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Introduced AOBasis
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@ -1,7 +1,9 @@
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PKG str unix bigarray lacaml
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S .
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S Nuclei
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S CI
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S Utils
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S Basis
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S SCF
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S MOBasis
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B _build/**
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43
Basis/AOBasis.ml
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43
Basis/AOBasis.ml
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@ -0,0 +1,43 @@
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open Lacaml.D
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type t =
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{
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basis : Basis.t ;
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overlap : Overlap.t lazy_t;
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ortho : Orthonormalization.t lazy_t;
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eN_ints : NucInt.t lazy_t;
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ee_ints : ERI.t lazy_t;
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kin_ints : KinInt.t lazy_t;
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cartesian : bool;
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}
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let make ~cartesian ~basis nuclei =
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let overlap = lazy (
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Overlap.of_basis basis
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) in
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let ortho = lazy (
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Orthonormalization.make ~cartesian ~basis (Lazy.force overlap)
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) in
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let eN_ints = lazy (
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NucInt.of_basis_nuclei ~basis nuclei
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) in
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let kin_ints = lazy (
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KinInt.of_basis basis
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) in
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let ee_ints = lazy (
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ERI.of_basis basis
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) in
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{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ;
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cartesian ;
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}
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19
Basis/AOBasis.mli
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19
Basis/AOBasis.mli
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@ -0,0 +1,19 @@
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(** Data structure for Atomic Orbitals. *)
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type t =
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{
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basis : Basis.t ; (* One-electron basis set *)
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overlap : Overlap.t lazy_t; (* Overlap matrix *)
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ortho : Orthonormalization.t lazy_t; (* Orthonormalization matrix of the overlap *)
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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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kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *)
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cartesian : bool ; (* If true, use cartesian Gaussians (6d, 10f, ...) *)
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}
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val make : cartesian:bool -> basis:Basis.t -> Nuclei.t -> t
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(** Creates the data structure for atomic orbitals from a {Basis.t} and the
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molecular geometry {Nuclei.t} *)
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17
Basis/KinInt.mli
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17
Basis/KinInt.mli
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@ -0,0 +1,17 @@
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(** Electronic kinetic energy integrals, expressed as a matrix in a {Basis.t}.
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{%
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$$
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T_{ij} = \left \langle \chi_i \left| -\frac{1}{2} \Delta \right| \chi_j \right \rangle
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$$
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%}
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*)
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type t = Lacaml.D.Mat.t
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val of_basis : Basis.t -> t
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(** Build from a {Basis.t}. *)
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val to_file : filename:string -> t -> unit
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(** Write the integrals in a file. *)
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@ -41,7 +41,7 @@ let cutoff2 = cutoff *. cutoff
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exception NullIntegral
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let of_basis_nuclei basis nuclei =
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let of_basis_nuclei ~basis nuclei =
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let to_powers x =
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let open Zkey in
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match to_powers x with
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15
Basis/NucInt.mli
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15
Basis/NucInt.mli
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@ -0,0 +1,15 @@
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(** Electron-Nucleus attractive potential integrals, expressed as a matrix in a {Basis.t}.
