QCaml/Basis/TwoElectronRR.ml

open Util

let cutoff2 = cutoff *. cutoff

exception NullQuartet

(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
    (totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
    (maxm, zero_m_array)
    (expo_b, expo_d)
    (expo_inv_p, expo_inv_q)
    (center_ab, center_cd, center_pq)
    map
  =

  let totAngMom_a = Angular_momentum.to_int totAngMom_a
  and totAngMom_b = Angular_momentum.to_int totAngMom_b
  and totAngMom_c = Angular_momentum.to_int totAngMom_c
  and totAngMom_d = Angular_momentum.to_int totAngMom_d
  in

  (** Vertical recurrence relations *)
  let rec vrr0 m angMom_a = function
    | 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
      in expo_inv_p *.( (Coordinate.coord center_pq i) *. zero_m_array.(m+1)
                        -. expo_b *. (Coordinate.coord center_ab i) *. zero_m_array.(m) )

    | 0 -> zero_m_array.(m)
    | totAngMom_a ->
      let key = Zkey.of_int_tuple (Zkey.Three
                                     (angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
      in

      let (found, result) =
        try (true, Zmap.find map.(m) key) with
        | Not_found -> (false,
                        let am  = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
                        and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
                        and xyz =
                        match angMom_a with
                          | [|0;0;_|] -> 2
                          | [|0;_;_|] -> 1
                          | _         -> 0
                        in
                        am.(xyz)  <- am.(xyz) - 1;
                        amm.(xyz) <- amm.(xyz) - 2;
                        if am.(xyz) < 0 then 0. else
                          chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
                            (fun () -> vrr0 m am (totAngMom_a-1) )
                          +. chop (expo_inv_p *. (Coordinate.coord center_pq xyz)) 
                            (fun () ->  vrr0 (m+1) am (totAngMom_a-1) )
                          +. (if amm.(xyz) < 0 then 0. else
                                chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
                                  (fun () ->  vrr0 m amm (totAngMom_a-2) 
                                              +. chop expo_inv_p (fun () ->
                                                  vrr0 (m+1) amm (totAngMom_a-2) ) ) )
                       )
      in
      if not found then
        Zmap.add map.(m) key result;
      result

  and vrr m angMom_a angMom_c totAngMom_a totAngMom_c =

    match (totAngMom_a, totAngMom_c) with
    | (0,0) -> zero_m_array.(m)
    | (_,0) -> vrr0 m angMom_a totAngMom_a
    | (_,_) ->

      let key =  Zkey.of_int_tuple (Zkey.Six
                                      ((angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1),
                                       (angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1)) )

      in

      let (found, result) =
        try (true, Zmap.find map.(m) key) with
        | Not_found -> (false,
                        let am  = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
                        and cm  = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
                        and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
                        and xyz =
                          match angMom_c with
                          | [|0;0;_|] -> 2
                          | [|0;_;_|] -> 1
                          | _         -> 0
                        in
                        am.(xyz)  <- am.(xyz)  - 1;
                        cm.(xyz)  <- cm.(xyz)  - 1;
                        cmm.(xyz) <- cmm.(xyz) - 2;
                        if cm.(xyz) < 0 then 0. else
                          chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
                            (fun () ->  vrr m angMom_a cm totAngMom_a (totAngMom_c-1) )
                          -. chop (expo_inv_q *. (Coordinate.coord center_pq xyz))
                            (fun () -> vrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) )
                          +. (if cmm.(xyz) < 0 then 0. else
                                chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
                                  (fun () -> vrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
                                             +. chop expo_inv_q
                                               (fun () -> vrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) ) )
                          -. (if am.(xyz) lor cm.(xyz) < 0 then 0. else
                                chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
                                  (fun () -> vrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) ))
      in
      if not found then
        Zmap.add map.(m) key result;
      result




  (** Horizontal recurrence relations *)
  and hrr0 m angMom_a angMom_b angMom_c 
      totAngMom_a totAngMom_b totAngMom_c =

    match totAngMom_b with
    | 0 -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
    | 1 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
      let ap  = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
      ap.(xyz) <- ap.(xyz) + 1;
      vrr m ap angMom_c (totAngMom_a+1) totAngMom_c
      +. chop (Coordinate.coord center_ab xyz) (fun () ->
          vrr m angMom_a angMom_c totAngMom_a totAngMom_c)
    | _ ->
      let ap  = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
      and bm  = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
      and xyz =
        match angMom_b with
        | [|0;0;_|] -> 2
        | [|0;_;_|] -> 1
        | _        -> 0
      in
      ap.(xyz) <- ap.(xyz) + 1;
      bm.(xyz) <- bm.(xyz) - 1;
      if (bm.(xyz) < 0) then 0. else
        hrr0 m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c 
        +. chop (Coordinate.coord center_ab xyz) (fun () ->
            hrr0 m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1)
              totAngMom_c )

  and hrr m angMom_a angMom_b angMom_c angMom_d
      totAngMom_a totAngMom_b totAngMom_c totAngMom_d =

