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723 lines
19 KiB
OCaml
723 lines
19 KiB
OCaml
open Linear_algebra
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open Particles
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open Common
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type ao = Ao.Ao_dim.t
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type mo = Mo_dim.t
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type hartree_fock_data =
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{
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iteration : int ;
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coefficients : (ao, mo) Matrix.t option ;
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eigenvalues : mo Vector.t option ;
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error : float option ;
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diis : (mo*mo) Diis.t option ;
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energy : float option ;
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density : (ao,ao) Matrix.t option ;
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density_a : (ao,ao) Matrix.t option ;
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density_b : (ao,ao) Matrix.t option ;
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fock : Fock.t option ;
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fock_a : Fock.t option ;
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fock_b : Fock.t option ;
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}
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and hartree_fock_kind =
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| RHF (** Restricted Hartree-Fock *)
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| ROHF (** Restricted Open-shell Hartree-Fock *)
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| UHF (** Unrestricted Hartree-Fock *)
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and t =
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{
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kind : hartree_fock_kind;
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simulation : Simulation.t;
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guess : Guess.t;
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data : hartree_fock_data option lazy_t array;
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nocc : int ;
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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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density_a = None ;
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density_b = None ;
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fock = None ;
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fock_a = None ;
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fock_b = None ;
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}
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module Si = Simulation
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module El = Electrons
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let kind t = t.kind
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let simulation t = t.simulation
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let guess t = t.guess
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let nocc t = t.nocc
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let n_iterations t =
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Array.fold_left (fun accu x ->
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match Lazy.force x with
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| Some _ -> accu + 1
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| None -> accu
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) 0 t.data
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let last_iteration t =
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Util.of_some @@ Lazy.force t.data.(n_iterations t - 1)
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let eigenvectors t =
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let data = last_iteration t in
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Util.of_some data.coefficients
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let eigenvalues t =
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let data = last_iteration t in
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Util.of_some data.eigenvalues
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let density t =
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let data = last_iteration t in
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match kind t with
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| RHF -> Util.of_some data.density
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| ROHF -> Matrix.add (Util.of_some data.density_a) (Util.of_some data.density_b)
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| _ -> failwith "Not implemented"
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let occupation t =
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let n_alfa, n_beta =
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El.n_alfa @@ Simulation.electrons @@ simulation t,
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El.n_beta @@ Simulation.electrons @@ simulation t
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in
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match kind t with
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| RHF -> Vector.init (Matrix.dim2 @@ eigenvectors t) (fun i ->
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if i <= nocc t then 2.0 else 0.0)
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| ROHF -> Vector.init (Matrix.dim2 @@ eigenvectors t) (fun i ->
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if i <= n_beta then 2.0 else
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if i <= n_alfa then 1.0 else
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0.0)
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| _ -> failwith "Not implemented"
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let energy t =
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let data = last_iteration t in
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Util.of_some data.energy
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let nuclear_repulsion t =
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Si.nuclear_repulsion (simulation t)
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let ao_basis t =
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Si.ao_basis (simulation t)
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let kin_energy t =
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let m_T =
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ao_basis t
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|> Ao.Basis.kin_ints
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in
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let m_P = density t in
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Matrix.gemm_trace m_P m_T
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let eN_energy t =
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let m_V =
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ao_basis t
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|> Ao.Basis.eN_ints
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in
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let m_P = density t in
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Matrix.gemm_trace m_P m_V
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let coulomb_energy t =
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let data =
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last_iteration t
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in
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match kind t with
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| RHF -> let m_P = Util.of_some data.density in
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let fock = Util.of_some data.fock in
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let m_J = Fock.coulomb fock in
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0.5 *. Matrix.gemm_trace m_P m_J
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| ROHF -> let m_P_a = Util.of_some data.density_a in
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let m_P_b = Util.of_some data.density_b in
