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203 lines
5.5 KiB
OCaml
203 lines
5.5 KiB
OCaml
open Lacaml.D
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open Util
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open Constants
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(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *)
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module HF = HartreeFock
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module Si = Simulation
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type mo_type =
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| RHF | ROHF | UHF | CASSCF | Projected
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| Natural of string
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| Localized of string
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type t =
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{
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simulation : Simulation.t; (* Simulation which produced the MOs *)
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mo_type : mo_type; (* Kind of MOs (RHF, CASSCF, Localized...) *)
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mo_occupation : Vec.t; (* Occupation numbers *)
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mo_coef : Mat.t; (* Matrix of the MO coefficients in the AO basis *)
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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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f12_ints : F12.t lazy_t; (* F12 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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let size t =
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Mat.dim2 t.mo_coef
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let simulation t = t.simulation
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let mo_type t = t.mo_type
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let ao_basis t = Si.ao_basis t.simulation
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let mo_occupation t = t.mo_occupation
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let mo_coef t = t.mo_coef
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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 f12_ints t = Lazy.force t.f12_ints
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let one_e_ints t = Lazy.force t.one_e_ints
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let mo_energies t =
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let m_C = mo_coef t in
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let f =
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let m_N = Mat.of_diag @@ mo_occupation t in
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let m_P = x_o_xt m_N m_C in
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match t.mo_type with
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| RHF -> Fock.make_rhf ~density:m_P (ao_basis t)
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| Projected
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| ROHF -> (Mat.scal 0.5 m_P;
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Fock.make_uhf ~density_same:m_P ~density_other:m_P (ao_basis t))
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| _ -> failwith "Not implemented"
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in
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let m_F0 = Fock.fock f in
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xt_o_x m_F0 m_C
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|> Mat.copy_diag
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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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let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix =
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let sc = gemm ao_overlap mo_coef in
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x_o_xt ~x:sc ~o:mo_matrix
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let make ~simulation ~mo_type ~mo_occupation ~mo_coef () =
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let ao_basis =
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Si.ao_basis simulation
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in
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let eN_ints = lazy (
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AOBasis.eN_ints ao_basis
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|> NucInt.matrix
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|> mo_matrix_of_ao_matrix ~mo_coef
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|> NucInt.of_matrix
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)
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and kin_ints = lazy (
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AOBasis.kin_ints ao_basis
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|> KinInt.matrix
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|> mo_matrix_of_ao_matrix ~mo_coef
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|> KinInt.of_matrix
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)
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and ee_ints = lazy (
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AOBasis.ee_ints ao_basis
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|> ERI.four_index_transform mo_coef
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)
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and f12_ints = lazy (
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AOBasis.f12_ints ao_basis
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|> F12.four_index_transform mo_coef
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)
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in
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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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f12_ints }
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let values t point =
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let c = mo_coef t in
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let a = AOBasis.values (Simulation.ao_basis t.simulation) point in
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gemv ~trans:`T c a
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let of_hartree_fock hf =
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let mo_coef = HF.eigenvectors hf in
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let simulation = HF.simulation hf in
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let mo_occupation = HF.occupation hf in
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let mo_type =
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match HF.kind hf with
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| HartreeFock.RHF -> RHF
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| HartreeFock.ROHF -> ROHF
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| HartreeFock.UHF -> UHF
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in
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make ~simulation ~mo_type ~mo_occupation ~mo_coef ()
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let of_mo_basis simulation other =
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let mo_coef =
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let basis = Simulation.ao_basis simulation in
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let basis_other = ao_basis other in
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let m_S =
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Overlap.(matrix @@ of_basis_pair
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(AOBasis.basis basis)
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(AOBasis.basis basis_other) )
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in
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let m_X = AOBasis.ortho basis in
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(* Project other vectors in the current basis *)
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let m_C =
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gemm m_S @@ mo_coef other
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in
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(* Append dummy vectors to the input vectors *)
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let result =
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let vecs = Mat.to_col_vecs m_X in
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Array.iteri (fun i v -> if (i < Array.length vecs) then vecs.(i) <- v)
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(Mat.to_col_vecs m_C) ;
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Mat.of_col_vecs vecs
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in
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(* Gram-Schmidt Orthonormalization *)
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gemm m_X @@ (Util.qr_ortho @@ gemm ~transa:`T m_X result)
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|> Util.remove_epsilons
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|> Conventions.rephase
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in
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let mo_occupation =
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let occ = mo_occupation other in
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Vec.init (Mat.dim2 mo_coef) (fun i ->
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if (i <= Vec.dim occ) then occ.{i}
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else 0.)
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in
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make ~simulation ~mo_type:Projected ~mo_occupation ~mo_coef ()
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let pp ?(start=1) ?(finish=0) ppf t =
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let open Lacaml.Io in
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let rows = Mat.dim1 t.mo_coef
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and cols = Mat.dim2 t.mo_coef
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in
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let finish =
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match finish with
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| 0 -> cols
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| x -> x
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in
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let rec aux first =
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if (first > finish) then ()
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else
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begin
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Format.fprintf ppf "@[<v>@[<v4>@[<h>%s@;" "Eigenvalues:";
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Array.iteri (fun i x ->
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if (i+1 >= first) && (i+1 <= first+4 ) then
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Format.fprintf ppf "%12f@ " x)
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(Vec.to_array @@ mo_energies t);
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Format.fprintf ppf "@]@;";
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Format.fprintf ppf "@[%a@]"
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(Lacaml.Io.pp_lfmat
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~row_labels:
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(Array.init rows (fun i -> Printf.sprintf "%d " (i + 1)))
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~col_labels:
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(Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) ))
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~print_right:false
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~print_foot:false
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() ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) (t.mo_coef)) ;
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Format.fprintf ppf "@]@;@;@]";
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(aux [@tailcall]) (first+5)
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end
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in
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aux start
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