mirror of https://gitlab.com/scemama/QCaml.git
464 lines
17 KiB
OCaml
464 lines
17 KiB
OCaml
open Util
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open Constants
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let debug=false
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let cutoff2 = cutoff *. cutoff
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exception NullQuartet
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(** Horizontal and Vertical Recurrence Relations (HVRR) *)
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let hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
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(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
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(maxm, zero_m_array)
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(expo_b, expo_d)
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(expo_inv_p, expo_inv_q)
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(center_ab, center_cd, center_pq)
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map_1d map_2d
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=
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let maxsze = maxm+1 in
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let totAngMom_a = Angular_momentum.to_int totAngMom_a
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and totAngMom_b = Angular_momentum.to_int totAngMom_b
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and totAngMom_c = Angular_momentum.to_int totAngMom_c
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and totAngMom_d = Angular_momentum.to_int totAngMom_d
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in
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let maxm = totAngMom_a + totAngMom_b + totAngMom_c + totAngMom_d in
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let empty = Array.make (maxm+1) 0.
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in
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if debug then begin
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Printf.printf "\n---- %d %d %d %d ----\n" totAngMom_a totAngMom_b totAngMom_c totAngMom_d;
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Printf.printf "%d %d %d\n" angMom_a.(0) angMom_a.(1) angMom_a.(2) ;
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Printf.printf "%d %d %d\n" angMom_b.(0) angMom_b.(1) angMom_b.(2) ;
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Printf.printf "%d %d %d\n" angMom_c.(0) angMom_c.(1) angMom_c.(2) ;
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Printf.printf "%d %d %d\n" angMom_d.(0) angMom_d.(1) angMom_d.(2) ;
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Printf.printf "%f %f %f %f\n%f %f %f\n%f %f %f\n%f %f %f\n" expo_b expo_d
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expo_inv_p expo_inv_q
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(Coordinate.coord center_ab 0) (Coordinate.coord center_ab 1) (Coordinate.coord center_ab 2)
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(Coordinate.coord center_cd 0) (Coordinate.coord center_cd 1) (Coordinate.coord center_cd 2)
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(Coordinate.coord center_pq 0) (Coordinate.coord center_pq 1) (Coordinate.coord center_pq 2)
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end;
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(** Vertical recurrence relations *)
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let rec vrr0 angMom_a totAngMom_a =
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if debug then
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begin
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let (x,y,z) = angMom_a in
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Printf.printf "vrr0: %d : %d %d %d\n" totAngMom_a x y z
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end;
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match totAngMom_a with
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| 0 -> zero_m_array
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| _ ->
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let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in
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try Zmap.find map_1d key with
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| Not_found ->
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let result =
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let am, amm, amxyz, xyz =
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match angMom_a with
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| (x,0,0) -> (x-1,0,0),(x-2,0,0), x-1, 0
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| (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
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| (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
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in
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if amxyz < 0 then empty else
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let f1 = expo_inv_p *. (Coordinate.coord center_pq xyz)
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and f2 = expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
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in
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if amxyz < 1 then
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let v1 =
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vrr0 am (totAngMom_a-1)
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in
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Array.init maxsze (fun m ->
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if m = maxm then 0. else (f1 *. v1.(m+1) ) -. f2 *. v1.(m) )
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else
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let v3 =
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vrr0 amm (totAngMom_a-2)
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in
