QCaml/Basis/ERI.ml

(** Electron-electron repulsion integrals *)

open Util

(** (00|00)^m : Fundamental electron repulsion integral
    $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $

    maxm        : Maximum total angular momentum
    expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of
                $\phi_p$ and $\phi_q$
    norm_pq_sq  : square of the distance between the centers of $\phi_p$
                and $\phi_q$
*)
let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
  let exp_pq =
    1. /. expo_pq_inv
  in
  let t =
    norm_pq_sq *. exp_pq
  in
  boys_function ~maxm t
  |> Array.mapi (fun m fm ->
      two_over_sq_pi *. (if m mod 2 = 0 then fm else -.fm) *.
      (pow exp_pq m) *. (sqrt exp_pq)
    )


(** Compute all the integrals of a contracted class *)
let contracted_class  shell_a shell_b shell_c shell_d : float Zmap.t =
  TwoElectronRR.contracted_class ~zero_m shell_a shell_b shell_c shell_d 


type n_cls = { n : int ; cls : Z.t array }
(** Write all integrals to a file *)
let to_file ~filename basis =
  let oc = open_out filename in
  let key_array =  Array.make 12 0 in
  let zkey = Array.map (fun b -> 
      let result =
        Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
      in
      { n=Array.length result ;  cls=result }
    ) basis
  in 
  let i_shift = ref 1 in
  let j_shift = ref 1 in
  let k_shift = ref 1 in
  let l_shift = ref 1 in
  for i=0 to (Array.length basis) - 1 do
    print_int !i_shift ; print_newline ();
    j_shift := 1;
    for j=0 to i do
      k_shift := 1;
      for k=0 to i do
        l_shift := 1;
        for l=0 to k do
          let cls =
            contracted_class basis.(i) basis.(j) basis.(k) basis.(l)
          in

          for i_c = 0 to zkey.(i).n - 1 do
            let x = Zkey.(to_int_array Kind_3 zkey.(i).cls.(i_c)) in
            key_array.(0) <- x.(0);
            key_array.(1) <- x.(1);
            key_array.(2) <- x.(2);
            for j_c = 0 to zkey.(j).n - 1 do
              let x = Zkey.(to_int_array Kind_3 zkey.(j).cls.(j_c)) in
              key_array.(3) <- x.(0);
              key_array.(4) <- x.(1);
              key_array.(5) <- x.(2);
              for k_c = 0 to zkey.(k).n - 1 do
                let x = Zkey.(to_int_array Kind_3 zkey.(k).cls.(k_c)) in
                key_array.(6) <- x.(0);
                key_array.(7) <- x.(1);
                key_array.(8) <- x.(2);
                for l_c = 0 to zkey.(l).n - 1 do
                  let x = Zkey.(to_int_array Kind_3 zkey.(l).cls.(l_c)) in
                  key_array.( 9) <- x.(0);
                  key_array.(10) <- x.(1);
                  key_array.(11) <- x.(2);
                  let key = 
                    Zkey.(of_int_array Kind_12  key_array)
                  in
                  let value = 
                    Zmap.find cls key 
                  in
                  if (abs_float value > cutoff) then
                    Printf.fprintf oc "%4d %4d %4d %4d %20.12e\n"
                      (!i_shift+i_c) (!j_shift+j_c) (!k_shift+k_c) (!l_shift+l_c) 
                      value
                done
              done
            done
          done;
          l_shift := !l_shift + zkey.(l).n
        done;
        k_shift := !k_shift + zkey.(k).n
      done;
      j_shift := !j_shift + zkey.(j).n
    done;
    i_shift := !i_shift + zkey.(i).n
  done
  ;
  close_out oc


(*
let to_file ~filename basis =
  let oc = open_out filename in
  let zkey = Array.map (fun b -> 
      let result =
        Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
      in
      { n=Array.length result ;  cls=result }
    ) basis
  in 

  let key_array =  Array.make 12 0 in
  let result = ref [] in

  let i_shift = ref 1 in
  for i=0 to (Array.length basis) - 1 do
    print_int !i_shift ; print_newline ();
    let j_shift = ref 1 in
    for j=0 to i do
      let k_shift = ref 1 in
      for k=0 to i do
        let l_shift = ref 1 in
        for l=0 to k do
          let cls =
            contracted_class basis.(i) basis.(j) basis.(k) basis.(l)
          in

          for i_c = 0 to zkey.(i).n - 1 do
            let x = Zkey.(to_int_array Kind_3 zkey.(i).cls.(i_c)) in
            key_array.(0) <- x.(0);
            key_array.(1) <- x.(1);
            key_array.(2) <- x.(2);
            for j_c = 0 to zkey.(j).n - 1 do
              let x = Zkey.(to_int_array Kind_3 zkey.(j).cls.(j_c)) in
              key_array.(3) <- x.(0);
              key_array.(4) <- x.(1);
              key_array.(5) <- x.(2);
              for k_c = 0 to zkey.(k).n - 1 do
                let x = Zkey.(to_int_array Kind_3 zkey.(k).cls.(k_c)) in
                key_array.(6) <- x.(0);
                key_array.(7) <- x.(1);
                key_array.(8) <- x.(2);
                for l_c = 0 to zkey.(l).n - 1 do
                  let x = Zkey.(to_int_array Kind_3 zkey.(l).cls.(l_c)) in
                  key_array.( 9) <- x.(0);
                  key_array.(10) <- x.(1);
                  key_array.(11) <- x.(2);
                  let key = 
                    Zkey.(of_int_array Kind_12  key_array)
                  in
                  let value = 
                    Zmap.find cls key 
                  in
                  if (abs_float value > cutoff) then
                    let key =
                      Zkey.of_int_array Zkey.Kind_4 [|
                          (!i_shift+i_c);(!j_shift+j_c);(!k_shift+k_c);(!l_shift+l_c) 
                        |] 
                    in
                    result := (key, value) :: !result
                done
              done
            done
          done;
          l_shift := !l_shift + zkey.(l).n
        done;
        k_shift := !k_shift + zkey.(k).n
      done;
      j_shift := !j_shift + zkey.(j).n
    done;
    i_shift := !i_shift + zkey.(i).n
  done
  ;

  let result = Array.of_list !result in
  let result = Zmap.create (Array.length result) in

  for i=0 to !i_shift - 2 do
    for j=0 to !i_shift - 2 do
      for k=0 to !i_shift - 2 do
        for l=0 to !i_shift - 2 do
          let key =
            Zkey.of_int_array Zkey.Kind_4 [| i;j;k;l |]
          in
          try
            let value = 
              Zmap.find result key 
            in
            Printf.fprintf oc "%4d %4d %4d %4d %20.12e\n"
                      i j k l value
          with Not_found -> ()
        done
      done
    done
  done;
  close_out oc
*)