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let fock_a = Util.of_some data.fock_a in
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let fock_b = Util.of_some data.fock_b in
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let m_J_a = Fock.coulomb fock_a in
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let m_J_b = Fock.coulomb fock_b in
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0.5 *. ( (Matrix.gemm_trace m_P_a m_J_a) +. (Matrix.gemm_trace m_P_b m_J_b) )
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| _ -> failwith "Not implemented"
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let exchange_energy t =
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let data =
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last_iteration t
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in
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match kind t with
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| RHF -> let m_P = Util.of_some data.density in
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let fock = Util.of_some data.fock in
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let m_K = Fock.exchange fock in
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-. 0.5 *. Matrix.gemm_trace m_P m_K
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| ROHF -> let m_P_a = Util.of_some data.density_a in
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let m_P_b = Util.of_some data.density_b in
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let fock_a = Util.of_some data.fock_a in
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let fock_b = Util.of_some data.fock_b in
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let m_K_a = Fock.exchange fock_a in
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let m_K_b = Fock.exchange fock_b in
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-. 0.5 *. ( (Matrix.gemm_trace m_P_a m_K_a) +. (Matrix.gemm_trace m_P_b m_K_b) )
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| _ -> failwith "Not implemented"
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let make
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?kind
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?guess:(guess=`GWH)
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?max_scf:(max_scf=64)
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?level_shift:(level_shift=0.2)
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?threshold_SCF:(threshold_SCF=1.e-8)
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simulation =
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(* Number of occupied MOs *)
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let n_alfa, n_beta =
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El.n_alfa @@ Si.electrons simulation,
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El.n_beta @@ Si.electrons simulation
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in
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let nocc = n_alfa in
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let kind =
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match kind with
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| Some kind -> kind
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| None -> if (n_alfa = n_beta) then RHF else ROHF
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in
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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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(* Orthogonalization matrix *)
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let m_X =
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Ao.Basis.ortho ao_basis
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in
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(* Overlap matrix *)
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let m_S =
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Ao.Basis.overlap ao_basis
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in
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(* Level shift in MO basis *)
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let m_LSmo =
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Array.init (Matrix.dim2 m_X) (fun i ->
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if i > nocc then level_shift else 0.)
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|> Vector.of_array
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|> Matrix.of_diag
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in
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(* Guess coefficients *)
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let guess =
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Guess.make ~nocc ~guess ao_basis
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in
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let m_C : (ao,mo) Matrix.t =
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let c_of_h m_H =
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let m_Hmo = Matrix.xt_o_x ~o:m_H ~x:m_X in
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let m_C', _ = Matrix.diagonalize_symm m_Hmo in
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Matrix.gemm_nn m_X m_C'
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in
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match guess with
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| Guess.Hcore m_H -> c_of_h m_H
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| Guess.GWH m_H -> c_of_h m_H
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| Guess.Huckel m_H -> c_of_h m_H
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| Guess.Matrix m_C -> m_C
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in
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(* A single SCF iteration *)
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let scf_iteration_rhf data =
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let nSCF = data.iteration + 1
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and m_C = Util.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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Matrix.gemm_nt ~alpha:2. ~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:(Matrix.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_F0, m_Hc, _, _ =
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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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Matrix.gemm_nn m_S m_C
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in
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Matrix.gemm_nn m_SC (Matrix.gemm_nt m_LSmo m_SC)
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|> Matrix.add m_F0
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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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Matrix.xt_o_x ~o:m_F ~x:m_X
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in
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let error_fock =
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let fps =
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Matrix.gemm_nn m_F (Matrix.gemm_nn m_P m_S)
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and spf =
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Matrix.gemm_nn m_S (Matrix.gemm_nn m_P m_F)
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in
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Matrix.xt_o_x ~o:(Matrix.sub fps spf) ~x:m_X
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in
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let diis, m_F_diis =
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let diis =
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Diis.append
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~p:(Matrix.as_vec_inplace m_F_ortho)
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~e:(Matrix.as_vec_inplace error_fock) diis
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in
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try
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let m_F_diis =
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Diis.next diis
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|> Matrix.reshape_vec_inplace (Matrix.dim1 m_F_ortho) (Matrix.dim2 m_F_ortho)
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in
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diis, m_F_diis
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with Failure _ -> (* Failure in DIIS.next *)
