Four-idx transformation

Basis/KinInt.ml

@@ -13,6 +13,7 @@ module Psp = PrimitiveShellPair
 
 type t = Mat.t
 external matrix : t -> Mat.t = "%identity"
+external of_matrix : Mat.t -> t = "%identity"
 
 let cutoff = integrals_cutoff
 

Basis/MatrixOnBasis.mli

@@ -11,4 +11,7 @@ val to_file : filename:string -> t -> unit
 (** Write the integrals in a file. *)
 
 val matrix : t -> Mat.t
-(** Returns the matrix suitable for Lacaml *)
+(** Returns the matrix suitable for Lacaml. *)
+
+val of_matrix : Mat.t -> t 
+(** Build from a Lacaml matrix. *)

Basis/NucInt.ml

@@ -6,6 +6,7 @@ open Lacaml.D
 
 type t = Mat.t
 external matrix : t -> Mat.t = "%identity"
+external of_matrix : Mat.t -> t = "%identity"
 
 module Am = AngularMomentum
 module Bs = Basis

Basis/Overlap.ml

@@ -4,6 +4,7 @@ open Lacaml.D
 
 type t = Mat.t
 external matrix : t -> Mat.t = "%identity"
+external of_matrix : Mat.t -> t = "%identity"
 
 
 module Am  = AngularMomentum

MOBasis/MOBasis.ml

@@ -0,0 +1,181 @@
+open Lacaml.D
+open Util
+
+(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *)
+
+module HF = HartreeFock_type
+module Si = Simulation
+
+type mo_class =
+| Core of int
+| Inactive of int
+| Active of int
+| Virtual of int
+| Deleted of int
+
+type mo_type =
+| RHF | ROHF | CASSCF
+| Natural of string
+| Localized of string
+
+type t = 
+{
+  ao_basis        : AOBasis.t;         (* Atomic basis set on which the MOs are built. *)
+  mo_type         : mo_type;           (* Kind of MOs (RHF, CASSCF, Localized...       *)
+  mo_class        : mo_class array;     (* CI-Class of the MOs *)
+  mo_occupation   : Vec.t;             (* Occupation numbers *)
+  mo_coef         : Mat.t;             (* Matrix of the MO coefficients in the AO basis *)
+  eN_ints         : NucInt.t lazy_t;   (* Electron-nucleus potential integrals *)
+  ee_ints         : ERI.t lazy_t;      (* Electron-electron potential integrals *)
+  kin_ints        : KinInt.t lazy_t;   (* Kinetic energy integrals *)
+}
+
+
+
+let mo_matrix_of_ao_matrix ~mo_coef ao_matrix = 
+  gemm ~transa:`T mo_coef   @@
+  gemm ao_matrix mo_coef  
+
+
+let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix =
+  let sc = gemm ao_overlap mo_coef  in
+  gemm sc @@
+  gemm ~transb:`T mo_matrix sc
+
+
+let four_index_transform ~mo_coef eri_ao =
+
+  let ao_num = Mat.dim1 mo_coef in
+  let mo_num = Mat.dim2 mo_coef in
+  let eri_mo = ERI.create ~size:mo_num `Dense in
+
+  let mo_num_2 = mo_num * mo_num in
+  let ao_num_2 = ao_num * ao_num in
+  let ao_mo_num = ao_num * mo_num in
+
+  let range_mo = list_range ~start:1 mo_num in
+  let range_ao = list_range ~start:1 ao_num in
+
+  let u = 
+      Mat.create mo_num_2 mo_num
+  and o = 
+      Mat.create ao_num ao_num_2 
+  and p = 
+      Mat.create ao_num_2 mo_num
+  and q = 
+      Mat.create ao_mo_num mo_num
+  in
+  Printf.eprintf "Transforming %d integrals : %!" mo_num;
+  List.iter (fun delta ->
+      Printf.eprintf "%d %!" delta;
+      Mat.fill u 0.;
+
+      List.iter (fun l ->
+
+          let jk = ref 0 in
