QCaml/Basis/ScreenedERI.ml

(** Screened Electron-electron repulsion integrals (Yukawa potential). Required for F12/r12. *)

open Constants
open Util

module Csp = ContractedShellPair
module Cspc = ContractedShellPairCouple

module T = struct

  let name = "Screened electron repulsion integrals"

  let f12_factor = F12factor.gaussian_geminal 1.0

  open Zero_m_parameters

  let zero_m z =
    let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in
    assert (expo_pq_inv <> 0.);
    (*
    let f12_factor = 
      match z.f12_factor with
      | Some f -> f
      | None -> assert false
    in
    *)

    let expo_G_inv, coef_G =
      f12_factor.F12factor.gaussian.GaussianOperator.expo_g_inv,
      f12_factor.F12factor.gaussian.GaussianOperator.coef_g
    in

    let expo_pq = 1. /. expo_pq_inv in
    let maxm = z.maxm in

    let result = Array.init (maxm+1) (fun _ -> 0.) in
    array_range 0 (Array.length coef_G)
    |> Array.iter (fun i -> 
      let fG_inv = expo_pq_inv +. expo_G_inv.(i) in
      let fG = 1. /. fG_inv in
      let t =
        if z.norm_pq_sq > integrals_cutoff then
          z.norm_pq_sq *. (expo_pq -. fG)
          else 0.
      in
      let fm = boys_function ~maxm t in

      let tmp_array =
        let result = Array.init (maxm+1) (fun k -> 1.) in
        array_range 1 maxm
        |> Array.iter (fun k -> result.(k) <- result.(k-1) *. expo_pq *. expo_G_inv.(i));
        result
      in

      let tmp_result = Array.init (maxm+1) (fun _ -> 0.) in
      let rec aux accu m = function
        | 0 -> tmp_result.(m) <- fm.(m) *. accu
        | j ->
          begin
            let f =
              array_range 0 m
              |> Array.fold_left (fun v k -> 
                v +. (binom_float m k) *. tmp_array.(k) *. fm.(k)) 0. 
            in
            tmp_result.(m) <- accu *. f;
            let new_accu = -. accu *. expo_pq in
            (aux [@tailcall]) new_accu (m+1) (j-1)
          end
      in
      let f =
        two_over_sq_pi *. (sqrt expo_pq) *. fG *. expo_G_inv.(i) *.  exp (-.fG *. z.norm_pq_sq)
      in
      aux f 0 maxm;
      Array.iteri (fun k v ->
        result.(k) <- result.(k) +. coef_G.(i) *. v
      ) tmp_result) ;
    result

  let class_of_contracted_shell_pair_couple shell_pair_couple = 
    let shell_p = Cspc.shell_pair_p shell_pair_couple
    and shell_q = Cspc.shell_pair_q shell_pair_couple                                         
    in
    if Array.length (Csp.shell_pairs shell_p) +
       (Array.length (Csp.shell_pairs shell_q))  < 4 then
      TwoElectronRR.contracted_class_shell_pair_couple
        ~zero_m shell_pair_couple
    else
      TwoElectronRRVectorized.contracted_class_shell_pairs
        ~zero_m shell_p shell_q

end

module M = TwoElectronIntegrals.Make(T) 
include M