QCaml/ci/lib/ci_matrix_element.ml

open Common

module De = Determinant
module Ex = Excitation
module Sp = Spindeterminant

type t = float list



(** Computes non-zero integral values.

    @param integrals A list of tuples containing one-electron, two-electron integrals, and optionally three-electron integrals.
    @param degree_a The degree of excitation in alpha spin orbitals.
    @param degree_b The degree of excitation in beta spin orbitals.
    @param ki The initial Slater determinant.
    @param kj The final Slater determinant.
    
    
    @return TODO A list of computed integral values based on the specified degrees and molecular orbitals.
    
    This function performs the following operations:
    - Converts spin determinants to lists of molecular orbitals for alpha and beta spins.
    - Defines helper functions for singly and doubly excited determinants, and diagonal elements
    - Uses lazy evaluation to defer computations until required.
    - Supports both two-electron and three-electron integrals, handling phase factors appropriately.
    
    Example usage:
    {[
      let integrals = [(one_e_integral, two_e_integral, None); (one_e_integral, two_e_integral, Some three_e_integral)] in
      let result = non_zero integrals 1 1 ki kj
    ]}
    
*)

let non_zero integrals degree_a degree_b ki kj =
  let kia = De.alfa ki and kib = De.beta ki
  and kja = De.alfa kj and kjb = De.beta kj
  in

  let single h p spin same opposite =
    let same_spin_mo_list =
      Sp.to_list same
    and opposite_spin_mo_list =
      Sp.to_list opposite
    in
    fun one_e two_e ->
      let same_spin =
        List.fold_left (fun accu i -> accu +. two_e h i p i spin spin) 0. same_spin_mo_list
      and opposite_spin =
        List.fold_left (fun accu i -> accu +. two_e h i p i spin (Spin.other spin) ) 0. opposite_spin_mo_list
      in (one_e h p spin) +. same_spin +. opposite_spin
  in

  let diag_element =
    let mo_a = Sp.to_list kia
    and mo_b = Sp.to_list kib
    in
    fun one_e two_e ->
      let one =
        (List.fold_left (fun accu i -> accu +. one_e i i Spin.Alfa) 0. mo_a)
        +.
        (List.fold_left (fun accu i -> accu +. one_e i i Spin.Beta) 0. mo_b)
      in
      let two =
        let rec aux_same spin accu = function
          | [] -> accu
          | i :: rest ->
            let new_accu =
              List.fold_left (fun accu j -> accu +. two_e i j i j spin spin) accu rest
            in
            (aux_same [@tailcall]) spin new_accu rest
        in
        let rec aux_opposite accu other = function
          | [] -> accu
          | i :: rest ->
            let new_accu =
              List.fold_left (fun accu j -> accu +. two_e i j i j Spin.Alfa Spin.Beta) accu other
            in
            (aux_opposite [@tailcall]) new_accu other rest
        in
        (aux_same Spin.Alfa 0. mo_a)  +.  (aux_same Spin.Beta 0. mo_b)  +.
        (aux_opposite 0. mo_a mo_b)
      in
      one +. two
  in

  let result_2e = lazy (
    match degree_a, degree_b with
    | 1, 1 -> (* alpha-beta double *)
      begin
        let ha, pa, phase_a = Ex.single_of_spindet kia kja in
        let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
        match phase_a, phase_b with
        | Phase.Pos, Phase.Pos
        | Phase.Neg, Phase.Neg -> fun _ two_e ->    two_e ha hb pa pb Spin.Alfa Spin.Beta
        | Phase.Neg, Phase.Pos
        | Phase.Pos, Phase.Neg -> fun _ two_e -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta
      end

    | 2, 0 -> (* alpha double *)
      begin
        let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
        match phase with
        | Phase.Pos -> fun _ two_e ->    two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
        | Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
      end

    | 0, 2 -> (* beta double *)
      begin
        let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
        match phase with
        | Phase.Pos -> fun _ two_e ->    two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
        | Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
      end

    | 1, 0 -> (* alpha single *)
      begin
        let h, p, phase = Ex.single_of_spindet kia kja in
        match phase with
        | Phase.Pos -> fun one_e two_e ->    single h p Spin.Alfa kia kib one_e two_e
        | Phase.Neg -> fun one_e two_e -> -. single h p Spin.Alfa kia kib one_e two_e
      end

    | 0, 1 -> (* beta single *)
      begin
        let h, p, phase = Ex.single_of_spindet kib kjb in
        match phase with
        | Phase.Pos -> fun one_e two_e ->    single h p Spin.Beta kib kia one_e two_e
        | Phase.Neg -> fun one_e two_e -> -. single h p Spin.Beta kib kia one_e two_e
      end

    | 0, 0 -> (* diagonal element *)
      diag_element

    | _ -> assert false
  ) in

  let result_3e = lazy (
    match degree_a, degree_b with
    | 1, 1 -> (* alpha-beta double *)
      begin
        let ha, pa, phase_a = Ex.single_of_spindet kia kja in
        let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
        match phase_a, phase_b with
        | Phase.Pos, Phase.Pos
        | Phase.Neg, Phase.Neg -> fun _ two_e _ ->    two_e ha hb pa pb Spin.Alfa Spin.Beta
        | Phase.Neg, Phase.Pos
        | Phase.Pos, Phase.Neg -> fun _ two_e _ -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta
      end