+          List.iter (fun k ->
+              List.iter (fun j ->
+                  incr jk;
+                  ERI.get_phys_all_i eri_ao ~j ~k ~l
+                  |> Array.iteri (fun i x -> o.{i+1,!jk} <- x)
+              ) range_ao
+          ) range_ao;
+          (* o_i_jk *)
+
+          let p =
+            gemm ~transa:`T ~c:p o mo_coef
+            (* p_jk_alpha  = \sum_i o_i_jk c_i_alpha *)
+          in
+          let p' = 
+            Bigarray.reshape_2 (Bigarray.genarray_of_array2 p) ao_num ao_mo_num
+            (* p_j_kalpha *)
+          in
+
+          let q =
+            gemm ~transa:`T ~c:q p' mo_coef
+            (* q_kalpha_beta  = \sum_j p_j_kalpha c_j_beta *)
+          in
+          let q' =
+            Bigarray.reshape_2 (Bigarray.genarray_of_array2 q) ao_num mo_num_2
+            (* q_k_alphabeta  = \sum_j p_j_kalpha c_j_beta *)
+          in
+
+          ignore @@
+            gemm ~transa:`T ~beta:1. ~c:u q' mo_coef 
+            (* u_alphabeta_gamma = \sum_k q_k_alphabeta c_k_gamma *)
+
+      ) range_ao;
+      let u =
+        Bigarray.reshape 
+          (Bigarray.genarray_of_array2 u)
+          [| mo_num ; mo_num ; mo_num |]
+        |> Bigarray.array3_of_genarray 
+      in
+      List.iter (fun gamma ->
+          List.iter (fun beta ->
+              List.iter (fun alpha ->
+                 let x = u.{alpha,beta,gamma} in
+                 if x <> 0. then
+                    ERI.set_phys eri_mo alpha beta gamma delta x
+              ) range_mo
+          ) range_mo
+      ) range_mo
+  ) range_mo;
+  Printf.eprintf "\n%!";
+
+  eri_mo
+
+
+let make ~ao_basis ~mo_type ~mo_class ~mo_occupation ~mo_coef ()  =
+  let eN_ints = lazy (
+    Lazy.force ao_basis.AOBasis.eN_ints 
+    |> NucInt.matrix
+    |> mo_matrix_of_ao_matrix ~mo_coef   
+    |> NucInt.of_matrix
+  )
+  and kin_ints = lazy (
+    Lazy.force ao_basis.AOBasis.kin_ints 
+    |> KinInt.matrix
+    |> mo_matrix_of_ao_matrix ~mo_coef  
+    |> KinInt.of_matrix
+  )
+  and ee_ints = lazy (
+    Lazy.force ao_basis.AOBasis.ee_ints 
+    |> four_index_transform ~mo_coef   
+  )
+  in
+  { ao_basis ; mo_type ; mo_class ; mo_occupation ; mo_coef   ;
+    eN_ints ; ee_ints ; kin_ints }
+
+
+let of_rhf ~frozen_core hf =
+  let simulation = hf.HF.simulation in
+  let nocc = hf.HF.nocc in
+  let ncore =
+    if frozen_core then Nuclei.small_core simulation.Si.nuclei
+    else 0
+  in
+  let mo_num = Vec.dim hf.HF.eigenvalues in
+
+  let ao_basis = simulation.Si.ao_basis in
+  let mo_type  = RHF in
+  let mo_class =
+    Array.init mo_num (fun i ->
+      if (i < ncore) then Core i
+      else 
+        if (i < nocc ) then Inactive i
+        else Virtual i)
+  in
+  let mo_occupation =
+      Array.init mo_num (fun i ->
+        if i < nocc then 2. else 0.)
+      |> Vec.of_array
+  in
+  let mo_coef = hf.HF.eigenvectors in
+  make ~ao_basis ~mo_type ~mo_class ~mo_occupation ~mo_coef ()
+
+
+let of_hartree_fock ~frozen_core = function
+| HF.RHF hf -> of_rhf ~frozen_core hf
+| _ -> assert false
+