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{% $$
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V_{ij} = \left \langle \chi_i \left| \sum_A \frac{-Z_A}{ | \mathbf{r} - \mathbf{R}_A |} \right| \chi_j \right \rangle
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$$ %}
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*)
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type t = Lacaml.D.Mat.t
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val of_basis_nuclei : basis:Basis.t -> Nuclei.t -> t
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(** Build from a {Basis.t} and the nuclei (coordinates and charges). *)
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val to_file : filename:string -> t -> unit
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(** Write the integrals in a file. *)
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11
SCF/Fock.ml
11
SCF/Fock.ml
@ -3,7 +3,6 @@ open Simulation
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open Constants
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type t =
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{
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fock : Mat.t ;
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@ -12,11 +11,13 @@ type t =
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exchange : Mat.t ;
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}
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let make ~density simulation =
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module Ao = AOBasis
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let make ~density ao_basis =
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let m_P = density
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and m_T = Lazy.force simulation.kin_ints
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and m_V = Lazy.force simulation.eN_ints
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and m_G = Lazy.force simulation.ee_ints
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and m_T = Lazy.force ao_basis.Ao.kin_ints
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and m_V = Lazy.force ao_basis.Ao.eN_ints
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and m_G = Lazy.force ao_basis.Ao.ee_ints
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in
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let nBas = Mat.dim1 m_T
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in
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47
SCF/Guess.ml
47
SCF/Guess.ml
@ -7,43 +7,44 @@ type guess =
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type t = guess
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module Si = Simulation
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module Ao = AOBasis
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module El = Electrons
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let hcore_guess simulation =
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let eN_ints = Lazy.force simulation.Si.eN_ints
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and kin_ints = Lazy.force simulation.Si.kin_ints
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let hcore_guess ao_basis =
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let eN_ints = Lazy.force ao_basis.Ao.eN_ints
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and kin_ints = Lazy.force ao_basis.Ao.kin_ints
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in
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Mat.add eN_ints kin_ints
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let huckel_guess simulation =
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let huckel_guess ao_basis =
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let c = 0.5 *. 1.75 in
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let ao_num = Basis.size simulation.Si.basis in
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let eN_ints = Lazy.force simulation.Si.eN_ints
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and kin_ints = Lazy.force simulation.Si.kin_ints
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and overlap = Lazy.force simulation.Si.overlap
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and m_X = Lazy.force simulation.Si.overlap_ortho
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let ao_num = Basis.size ao_basis.Ao.basis in
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let eN_ints = Lazy.force ao_basis.Ao.eN_ints
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and kin_ints = Lazy.force ao_basis.Ao.kin_ints
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and overlap = Lazy.force ao_basis.Ao.overlap
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and m_X = Lazy.force ao_basis.Ao.ortho
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in
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let diag = Array.init (ao_num+1) (fun i -> if i=0 then 0. else
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eN_ints.{i,i} +. kin_ints.{i,i})
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in
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let nocc =
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simulation.Si.electrons.El.n_alpha
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in
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let m_F = (Fock.make ~density:(gemm ~alpha:2. ~transb:`T ~k:nocc m_X m_X) simulation).Fock.fock in
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for j=1 to ao_num do
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for i=1 to ao_num do
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if (i <> j) then
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m_F.{i,j} <- c *. overlap.{i,j} *. (diag.(i) +. diag.(j)) (*TODO Pseudo *)
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function
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| 0 -> invalid_arg "Huckel guess needs a non-zero number of occupied MOs."
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| nocc ->
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let m_F = (Fock.make ~density:(gemm ~alpha:2. ~transb:`T ~k:nocc m_X m_X) ao_basis).Fock.fock in
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for j=1 to ao_num do
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for i=1 to ao_num do
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if (i <> j) then
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m_F.{i,j} <- c *. overlap.{i,j} *. (diag.(i) +. diag.(j)) (*TODO Pseudo *)
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done;
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done;
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done;
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m_F
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m_F
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let make ~guess simulation =
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let make ?(nocc=0) ~guess ao_basis =
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match guess with
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| `Hcore -> Hcore (hcore_guess simulation)
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| `Huckel -> Huckel (huckel_guess simulation)
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| `Hcore -> Hcore (hcore_guess ao_basis)
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| `Huckel -> Huckel (huckel_guess ao_basis nocc)
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@ -7,7 +7,7 @@ type guess =
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type t = guess
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val make : guess:[ `Hcore | `Huckel ] -> Simulation.t -> t
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val make : ?nocc:int -> guess:[ `Hcore | `Huckel ] -> AOBasis.t -> t
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25
SCF/RHF.ml
25
SCF/RHF.ml
@ -1,37 +1,44 @@
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open Util
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open Lacaml.D
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open Simulation
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module Si = Simulation
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module El = Electrons
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module Ao = AOBasis
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let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=0.1)
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?threshold_SCF:(threshold_SCF=1.e-5) simulation =