    match (totAngMom_b, totAngMom_d) with
    | (0,0) ->
      vrr m angMom_a angMom_c totAngMom_a totAngMom_c
    | (_,0) -> hrr0 m angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
    | (_,_) ->
      let cp  = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
      and dm  = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
      and xyz =
        match angMom_d with
        | [|0;0;_|] -> 2
        | [|0;_;_|] -> 1
        | _        -> 0
      in
      cp.(xyz) <- cp.(xyz) + 1;
      dm.(xyz) <- dm.(xyz) - 1;
      hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
        (totAngMom_c+1) (totAngMom_d-1) 
      +. chop (Coordinate.coord center_cd xyz) (fun () ->
          hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
            totAngMom_c (totAngMom_d-1) )
  in
  hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
    totAngMom_c totAngMom_d




let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =

  let shell_a = shell_p.(0).Shell_pair.shell_a
  and shell_b = shell_p.(0).Shell_pair.shell_b
  and shell_c = shell_q.(0).Shell_pair.shell_a
  and shell_d = shell_q.(0).Shell_pair.shell_b
  in
  let maxm = 
    let open Angular_momentum in
    (to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b) 
    + (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
  in

  (* Pre-computation of integral class indices *)
  let class_indices = 
    Angular_momentum.zkey_array
      (Angular_momentum.Quartet
         Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
                           totAngMom shell_c, totAngMom shell_d))
  in

  let contracted_class = 
    Array.make (Array.length class_indices) 0.;
  in

  (* Compute all integrals in the shell for each pair of significant shell pairs *)

  for ab=0 to (Array.length shell_p - 1) do
    let cab = shell_p.(ab).Shell_pair.coef  in
    let b = shell_p.(ab).Shell_pair.j in
    for cd=0 to (Array.length shell_q - 1) do
      let coef_prod =
        cab *. shell_q.(cd).Shell_pair.coef
      in
      (** Screening on the product of coefficients *)
      try
        if (abs_float coef_prod) < 1.e-4*.cutoff then
          raise NullQuartet;

        let expo_pq_inv =
          shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
        in
        let center_pq = 
          Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
        in
        let norm_pq_sq =
          Coordinate.dot center_pq center_pq
        in

        let zero_m_array = 
          zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
        in
        begin
          match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
                                  totAngMom shell_c, totAngMom shell_d) with
          | Angular_momentum.(S,S,S,S) ->
              let integral =
                zero_m_array.(0)
              in
              contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
          | _ -> 
              let d = shell_q.(cd).Shell_pair.j in
              let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
              (* Compute the integral class from the primitive shell quartet *)
              Array.iteri (fun i key ->
                  let a = Zkey.to_int_array Zkey.Kind_12 key in
                  let (angMomA,angMomB,angMomC,angMomD) =
                    ( [| a.(0) ;  a.(1) ;  a.(2) |], 
                      [| a.(3) ;  a.(4) ;  a.(5) |], 
                      [| a.(6) ;  a.(7) ;  a.(8) |], 
                      [| a.(9) ; a.(10) ; a.(11) |] )
                  in
                  try
                    (* Schwartz screening *)
                  (*
                  let schwartz_p = 
                    let key =
                    Zkey.of_int_array Zkey.Kind_12 
                        [| a.(0) ;  a.(1) ;  a.(2) ;
                          a.(3) ;  a.(4) ;  a.(5) ;
                          a.(0) ;  a.(1) ;  a.(2) ;
                          a.(3) ;  a.(4) ;  a.(5) |]
                    in
                    match schwartz_p with
                    | None -> 1.
                    | Some schwartz_p -> Zmap.find schwartz_p key
                  in
                  if schwartz_p < cutoff then raise NullQuartet;
                  let schwartz_q = 
                    let key =
                    Zkey.of_int_array Zkey.Kind_12 
                        [| a.(6) ;  a.(7) ;  a.(8) ;
                          a.(9) ; a.(10) ; a.(11) ;
                          a.(6) ;  a.(7) ;  a.(8) ;
                          a.(9) ; a.(10) ; a.(11) |]
                    in
                    match schwartz_q with
                    | None -> 1.
                    | Some schwartz_q -> Zmap.find schwartz_q key
                  in
                  if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
                  *)


                    let norm = 
                      shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD 
                    in
                    let integral = chop norm (fun () ->
                        hvrr_two_e 0 (angMomA, angMomB, angMomC, angMomD)
                          (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
                           Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
                          (maxm, zero_m_array)
                          (Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d)
                          (shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv)
                          (shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq)
                          map )
                    in
                    contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
                  with NullQuartet -> ()
                ) class_indices
        end
    with NullQuartet -> ()
    done
  done;

  let result = 
    Zmap.create (Array.length contracted_class)
  in
  Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
  result



(** Computes all the two-electron integrals of the contracted shell quartet *)
let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =

  let shell_p = Shell_pair.create_array ~cutoff shell_a shell_b
  and shell_q = Shell_pair.create_array ~cutoff shell_c shell_d
  in
  contracted_class_shell_pairs ~zero_m shell_p shell_q