MOBasis/MOBasis.mli

@@ -0,0 +1,43 @@
+(** Data structure to represent the molecular orbitals.  *)
+open Lacaml.D
+
+type mo_class =
+| Core of int
+| Inactive of int
+| Active of int
+| Virtual of int
+| Deleted of int
+
+
+type mo_type =
+| RHF | ROHF | CASSCF
+| Natural of string
+| Localized of string
+
+
+type t = private
+{
+  ao_basis        : AOBasis.t;         (* Atomic basis set on which the MOs are built. *)
+  mo_type         : mo_type;           (* Kind of MOs (RHF, CASSCF, Localized...       *)
+  mo_class        : mo_class array;    (* CI-Class of the MOs *)
+  mo_occupation   : Vec.t;             (* Occupation numbers *)
+  mo_coef         : Mat.t;             (* Matrix of the MO coefficients in the AO basis *)
+  eN_ints         : NucInt.t lazy_t;   (* Electron-nucleus potential integrals *)
+  ee_ints         : ERI.t lazy_t;      (* Electron-electron potential integrals *)
+  kin_ints        : KinInt.t lazy_t;   (* Kinetic energy integrals *)
+}
+
+
+
+val make :  ao_basis:AOBasis.t ->
+            mo_type:mo_type ->
+            mo_class:mo_class array ->
+            mo_occupation:Vec.t ->
+            mo_coef:Mat.t ->
+            unit -> t
+(** Function to build a data structure representing the molecular orbitals. *)
+
+val of_hartree_fock : frozen_core:bool -> HartreeFock_type.t -> t
+(** Build MOs from a Restricted Hartree-Fock calculation. *)
+
+

Makefile.include

@@ -1,6 +1,6 @@
 .NOPARALLEL:
 
-INCLUDE_DIRS=Nuclei,Utils,Basis,SCF
+INCLUDE_DIRS=Nuclei,Utils,Basis,SCF,MOBasis
 LIBS=
 PKGS=
 OCAMLBUILD=ocamlbuild -j 0 -cflags $(ocamlcflags) -lflags $(ocamlcflags) $(ocamldocflags) -Is $(INCLUDE_DIRS) -ocamlopt $(ocamloptflags)

SCF/HartreeFock_type.ml

@@ -1,8 +1,9 @@
 open Lacaml.D
 open Util
 
-type t =
+type s =
   {
+    simulation        : Simulation.t;
     guess             : Guess.t;
     eigenvectors      : Lacaml.D.Mat.t ;
     eigenvalues       : Lacaml.D.Vec.t ;
@@ -17,6 +18,12 @@ type t =
   }
 
 
+type t =
+| RHF of s  (** Restricted Hartree-Fock *)
+| ROHF of s (** Restricted Open-shell Hartree-Fock *)
+| UHF of s  (** Unrestricted Hartree-Fock *)
+
+
 let iterations_to_string hf_calc =
   " #       HF energy     Convergence    HOMO-LUMO   
    ---------------------------------------------------" ::
@@ -100,15 +107,21 @@ let mos_to_string hf_calc =
   " ]
 
 
-let to_string hf_calc =
-  String.concat "\n" [ "
+let to_string hf =
+  let aux hf_calc r =
+    String.concat "\n" [ Printf.sprintf "
     =====================================================
-                     Hartree-Fock                     
-  =====================================================" ; "" ;
+                  %s Hartree-Fock                     
+    =====================================================" r ; "" ;
     iterations_to_string hf_calc ; "" ;
     summary hf_calc ; "" ;
     mos_to_string hf_calc ; "" ;
     ]
+  in
+  match hf with
+  | RHF  hf_calc -> aux hf_calc "Restricted"
+  | UHF  hf_calc -> aux hf_calc "Unrestricted"
+  | ROHF hf_calc -> aux hf_calc "Restricted Open-shell"
 
 
 

SCF/HartreeFock_type.mli

@@ -1,7 +1,8 @@
 (** Data structure representing the output of a Hartree-Fock caculation *)
 
-type t = 
+type s = 
   {
+    simulation        : Simulation.t;    (** Simulation which was used for HF calculation *)
     guess             : Guess.t;         (** Initial guess *)
     eigenvectors      : Lacaml.D.Mat.t ; (** Final eigenvectors *)
     eigenvalues       : Lacaml.D.Vec.t ; (** Final eigenvalues  *)
@@ -16,6 +17,12 @@ type t =
                                          (** Energy, convergence and HOMO-LUMO gap of all iterations *)
   }
 