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(* Number of occupied MOs *)
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let nocc =
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simulation.electrons.Electrons.n_alpha
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simulation.Si.electrons.El.n_alpha
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in
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let nuclear_repulsion =
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simulation.nuclear_repulsion
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simulation.Si.nuclear_repulsion
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in
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let ao_basis =
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simulation.Si.ao_basis
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in
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(* Initial guess *)
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let guess =
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Guess.make ~guess simulation
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Guess.make ~nocc ~guess ao_basis
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in
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(* Orthogonalization matrix *)
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let m_X =
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Lazy.force simulation.overlap_ortho
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Lazy.force ao_basis.Ao.ortho
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in
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(* Overlap matrix *)
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let m_S =
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Lazy.force simulation.overlap
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Lazy.force ao_basis.Ao.overlap
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in
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let m_T = Lazy.force simulation.kin_ints
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and m_V = Lazy.force simulation.eN_ints
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let m_T = Lazy.force ao_basis.Ao.kin_ints
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and m_V = Lazy.force ao_basis.Ao.eN_ints
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in
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(* Level shift in MO basis *)
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@ -53,7 +60,7 @@ let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=
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(* Fock matrix in AO basis *)
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let m_F, m_Hc, m_J, m_K =
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let x =
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Fock.make ~density:m_P simulation
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Fock.make ~density:m_P ao_basis
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in
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x.Fock.fock, x.Fock.core, x.Fock.coulomb, x.Fock.exchange
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in
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@ -1,15 +1,10 @@
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type t = {
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charge : Charge.t;
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electrons : Electrons.t ;
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basis : Basis.t;
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nuclei : Nuclei.t;
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overlap : Overlap.t lazy_t;
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overlap_ortho : Orthonormalization.t lazy_t;
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eN_ints : NucInt.t lazy_t;
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kin_ints : KinInt.t lazy_t;
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ee_ints : ERI.t lazy_t;
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charge : Charge.t;
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electrons : Electrons.t ;
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nuclei : Nuclei.t;
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basis : Basis.t;
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ao_basis : AOBasis.t;
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nuclear_repulsion : float;
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cartesian : bool;
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}
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let make ?cartesian:(cartesian=false)
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@ -26,21 +21,22 @@ let make ?cartesian:(cartesian=false)
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let electrons =
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Electrons.make ~multiplicity ~charge nuclei
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in
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let charge =
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Charge.(Nuclei.charge nuclei + Electrons.charge electrons)
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in
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let overlap =
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lazy (Overlap.of_basis basis)
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let ao_basis =
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AOBasis.make ~basis ~cartesian nuclei
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in
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let nuclear_repulsion =
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Nuclei.repulsion nuclei
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in
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{
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charge ;
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basis ; nuclei ; electrons ; overlap ;
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overlap_ortho = lazy (Orthonormalization.make ~cartesian ~basis (Lazy.force overlap));
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eN_ints = lazy (NucInt.of_basis_nuclei basis nuclei);
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kin_ints = lazy (KinInt.of_basis basis);
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ee_ints = lazy (ERI.of_basis basis);
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nuclear_repulsion = Nuclei.repulsion nuclei;
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cartesian ;
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charge ; basis ; nuclei ; electrons ; ao_basis ;
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nuclear_repulsion ;
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}
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@ -36,10 +36,11 @@ let run ~out =
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print_float s.Simulation.nuclear_repulsion; print_newline ();
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print_endline @@ Basis.to_string s.Simulation.basis;
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let overlap = Lazy.force s.Simulation.overlap in
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let eN_ints = Lazy.force s.Simulation.eN_ints in
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let kin_ints = Lazy.force s.Simulation.kin_ints in
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let ee_ints = Lazy.force s.Simulation.ee_ints in
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let ao_basis = s.Simulation.ao_basis in
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let overlap = Lazy.force ao_basis.AOBasis.overlap in
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let eN_ints = Lazy.force ao_basis.AOBasis.eN_ints in
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let kin_ints = Lazy.force ao_basis.AOBasis.kin_ints in
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let ee_ints = Lazy.force ao_basis.AOBasis.ee_ints in
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Overlap.to_file ~filename:(out_file^".overlap") overlap;
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NucInt.to_file ~filename:(out_file^".nuc") eN_ints;
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KinInt.to_file ~filename:(out_file^".kin") kin_ints;
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