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let v1 =
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vrr0 am (totAngMom_a-1)
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in
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let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
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Array.init maxsze (fun m ->
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(if m = maxm then 0. else
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(f1 *. v1.(m+1) ) -. f2 *. v1.(m) )
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+. f3 *. (v3.(m) +. if m = maxm then 0. else
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expo_inv_p *. v3.(m+1))
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)
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in Zmap.add map_1d key result;
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result
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and vrr angMom_a angMom_c totAngMom_a totAngMom_c =
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if debug then
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begin
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let angMom_ax, angMom_ay, angMom_az = angMom_a in
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let angMom_cx, angMom_cy, angMom_cz = angMom_c in
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Printf.printf "vrr : %d %d : %d %d %d %d %d %d\n" totAngMom_a totAngMom_c
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angMom_ax angMom_ay angMom_az angMom_cx angMom_cy angMom_cz
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end;
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match (totAngMom_a, totAngMom_c) with
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| (i,0) -> if (i>0) then vrr0 angMom_a totAngMom_a else zero_m_array
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| (_,_) ->
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let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c) ) in
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try Zmap.find map_2d key with
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| Not_found ->
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let result =
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let am, cm, cmm, axyz, cmxyz, xyz =
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let angMom_ax, angMom_ay, angMom_az = angMom_a
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and angMom_cx, angMom_cy, angMom_cz = angMom_c in
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match angMom_c with
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| (_,0,0) -> (* 321_984 *)
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(angMom_ax-1, angMom_ay, angMom_az),
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(angMom_cx-1, angMom_cy, angMom_cz),
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(angMom_cx-2, angMom_cy, angMom_cz),
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angMom_ax,angMom_cx-1, 0
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| (_,_,0) -> (* 612_002 *)
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(angMom_ax, angMom_ay-1, angMom_az),
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(angMom_cx, angMom_cy-1, angMom_cz),
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(angMom_cx, angMom_cy-2, angMom_cz),
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angMom_ay,angMom_cy-1, 1
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| _ -> (* 1_067_324 *)
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(angMom_ax, angMom_ay, angMom_az-1),
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(angMom_cx, angMom_cy, angMom_cz-1),
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(angMom_cx, angMom_cy, angMom_cz-2),
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angMom_az,angMom_cz-1, 2
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in
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if cmxyz < 0 then empty else
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let f1 =
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-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz)
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in
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let f2 =
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expo_inv_q *. (Coordinate.coord center_pq xyz)
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in
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let result = empty in
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let result =
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if ( (abs_float f1 < cutoff) && (abs_float f2 < cutoff) ) then result else
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let v1 =
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vrr angMom_a cm totAngMom_a (totAngMom_c-1)
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in
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Array.init maxsze (fun m -> result.(m) +.
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f1 *. v1.(m) -. (if m = maxm then 0. else f2 *. v1.(m+1)) )
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in
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let result =
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if cmxyz < 1 then result else
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let f3 =
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(float_of_int cmxyz) *. expo_inv_q *. 0.5
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in
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if (abs_float f3 < cutoff) && (abs_float (f3 *. expo_inv_q) < cutoff) then result else
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(
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let v3 =
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vrr angMom_a cmm totAngMom_a (totAngMom_c-2)
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in
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Array.init maxsze (fun m -> result.(m) +.