+type t =
+| RHF of s  (** Restricted Hartree-Fock *)
+| ROHF of s (** Restricted Open-shell Hartree-Fock *)
+| UHF of s  (** Unrestricted Hartree-Fock *)
+
+
 val to_string : t -> string
 (** Results of a Hartree-Fock calculation pretty-printed in a string. *)
 

SCF/RHF.ml

@@ -158,7 +158,9 @@ let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=
             List.rev ( (energy, error, gap) :: iterations )
             |> Array.of_list
           in
-          { HartreeFock_type.
+          HartreeFock_type.(RHF
+          { 
+            simulation;
             nocc;
             guess ;
             eigenvectors = m_C ;
@@ -170,7 +172,7 @@ let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=
             eN_energy = Mat.gemm_trace m_P m_V;
             coulomb_energy  = 0.5 *. Mat.gemm_trace m_P m_J;
             exchange_energy = 0.5 *. Mat.gemm_trace m_P m_K;
-          }
+          })
   in
 
 

Utils/FourIdxStorage.ml

@@ -166,6 +166,23 @@ type element = (** Element for the stream *)
 }
 
 
+let get_phys_all_i d ~j ~k ~l  =
+  Array.init d.size (fun i -> get_phys d (i+1) j k l)
+    
+
+let get_chem_all_i d ~j ~k ~l  =
+  Array.init d.size (fun i -> get_chem d (i+1) j k l)
+
+
+let get_phys_all_ji d ~k ~l  =
+  Array.init d.size (fun j -> get_phys_all_i d ~j:(j+1) ~k ~l)
+    
+
+let get_chem_all_ji d ~k ~l  =
+  Array.init d.size (fun j -> get_chem_all_i d ~j:(j+1) ~k ~l)
+    
+
+    
 let to_stream d =
 
   let i = ref 0

Utils/FourIdxStorage.mli

@@ -36,6 +36,18 @@ val set_chem : t -> int -> int -> int -> int -> float -> unit
 val set_phys : t -> int -> int -> int -> int -> float -> unit
 (** Set an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
 
+val get_chem_all_i : t -> j:int -> k:int -> l:int -> float array
+(** Get all integrals in an array [a.(i-1) =] {% $(\cdot j|kl)$ %} . *)
+
+val get_phys_all_i : t -> j:int -> k:int -> l:int -> float array
+(** Get all integrals in an array [a.(i-1) =] {% $\langle \cdot j|kl \rangle$ %} . *)
+
+val get_chem_all_ji : t -> k:int -> l:int -> float array array
+(** Get all integrals in an array [a.(j-1).(i-1) =] {% $(\cdot \cdot|kl)$ %} . *)
+
+val get_phys_all_ji : t -> k:int -> l:int -> float array array
+(** Get all integrals in an array [a.(j-1).(i-1) =] {% $\langle \cdot \cdot|kl \rangle$ %} . *)
+
 val to_stream : t -> element Stream.t
 (** Retrun the data structure as a stream. *)
 

Utils/Util.ml

@@ -169,7 +169,7 @@ let list_some l =
 
 (** {2 Stream functions} *)
 
-let range ?(start=0) n = 
+let stream_range ?(start=0) n = 
   Stream.from (fun i ->
     let result = i+start in
     if result < n then
@@ -178,6 +178,10 @@ let range ?(start=0) n =
   )
 
 
+let list_range ?(start=0) n = 
+  Array.init n (fun i -> start+i) |> Array.to_list
+
+
 
 
 (** {2 Linear algebra} *)

Utils/Util.mli

@@ -63,8 +63,13 @@ val list_some : 'a option list -> 'a list
 (** Filters out all [None] elements of the list, and returns the elements without
     the [Some]. *)
 
+val list_range : ?start:int -> int -> int list
+(** Returns a list [start ; start+1 ; ... ; start+(n-1)]. Default is [start=0]. *)
+
 (** {2 Useful streams} *)
-val range : ?start:int -> int -> int Stream.t
+val stream_range : ?start:int -> int -> int Stream.t
+(** Returns a stream <start ; start+1 ; ... ; start+(n-1)>. Default is [start=0]. *)
+
 
 (** {2 Linear algebra } *)