QCaml/Basis/NucInt.ml

(** Electron-nucleus repulsion integrals *)

open Util
open Constants
open Lacaml.D

type t = Mat.t

(** (0|0)^m : Fundamental electron-nucleus repulsion integral
    $ \int \phi_p(r1) 1/r_{C} dr_1 $

    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 *. fm *.
      (pow exp_pq m) *. (sqrt exp_pq)
    )


(** Compute all the integrals of a contracted class *)
let contracted_class_shell_pair shell_p geometry: float Zmap.t =
  OneElectronRR.contracted_class_shell_pair ~zero_m shell_p geometry


let cutoff2 = cutoff *. cutoff
exception NullIntegral


let of_basis_nuclei basis nuclei =
  let to_powers x = 
    let open Zkey in
    match to_powers Kind_3 x with
    | Three x -> x
    | _ -> assert false
  in

  let n =
    Basis.size basis
  and shell =
    Basis.contracted_shells basis
  in

  let eni_array = Mat.create n n in

  (* Pre-compute all shell pairs *)
  let shell_pairs =
    Array.mapi (fun i shell_a -> Array.map (fun shell_b -> 
        ContractedShellPair.create shell_a shell_b) (Array.sub shell 0 (i+1)) ) shell
  in

  (* Compute Integrals *)
  for i=0 to (Array.length shell) - 1 do
    for j=0 to i do
      let
        shell_p = shell_pairs.(i).(j)
      in

      (* Compute all the integrals of the class *)
      let cls =
        contracted_class_shell_pair shell_p nuclei
      in

      (* Write the data in the output file *)
      Array.iteri (fun i_c powers_i ->
          let i_c = (Contracted_shell.index shell.(i)) + i_c + 1 in
          let xi = to_powers powers_i in
          Array.iteri (fun j_c powers_j ->
              let j_c = (Contracted_shell.index shell.(j)) + j_c + 1 in
              let xj = to_powers powers_j in
              let key = 
                Zkey.of_powers (Zkey.Six (xi,xj))
              in
              let value = 
                Zmap.find cls key 
              in
              eni_array.{j_c,i_c} <- value;
            ) (Contracted_shell.powers shell.(j))
        ) (Contracted_shell.powers shell.(i));
    done;
  done;
  Mat.detri eni_array;
  eni_array


let to_file ~filename eni_array =
  let n = Mat.dim1 eni_array in
  let oc = open_out filename in

  for j=1 to n do
    for i=1 to j do
      let value = eni_array.{i,j} in
      if (value <> 0.) then
        Printf.fprintf oc " %5d %5d %20.15f\n" i j value;
    done;
  done;
  close_out oc