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Diis.make (), m_F_ortho
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in
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let diis =
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Diis.append
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~p:(Matrix.as_vec_inplace m_F_ortho)
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~e:(Matrix.as_vec_inplace error_fock) diis
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in
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(* MOs in orthogonal MO basis *)
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let m_C', _ =
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Matrix.diagonalize_symm m_F_diis
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in
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(* Re-compute eigenvalues to remove level-shift *)
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let eigenvalues =
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let m_F_ortho =
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Matrix.xt_o_x ~o:m_F0 ~x:m_X
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in
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Matrix.xt_o_x ~o:m_F_ortho ~x:m_C'
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|> Matrix.diag
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in
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(* MOs in AO basis *)
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let m_C =
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Matrix.gemm_nn m_X m_C'
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|> Conventions.rephase
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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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Matrix.gemm_trace m_P (Matrix.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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|> Matrix.amax
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|> abs_float
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in
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{ empty with
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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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in
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let scf_iteration_rohf data =
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let nSCF = data.iteration + 1
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and m_C = Util.of_some data.coefficients
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and m_P_a_prev = data.density_a
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and m_P_b_prev = data.density_b
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and fock_a_prev = data.fock_a
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and fock_b_prev = data.fock_b
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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 *)
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let m_P_a =
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Matrix.gemm_nt ~alpha:1. ~k:n_alfa m_C m_C
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in
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let m_P_b =
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Matrix.gemm_nt ~alpha:1. ~k:n_beta m_C m_C
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in
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let m_P =
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Matrix.add m_P_a m_P_b
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in
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(* Fock matrix in AO basis *)
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let fock_a =
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match fock_a_prev, threshold > 100. *. threshold_SCF with
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| Some fock_a_prev, true ->
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let threshold = 1.e-8 in
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Fock.make_uhf ~density_same:(Matrix.sub m_P_a @@ Util.of_some m_P_a_prev) ~density_other:(Matrix.sub m_P_b @@ Util.of_some m_P_b_prev) ~threshold ao_basis
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|> Fock.add fock_a_prev
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| _ -> Fock.make_uhf ~density_same:m_P_a ~density_other:m_P_b ao_basis
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in
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let fock_b =
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match fock_b_prev, threshold > 100. *. threshold_SCF with
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| Some fock_b_prev, true ->
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let threshold = 1.e-8 in
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Fock.make_uhf ~density_same:(Matrix.sub m_P_b @@ Util.of_some m_P_b_prev) ~density_other:(Matrix.sub m_P_a @@ Util.of_some m_P_a_prev) ~threshold ao_basis
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|> Fock.add fock_b_prev
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| _ -> Fock.make_uhf ~density_same:m_P_b ~density_other:m_P_a ao_basis
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in
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let m_F_a, m_Hc_a, _, _ =
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let x = fock_a in
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Fock.(fock x, core x, coulomb x, exchange x)
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in
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let m_F_b, m_Hc_b, _, _ =
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let x = fock_b in
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Fock.(fock x, core x, coulomb x, exchange x)
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in
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let m_F_mo_a =
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Matrix.xt_o_x ~o:m_F_a ~x:m_C
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in
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let m_F_mo_b =
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Matrix.xt_o_x ~o:m_F_b ~x:m_C
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in
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let m_F_mo =
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let space k =
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if k <= n_beta then
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`Core
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else if k <= n_alfa then
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`Active
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else
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`Virtual
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in
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Array.init (Matrix.dim2 m_F_mo_a) (fun i ->
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let i = i+1 in
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Array.init (Matrix.dim1 m_F_mo_a) (fun j ->
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let j = j+1 in
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match (space i), (space j) with
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| `Core , `Core ->
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0.5 *. (m_F_mo_a%:(i,j) +. m_F_mo_b%:(i,j)) -.
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(m_F_mo_b%:(i,j) -. m_F_mo_a%:(i,j))
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| `Active , `Core
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| `Core , `Active ->
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m_F_mo_b%:(i,j)
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| `Core , `Virtual
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| `Virtual , `Core
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| `Active , `Active ->
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0.5 *. (m_F_mo_a%:(i,j) +. m_F_mo_b%:(i,j))
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| `Virtual , `Active
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| `Active , `Virtual ->
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m_F_mo_a%:(i,j)
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| `Virtual , `Virtual ->
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0.5 *. (m_F_mo_a%:(i,j) +. m_F_mo_b%:(i,j)) +.