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f3 *. (v3.(m) +. (if m=maxm then 0. else expo_inv_q *. v3.(m+1)) ))
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)
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in
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let result =
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if (axyz < 1) || (cmxyz < 0) then result else
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let f5 =
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(float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5
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in
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if (abs_float f5 < cutoff) then result else
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let v5 =
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vrr am cm (totAngMom_a-1) (totAngMom_c-1)
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in
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Array.init (maxsze) (fun m ->
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result.(m) -. (if m = maxm then 0. else f5 *. v5.(m+1)))
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in
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result
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in Zmap.add map_2d key result;
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result
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(** Horizontal recurrence relations *)
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and hrr0 angMom_a angMom_b angMom_c
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totAngMom_a totAngMom_b totAngMom_c =
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if debug then
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begin
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let angMom_ax, angMom_ay, angMom_az = angMom_a
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and angMom_bx, angMom_by, angMom_bz = angMom_b
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and angMom_cx, angMom_cy, angMom_cz = angMom_c in
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Printf.printf "hrr0: %d %d %d : %d %d %d %d %d %d %d %d %d\n"
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totAngMom_a totAngMom_b totAngMom_c
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angMom_ax angMom_ay angMom_az
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angMom_bx angMom_by angMom_bz
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angMom_cx angMom_cy angMom_cz
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end;
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match totAngMom_b with
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| 0 -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
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| 1 ->
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let angMom_ax, angMom_ay, angMom_az = angMom_a in
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let ap, xyz =
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match angMom_b with
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| (1,_,_) -> (angMom_ax+1,angMom_ay,angMom_az), 0
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| (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), 1
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| _ -> (angMom_ax,angMom_ay,angMom_az+1), 2
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in
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let v1 =
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vrr ap angMom_c (totAngMom_a+1) totAngMom_c
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in
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let f2 =
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(Coordinate.coord center_ab xyz)
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in
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if (abs_float f2 < cutoff) then v1.(0) else
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let v2 =
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vrr angMom_a angMom_c totAngMom_a totAngMom_c
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in
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v1.(0) +. f2 *. v2.(0)
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| _ ->
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let angMom_ax, angMom_ay, angMom_az = angMom_a
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and angMom_bx, angMom_by, angMom_bz = angMom_b in
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let bxyz, xyz =
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match angMom_b with
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| (_,0,0) -> angMom_bx, 0
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| (_,_,0) -> angMom_by, 1
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| (_,_,_) -> angMom_bz, 2
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in
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if (bxyz < 1) then 0. else
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let ap, bm =
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match xyz with
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| 0 -> (angMom_ax+1,angMom_ay,angMom_az),(angMom_bx-1,angMom_by,angMom_bz)
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| 1 -> (angMom_ax,angMom_ay+1,angMom_az),(angMom_bx,angMom_by-1,angMom_bz)
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| _ -> (angMom_ax,angMom_ay,angMom_az+1),(angMom_bx,angMom_by,angMom_bz-1)
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in
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let h1 =
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hrr0 ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
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in
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let f2 =
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(Coordinate.coord center_ab xyz)
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in
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if (abs_float f2 < cutoff) then h1 else
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let h2 =
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hrr0 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
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in
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h1 +. f2 *. h2
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and hrr angMom_a angMom_b angMom_c angMom_d
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
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if debug then
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begin
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let angMom_ax, angMom_ay, angMom_az = angMom_a in
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let angMom_bx, angMom_by, angMom_bz = angMom_b in
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let angMom_cx, angMom_cy, angMom_cz = angMom_c in
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let angMom_dx, angMom_dy, angMom_dz = angMom_d in
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Printf.printf "hrr : %d %d %d %d : %d %d %d %d %d %d %d %d %d %d %d %d\n"
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d
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angMom_ax angMom_ay angMom_az
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angMom_bx angMom_by angMom_bz
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angMom_cx angMom_cy angMom_cz
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angMom_dx angMom_dy angMom_dz
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end;
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match (totAngMom_b, totAngMom_d) with
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| (_,0) -> if (totAngMom_b = 0) then
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(vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
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else
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hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let (angMom_cx, angMom_cy, angMom_cz) = angMom_c
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and (angMom_dx, angMom_dy, angMom_dz) = angMom_d in
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let cp, dm, xyz =
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match angMom_d with
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| (_,0,0) -> (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), 0
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| (_,_,0) -> (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), 1
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| _ -> (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), 2
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in
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let h1 =
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hrr angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
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in
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let f2 = Coordinate.coord center_cd xyz in
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if (abs_float f2 < cutoff) then h1 else
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let h2 =