    | 2, 0 -> (* alpha double *)
      begin
        let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
        match phase with
        | Phase.Pos -> fun _ two_e _ ->    two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
        | Phase.Neg -> fun _ two_e _ -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa
      end

    | 0, 2 -> (* beta double *)
      begin
        let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in
        match phase with
        | Phase.Pos -> fun _ two_e _ ->    two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
        | Phase.Neg -> fun _ two_e _ -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta
      end

    | 1, 0 -> (* alpha single *)
      begin
        let h, p, phase = Ex.single_of_spindet kia kja in
        match phase with
        | Phase.Pos -> fun one_e two_e _ ->    single h p Spin.Alfa kia kib one_e two_e
        | Phase.Neg -> fun one_e two_e _ -> -. single h p Spin.Alfa kia kib one_e two_e
      end

    | 0, 1 -> (* beta single *)
      begin
        let h, p, phase = Ex.single_of_spindet kib kjb in
        match phase with
        | Phase.Pos -> fun one_e two_e _ ->    single h p Spin.Beta kib kia one_e two_e
        | Phase.Neg -> fun one_e two_e _ -> -. single h p Spin.Beta kib kia one_e two_e
      end

    | 0, 0 -> (* diagonal element *)
       fun one_e two_e _ -> diag_element one_e two_e

    | 3, 0 -> (* alpha triple *)
      begin
        let h1, p1, h2, p2, h3, p3, phase = Ex.triple_of_spindet kia kja in
        match phase with
        | Phase.Pos -> fun _ _ three_e ->    three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Alfa
        | Phase.Neg -> fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Alfa
      end

    | 0, 3 -> (* beta  triple *)
      begin
        let h1, p1, h2, p2, h3, p3, phase = Ex.triple_of_spindet kib kja in
        match phase with
        | Phase.Pos -> fun _ _ three_e ->    three_e h1 h2 h3 p1 p2 p3 Spin.Beta Spin.Beta Spin.Beta
        | Phase.Neg -> fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Beta Spin.Beta Spin.Beta
      end

    | 2, 1 -> (* alpha2 beta triple *)
      begin
        let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in
        let h3, p3, phase' = Ex.single_of_spindet kib kjb in
        match phase, phase' with
        | Phase.Pos, Phase.Pos
        | Phase.Neg, Phase.Neg ->
            fun _ _ three_e ->    three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Beta
        | Phase.Neg, Phase.Pos
        | Phase.Pos, Phase.Neg ->
            fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Beta
      end

    | 1, 2 -> (* alpha beta2 triple *)
      begin
        let h1, p1, phase = Ex.single_of_spindet kia kja in
        let h2, p2, h3, p3, phase' = Ex.double_of_spindet kib kjb in
        match phase, phase' with
        | Phase.Pos, Phase.Pos
        | Phase.Neg, Phase.Neg ->
            fun _ _ three_e ->    three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Beta Spin.Beta
        | Phase.Neg, Phase.Pos
        | Phase.Pos, Phase.Neg ->
            fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Beta Spin.Beta
      end

    | _ -> fun _ _ _ -> 0.
  ) in

  List.map (fun (one_e, two_e, x) ->
    match x with
    | None         -> (Lazy.force result_2e) one_e two_e
    | Some three_e -> (Lazy.force result_3e) one_e two_e three_e
  ) integrals



let make integrals ki kj =
  let degree_a, degree_b =
    De.excitation_levels ki kj
  in
  if degree_a+degree_b > 2 then
    List.map (fun _ -> 0.) integrals
  else
    non_zero integrals degree_a degree_b ki kj




let make_s2 ki kj =
  let degree_a = De.excitation_level_alfa ki kj in
  let kia = De.alfa ki in
  let kja = De.alfa kj in
  if degree_a > 1 then 0.
  else
    let degree_b = De.excitation_level_beta ki kj in
    let kib = De.beta ki in
    let kjb = De.beta kj in
    match degree_a, degree_b with
    | 1, 1 -> (* alpha-beta double *)
      let ha, pa, phase_a = Ex.single_of_spindet kia kja in
      let hb, pb, phase_b = Ex.single_of_spindet kib kjb in
      if ha = pb && hb = pa then
        begin
          match phase_a, phase_b with
          | Phase.Pos, Phase.Pos
          | Phase.Neg, Phase.Neg -> -1.
          | Phase.Neg, Phase.Pos
          | Phase.Pos, Phase.Neg -> 1.
        end
      else 0.
    | 0, 0 ->
      let ba = Sp.bitstring kia and bb = Sp.bitstring kib in
      let tmp = Bitstring.logxor ba bb in
      let n_a = Bitstring.logand ba tmp |> Bitstring.popcount in
      let n_b = Bitstring.logand bb tmp |> Bitstring.popcount in
      let s_z = 0.5 *. float_of_int (n_a - n_b) in
      float_of_int n_a +. s_z *. (s_z -. 1.)
    | _ -> 0.