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(m_F_mo_b%:(i,j) -. m_F_mo_a%:(i,j))
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) )
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|> Matrix.of_array
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in
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let m_SC =
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Matrix.gemm_nn m_S m_C
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in
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let m_F0 =
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Matrix.x_o_xt ~x:m_SC ~o:m_F_mo
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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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Matrix.x_o_xt ~x:m_SC ~o:m_LSmo
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|> Matrix.add m_F0
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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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Matrix.xt_o_x ~o:m_F ~x:m_X
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in
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let error_fock =
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let fps =
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Matrix.gemm_nn m_F (Matrix.gemm_nn m_P m_S)
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and spf =
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Matrix.gemm_nn m_S (Matrix.gemm_nn m_P m_F)
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in
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Matrix.xt_o_x ~o:(Matrix.sub fps spf) ~x:m_X
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in
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let diis, m_F_diis =
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let diis =
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Diis.append
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~p:(Matrix.as_vec_inplace m_F_ortho)
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~e:(Matrix.as_vec_inplace error_fock) diis
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in
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try
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let m_F_diis =
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Diis.next diis
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|> Matrix.reshape_vec_inplace (Matrix.dim1 m_F_ortho) (Matrix.dim2 m_F_ortho)
|
|
in
|
|
diis, m_F_diis
|
|
|
|
with Failure _ -> (* Failure in DIIS.next *)
|
|
Diis.make (), m_F_ortho
|
|
in
|
|
|
|
|
|
(* MOs in orthogonal MO basis *)
|
|
let m_C', _ =
|
|
Matrix.diagonalize_symm m_F_diis
|
|
in
|
|
|
|
(* Re-compute eigenvalues to remove level-shift *)
|
|
let eigenvalues =
|
|
let m_F_ortho =
|
|
Matrix.xt_o_x ~o:m_F0 ~x:m_X
|
|
in
|
|
Matrix.xt_o_x ~o:m_F_ortho ~x:m_C'
|
|
|> Matrix.diag
|
|
in
|
|
|
|
(* MOs in AO basis *)
|
|
let m_C =
|
|
Matrix.gemm_nn m_X m_C'
|
|
|> Conventions.rephase
|
|
in
|
|
|
|
(* Hartree-Fock energy *)
|
|
let energy =
|
|
nuclear_repulsion +. 0.5 *. ( Matrix.gemm_trace m_P_a (Matrix.add m_Hc_a m_F_a) +.
|
|
Matrix.gemm_trace m_P_b (Matrix.add m_Hc_b m_F_b) )
|
|
in
|
|
|
|
(* Convergence criterion *)
|
|
let error =
|
|
error_fock
|
|
|> Matrix.amax
|
|
|> abs_float
|
|
in
|
|
{ empty with
|
|
iteration = nSCF ;
|
|
eigenvalues = Some eigenvalues ;
|
|
coefficients = Some m_C ;
|
|
error = Some error ;
|
|
diis = Some diis ;
|
|
energy = Some energy ;
|
|
density_a = Some m_P_a ;
|
|
density_b = Some m_P_b ;
|
|
fock_a = Some fock_a ;
|
|
fock_b = Some fock_b ;
|
|
}
|
|
|
|
in
|
|
|
|
|
|
let scf_iteration data =
|
|
match kind with
|
|
| RHF -> scf_iteration_rhf data
|
|
| ROHF -> scf_iteration_rohf data
|
|
| _ -> failwith "Not implemented"
|
|
in
|
|
|
|
let array_data =
|
|
|
|
let storage =
|
|
Array.make max_scf None
|
|
in
|
|
|
|
let rec iteration = function
|
|
| 0 -> Some (scf_iteration { empty with coefficients = Some m_C })
|
|
| n -> begin
|
|
match storage.(n) with
|
|
| Some result -> Some result
|
|
| None ->
|
|
begin
|
|
let data = iteration (n-1) in
|
|
match data with
|
|
| None -> None
|
|
| Some data ->
|
|
begin
|
|
(* Check convergence *)
|
|
let converged, _error =
|
|
match data.error with
|
|
| None -> false, 0.