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hrr angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
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in
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h1 +. f2 *. h2
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in
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hrr
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(angMom_a.(0),angMom_a.(1),angMom_a.(2))
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(angMom_b.(0),angMom_b.(1),angMom_b.(2))
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(angMom_c.(0),angMom_c.(1),angMom_c.(2))
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(angMom_d.(0),angMom_d.(1),angMom_d.(2))
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d
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let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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let shell_a = shell_p.(0).Shell_pair.shell_a
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and shell_b = shell_p.(0).Shell_pair.shell_b
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and shell_c = shell_q.(0).Shell_pair.shell_a
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and shell_d = shell_q.(0).Shell_pair.shell_b
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in
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let maxm =
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let open Angular_momentum in
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(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
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+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
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in
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(* Pre-computation of integral class indices *)
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let class_indices =
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Angular_momentum.zkey_array
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(Angular_momentum.Quartet
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Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d))
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in
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let contracted_class =
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Array.make (Array.length class_indices) 0.;
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in
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(* Compute all integrals in the shell for each pair of significant shell pairs *)
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for ab=0 to (Array.length shell_p - 1) do
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let cab = shell_p.(ab).Shell_pair.coef in
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let b = shell_p.(ab).Shell_pair.j in
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let norm_coef_scale_p = shell_p.(ab).Shell_pair.norm_coef_scale in
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for cd=0 to (Array.length shell_q - 1) do
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let coef_prod =
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cab *. shell_q.(cd).Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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try
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if (abs_float coef_prod) < 1.e-4*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
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in
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let norm_pq_sq =
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Coordinate.dot center_pq center_pq
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in
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let zero_m_array =
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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in
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begin
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match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d) with
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| Angular_momentum.(S,S,S,S) ->
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let integral =
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zero_m_array.(0)
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in
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contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
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| _ ->
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let d = shell_q.(cd).Shell_pair.j in
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let map_1d = Zmap.create (4*maxm) in
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let map_2d = Zmap.create (Array.length class_indices) in
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let norm_coef_scale_q = shell_q.(cd).Shell_pair.norm_coef_scale in
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let norm_coef_scale =
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Array.map (fun v1 ->
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Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
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) norm_coef_scale_p
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|> Array.to_list
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|> Array.concat
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in
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(*
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let monocentric =
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shell_p.(ab).Shell_pair.monocentric &&
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shell_q.(cd).Shell_pair.monocentric
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in
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*)
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(* Compute the integral class from the primitive shell quartet *)
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class_indices
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|> Array.iteri (fun i key ->
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let a = Zkey.to_int_array Zkey.Kind_12 key in
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let (angMomA,angMomB,angMomC,angMomD) =
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( [| a.(0) ; a.(1) ; a.(2) |],
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[| a.(3) ; a.(4) ; a.(5) |],
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[| a.(6) ; a.(7) ; a.(8) |],
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[| a.(9) ; a.(10) ; a.(11) |] )
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in
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try
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(*
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if monocentric then
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begin
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if ( ((1 land (a.(0) + a.(3) + a.(6) + a.( 9)))=1) ||
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((1 land (a.(1) + a.(4) + a.(7) + a.(10)))=1) ||
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((1 land (a.(2) + a.(5) + a.(8) + a.(11)))=1)
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) then
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raise NullQuartet
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end;
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*)
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(* Schwartz screening *)
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(*
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let schwartz_p =
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let key =
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Zkey.of_int_array Zkey.Kind_12
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[| a.(0) ; a.(1) ; a.(2) ;
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a.(3) ; a.(4) ; a.(5) ;
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a.(0) ; a.(1) ; a.(2) ;
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a.(3) ; a.(4) ; a.(5) |]
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in
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match schwartz_p with
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| None -> 1.
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| Some schwartz_p -> Zmap.find schwartz_p key
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in
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if schwartz_p < cutoff then raise NullQuartet;
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let schwartz_q =
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let key =
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Zkey.of_int_array Zkey.Kind_12
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[| a.(6) ; a.(7) ; a.(8) ;
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|
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 = norm_coef_scale.(i) in
|
|
let coef_prod = coef_prod *. norm in
|
|
let integral =
|
|
hvrr_two_e (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_1d map_2d
|
|
in
|
|
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
|
|
with NullQuartet -> ()
|
|
)
|
|
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
|
|
|
|
|