|
Format.fprintf ppf "%12f@ " x)
|
|
(Vec.to_array @@ mo_energies t);
|
|
|
|
Format.fprintf ppf "@]@;";
|
|
Format.fprintf ppf "@[%a@]"
|
|
(Lacaml.Io.pp_lfmat
|
|
~row_labels:
|
|
(Array.init rows (fun i -> Printf.sprintf "%d " (i + 1)))
|
|
~col_labels:
|
|
(Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) ))
|
|
~print_right:false
|
|
~print_foot:false
|
|
() ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) (t.mo_coef)) ;
|
|
Format.fprintf ppf "@]@;@;@]";
|
|
aux (first+5)
|
|
end
|
|
in
|
|
aux start
|
|
|
|
|