|
|
| Some error -> (data.iteration = max_scf || error < threshold_SCF), error
|
|
in
|
|
if converged then
|
|
None
|
|
else
|
|
begin
|
|
storage.(n-1) <- Some { empty with
|
|
iteration = data.iteration;
|
|
energy = data.energy ;
|
|
eigenvalues = data.eigenvalues ;
|
|
error = data.error ;
|
|
};
|
|
storage.(n) <- Some (scf_iteration data);
|
|
storage.(n);
|
|
end
|
|
end
|
|
end
|
|
end
|
|
in
|
|
Array.init max_scf (fun i -> lazy (iteration i))
|
|
in
|
|
{
|
|
kind;
|
|
simulation;
|
|
guess ;
|
|
data = array_data;
|
|
nocc;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
let linewidth = 60
|
|
|
|
let pp_iterations ppf t =
|
|
let line = (String.make linewidth '-') in
|
|
Format.fprintf ppf "@[%4s%s@]@." "" line;
|
|
Format.fprintf ppf "@[%4s@[%5s@]@,@[%16s@]@,@[%16s@]@,@[%11s@]@]@."
|
|
"" "#" "HF energy " "Convergence" "HOMO-LUMO";
|
|
Format.fprintf ppf "@[%4s%s@]@." "" line;
|
|
let nocc = nocc t in
|
|
Array.iter (fun data ->
|
|
let data = Lazy.force data in
|
|
match data with
|
|
| None -> ()
|
|
| Some data ->
|
|
let e = Util.of_some data.eigenvalues in
|
|
let gap = e%.(nocc+1) -. e%.(nocc) in
|
|
begin
|
|
Format.fprintf ppf "@[%4s@[%5d@]@,@[%16.8f@]@,@[%16.4e@]@,@[%11.4f@]@]@." ""
|
|
(data.iteration) (Util.of_some data.energy) (Util.of_some data.error) gap;
|
|
end
|
|
) t.data;
|
|
Format.fprintf ppf "@[%4s%s@]@." "" line
|
|
|
|
|
|
let pp_summary ppf t =
|
|
let print text value =
|
|
Format.fprintf ppf "@[@[%30s@]@,@[%16.10f@]@]@;" text value;
|
|
and line () =
|
|
Format.fprintf ppf "@[ %s @]@;" (String.make (linewidth-4) '-');
|
|
in
|
|
let ha_to_ev = Constants.ha_to_ev in
|
|
let e = eigenvalues t in
|
|
|
|
Format.fprintf ppf "@[%s@]@;" (String.make linewidth '=')
|
|
; Format.fprintf ppf "@[<v>"
|
|
; print "One-electron energy" (kin_energy t +. eN_energy t)
|
|
; print "Kinetic" (kin_energy t)
|
|
; print "Potential" (eN_energy t)
|
|
; line ()
|
|
; print "Two-electron energy" (coulomb_energy t +. exchange_energy t)
|
|
; print "Coulomb" (coulomb_energy t)
|
|
; print "Exchange" (exchange_energy t)
|
|
; line ()
|
|
; print "HF HOMO" (ha_to_ev *. (e%.(nocc t)))
|
|
; print "HF LUMO" (ha_to_ev *. (e%.(nocc t + 1)))
|
|
; print "HF LUMO-LUMO" (ha_to_ev *. (e%.(nocc t + 1) -. e%.(nocc t)))
|
|
; line ()
|
|
; print "Electronic energy" (energy t -. nuclear_repulsion t)
|
|
; print "Nuclear repulsion" (nuclear_repulsion t)
|
|
; print "Hartree-Fock energy" (energy t)
|
|
; Format.fprintf ppf "@]"
|
|
; Format.fprintf ppf "@[%s@]@;" (String.make linewidth '=')
|
|
|
|
|
|
|
|
|
|
let pp ppf t =
|
|
Format.fprintf ppf "@.@[%s@]@." (String.make 70 '=');
|
|
Format.fprintf ppf "@[%34s %-34s@]@." (match t.kind with
|
|
| UHF -> "Unrestricted"
|
|
| RHF -> "Restricted"
|
|
| ROHF -> "Restricted Open-shell") "Hartree-Fock";
|
|
Format.fprintf ppf "@[%s@]@.@." (String.make 70 '=');
|
|
Format.fprintf ppf "@[%a@]@." pp_iterations t;
|
|
Format.fprintf ppf "@[<v 4>@;%a@]@." pp_summary t
|