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Cleaned RHF
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SCF/RHF.ml
323
SCF/RHF.ml
@ -7,6 +7,31 @@ module El = Electrons
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module Ao = AOBasis
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module Ov = Overlap
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type hartree_fock_data =
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{
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iteration : int ;
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coefficients : Mat.t option ;
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eigenvalues : Vec.t option ;
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error : float option ;
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diis : DIIS.t option ;
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energy : float option ;
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density : Mat.t option ;
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fock : Fock.t option ;
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}
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let empty =
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{
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iteration = 0 ;
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coefficients = None ;
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eigenvalues = None ;
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error = None ;
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diis = None ;
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energy = None ;
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density = None ;
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fock = None ;
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}
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let make ~guess ~max_scf ~level_shift ~threshold_SCF simulation =
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(* Number of occupied MOs *)
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let nocc =
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@ -16,7 +41,7 @@ let make ~guess ~max_scf ~level_shift ~threshold_SCF simulation =
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let nuclear_repulsion =
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Si.nuclear_repulsion simulation
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in
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let ao_basis =
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Si.ao_basis simulation
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in
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@ -45,138 +70,162 @@ let make ~guess ~max_scf ~level_shift ~threshold_SCF simulation =
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(* Level shift in MO basis *)
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let m_LSmo =
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Array.init (Mat.dim2 m_X) (fun i ->
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if i > nocc then level_shift else 0.)
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if i > nocc then level_shift else 0.)
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|> Vec.of_array
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|> Mat.of_diag
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in
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(* SCF iterations *)
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let rec loop nSCF iterations energy_prev m_C m_P_prev fock_prev threshold diis =
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(* Density matrix over nocc occupied MOs *)
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let m_P =
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gemm ~alpha:2. ~transb:`T ~k:nocc m_C m_C
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(* A single SCF iteration *)
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let scf_iteration data =
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let nSCF = data.iteration + 1
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and m_C = of_some data.coefficients
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and m_P_prev = data.density
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and fock_prev = data.fock
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and diis =
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match data.diis with
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| Some diis -> diis
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| None -> DIIS.make ()
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and threshold =
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match data.error with
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| Some error -> error
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| None -> threshold_SCF *. 2.
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in
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(* Density matrix over nocc occupied MOs *)
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let m_P =
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gemm ~alpha:2. ~transb:`T ~k:nocc m_C m_C
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in
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(* Fock matrix in AO basis *)
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let fock =
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match fock_prev, m_P_prev, threshold > 100. *. threshold_SCF with
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| Some fock_prev, Some m_P_prev, true ->
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let threshold = 1.e-8 in
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Fock.make_rhf ~density:(Mat.sub m_P m_P_prev) ~threshold ao_basis
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|> Fock.add fock_prev
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| _ -> Fock.make_rhf ~density:m_P ao_basis
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in
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let m_F, m_Hc, m_J, m_K =
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let x = fock in
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Fock.(fock x, core x, coulomb x, exchange x)
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in
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(* Add level shift in AO basis *)
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let m_F =
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let m_SC =
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gemm m_S m_C
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in
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gemm m_SC (gemm m_LSmo m_SC ~transb:`T)
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|> Mat.add m_F
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in
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(* Fock matrix in AO basis *)
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let fock =
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match fock_prev, threshold > 100. *. threshold_SCF with
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| Some fock_prev, true ->
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let threshold = 1.e-8 in
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Fock.make_rhf ~density:(Mat.sub m_P m_P_prev) ~threshold ao_basis
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|> Fock.add fock_prev
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| _ -> Fock.make_rhf ~density:m_P ao_basis
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(* Fock matrix in orthogonal basis *)
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let m_F_ortho =
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xt_o_x m_F m_X
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in
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let error_fock =
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let fps =
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gemm m_F (gemm m_P m_S)
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and spf =
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gemm m_S (gemm m_P m_F)
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in
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xt_o_x (Mat.sub fps spf) m_X
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in
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let m_F, m_Hc, m_J, m_K =
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let x = fock in
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Fock.(fock x, core x, coulomb x, exchange x)
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in
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(* Add level shift in AO basis *)
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let m_F =
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let m_SC =
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gemm m_S m_C
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in
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gemm m_SC (gemm m_LSmo m_SC ~transb:`T)
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|> Mat.add m_F
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let diis =
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DIIS.append ~p:(Mat.as_vec m_F_ortho) ~e:(Mat.as_vec error_fock) diis
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in
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let m_F_diis =
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let x =
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Bigarray.genarray_of_array1 (DIIS.next diis)
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in
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Bigarray.reshape_2 x (Mat.dim1 m_F_ortho) (Mat.dim2 m_F_ortho)
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in
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(* Fock matrix in orthogonal basis *)
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let m_F_ortho =
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xt_o_x m_F m_X
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in
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(* MOs in orthogonal MO basis *)
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let m_C', eigenvalues =
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diagonalize_symm m_F_diis
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in
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let error_fock =
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let fps =
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gemm m_F (gemm m_P m_S)
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and spf =
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gemm m_S (gemm m_P m_F)
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in
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xt_o_x (Mat.sub fps spf) m_X
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in
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(* MOs in AO basis *)
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let m_C =
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gemm m_X m_C'
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in
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let diis =
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DIIS.append ~p:(Mat.as_vec m_F_ortho) ~e:(Mat.as_vec error_fock) diis
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in
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(* Hartree-Fock energy *)
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let energy =
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nuclear_repulsion +. 0.5 *.
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Mat.gemm_trace m_P (Mat.add m_Hc m_F)
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in
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let m_F_diis =
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let x =
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Bigarray.genarray_of_array1 (DIIS.next diis)
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in
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Bigarray.reshape_2 x (Mat.dim1 m_F_ortho) (Mat.dim2 m_F_ortho)
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in
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(* Convergence criterion *)
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let error =
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error_fock
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|> Mat.as_vec
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|> amax
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|> abs_float
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in
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{
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iteration = nSCF ;
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eigenvalues = Some eigenvalues ;
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coefficients = Some m_C ;
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error = Some error ;
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diis = Some diis ;
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energy = Some energy ;
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density = Some m_P ;
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fock = Some fock ;
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}
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(* MOs in orthogonal MO basis *)
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let m_C', eigenvalues =
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diagonalize_symm m_F_diis
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in
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(* MOs in AO basis *)
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let m_C =
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gemm m_X m_C'
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in
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(* Hartree-Fock energy *)
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let energy =
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nuclear_repulsion +. 0.5 *.
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Mat.gemm_trace m_P (Mat.add m_Hc m_F)
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in
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(* Convergence criterion *)
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let error =
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error_fock
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|> Mat.as_vec
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|> amax
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|> abs_float
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in
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let converged =
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nSCF = max_scf || error < threshold_SCF
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in
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let gap =
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if nocc < Vec.dim eigenvalues then
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eigenvalues.{nocc+1} -. eigenvalues.{nocc}
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else 0.
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in
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let () =
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match energy_prev with
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| Some energy_prev ->
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Printf.eprintf "%3d %16.10f %16.10f %11.4e %10.4f\n%!" nSCF energy (energy -. energy_prev) error gap
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| None ->
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Printf.eprintf "%3d %16.10f %16s %11.4e %10.4f\n%!" nSCF energy "" error gap
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in
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if not converged then
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loop (nSCF+1) ( (energy, error, gap) :: iterations) (Some energy) m_C m_P (Some fock) error diis
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else
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let iterations =
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List.rev ( (energy, error, gap) :: iterations )
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|> Array.of_list
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in
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HartreeFock_type.(RHF
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{
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simulation;
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nocc;
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guess ;
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eigenvectors = m_C ;
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eigenvalues ;
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energy ;
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nuclear_repulsion;
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iterations ;
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kin_energy = Mat.gemm_trace m_P m_T;
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eN_energy = Mat.gemm_trace m_P m_V;
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coulomb_energy = 0.5 *. Mat.gemm_trace m_P m_J;
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exchange_energy = 0.5 *. Mat.gemm_trace m_P m_K;
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occupation = Mat.copy_diag m_P;
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})
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in
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let rec make_iterations_list data =
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let energy_prev = data.energy in
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(** Perform SCF iteration *)
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let data = scf_iteration data in
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(** Check convergence *)
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let converged, error =
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match data.error with
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| None -> false, 0.
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| Some error -> (data.iteration = max_scf || error < threshold_SCF), error
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in
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(** Print values *)
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let nSCF = data.iteration in
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let energy = of_some data.energy in
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let () =
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match energy_prev with
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| Some energy_prev ->
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Printf.eprintf "%3d %16.10f %16.10f %11.4e\n%!" nSCF energy (energy -. energy_prev) error
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| None ->
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Printf.eprintf "%3d %16.10f %16s %11.4e\n%!" nSCF energy "" error
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in
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if converged then
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[ data ]
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else
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{ empty with
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iteration = data.iteration;
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energy = data.energy ;
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eigenvalues = data.eigenvalues ;
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error = data.error ;
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} :: (make_iterations_list data)
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in
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(* Guess coefficients *)
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let m_H =
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match guess with
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@ -193,8 +242,50 @@ let make ~guess ~max_scf ~level_shift ~threshold_SCF simulation =
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gemm m_X m_C'
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in
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let diis = DIIS.make () in
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loop 1 [] None m_C m_C None threshold_SCF diis
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let iterations_list =
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make_iterations_list { empty with coefficients = Some m_C }
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in
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let iterations, data =
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List.map (fun data ->
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let gap =
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let eigenvalues = of_some data.eigenvalues in
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if nocc < Vec.dim eigenvalues then
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eigenvalues.{nocc+1} -. eigenvalues.{nocc}
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else 0.
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and energy = of_some data.energy
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and error = of_some data.error
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in
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(energy, error, gap)
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) iterations_list
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|> Array.of_list,
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List.hd (List.rev iterations_list)
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in
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let energy = of_some data.energy in
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let m_P = of_some data.density in
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let fock = of_some data.fock in
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let m_J = Fock.coulomb fock in
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let m_K = Fock.exchange fock in
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HartreeFock_type.(
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RHF {
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simulation;
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nocc;
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guess ;
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eigenvectors = of_some data.coefficients ;
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eigenvalues = of_some data.eigenvalues ;
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energy ;
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nuclear_repulsion;
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iterations ;
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kin_energy = Mat.gemm_trace m_P m_T;
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eN_energy = Mat.gemm_trace m_P m_V;
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coulomb_energy = 0.5 *. Mat.gemm_trace m_P m_J;
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exchange_energy = 0.5 *. Mat.gemm_trace m_P m_K;
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occupation = Mat.copy_diag m_P;
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}
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)
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@ -171,6 +171,11 @@ let boys_function ~maxm t =
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end
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let of_some = function
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| Some a -> a
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| None -> assert false
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(** {2 List functions} *)
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let list_some l =
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@ -36,6 +36,7 @@ val chop : float -> (unit -> float) -> float
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than {!Constants.epsilon}, and return [a *. f ()].
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*)
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val of_some : 'a option -> 'a
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(** {2 Functions related to the Boys function} *)
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