10
1
mirror of https://gitlab.com/scemama/QCaml.git synced 2024-11-07 06:33:39 +01:00
QCaml/Basis/TwoElectronRR.ml

439 lines
14 KiB
OCaml
Raw Normal View History

2018-01-18 23:42:48 +01:00
open Util
2018-02-02 01:25:10 +01:00
open Constants
2018-02-23 15:49:27 +01:00
module Am = Angular_momentum
module Co = Coordinate
module Cs = Contracted_shell
module Csp = ContractedShellPair
module Sp = ShellPair
module Po = Powers
2018-01-18 23:42:48 +01:00
2018-02-03 18:53:44 +01:00
let debug=false
2018-01-23 00:48:45 +01:00
let cutoff2 = cutoff *. cutoff
exception NullQuartet
2018-01-18 23:42:48 +01:00
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
2018-02-23 15:49:27 +01:00
let rec hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
2018-02-19 16:01:13 +01:00
zero_m_array
2018-02-23 15:49:27 +01:00
expo_b expo_d
expo_inv_p expo_inv_q
center_ab center_cd center_pq
center_pa center_qc
map_1d map_2d =
2018-01-18 23:42:48 +01:00
2018-02-09 10:49:27 +01:00
(* Swap electrons 1 and 2 so that the max angular momentum is on 1 *)
2018-02-23 15:49:27 +01:00
if angMom_a.Po.tot + angMom_b.Po.tot < angMom_c.Po.tot + angMom_d.Po.tot then
hvrr_two_e
angMom_c angMom_d angMom_a angMom_b
2018-02-19 16:01:13 +01:00
zero_m_array
2018-02-23 15:49:27 +01:00
expo_d expo_b
expo_inv_q expo_inv_p
center_cd center_ab (Co.neg center_pq)
center_qc center_pa
2018-02-21 20:21:45 +01:00
map_1d map_2d
2018-02-19 16:01:13 +01:00
2018-02-09 10:49:27 +01:00
else
2018-02-19 16:01:13 +01:00
2018-02-23 15:49:27 +01:00
let maxm = angMom_a.Po.tot + angMom_b.Po.tot + angMom_c.Po.tot + angMom_d.Po.tot in
2018-02-19 16:01:13 +01:00
let maxsze = maxm+1 in
let get_xyz angMom =
match angMom with
2018-02-23 15:49:27 +01:00
| { Po.y=0 ; z=0 ; _ } -> Co.X
| { z=0 ; _ } -> Co.Y
| _ -> Co.Z
2018-02-09 10:49:27 +01:00
in
2018-02-19 16:01:13 +01:00
2018-02-09 10:49:27 +01:00
(** Vertical recurrence relations *)
2018-02-19 16:01:13 +01:00
let rec vrr0 angMom_a =
2018-02-09 10:49:27 +01:00
2018-02-23 15:49:27 +01:00
match angMom_a.Po.tot with
2018-02-09 10:49:27 +01:00
| 0 -> zero_m_array
| _ ->
2018-02-22 01:38:47 +01:00
let key = Zkey.of_powers_three angMom_a in
2018-02-09 10:49:27 +01:00
try Zmap.find map_1d key with
| Not_found ->
let result =
2018-02-19 16:01:13 +01:00
let xyz = get_xyz angMom_a in
2018-02-23 15:49:27 +01:00
let am = Po.decr xyz angMom_a in
let amxyz = Po.get xyz am in
2018-02-19 16:01:13 +01:00
2018-02-23 15:49:27 +01:00
let f1 = expo_inv_p *. Co.get xyz center_pq
and f2 = expo_b *. expo_inv_p *. Co.get xyz center_ab
2018-02-21 17:27:31 +01:00
in
2018-02-23 15:49:27 +01:00
let result = Array.create_float (maxsze - angMom_a.Po.tot) in
2018-02-21 17:27:31 +01:00
if amxyz = 0 then
begin
2018-02-23 02:02:53 +01:00
let v1 = vrr0 am in
Array.iteri (fun m _ ->
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)) result
2018-02-21 17:27:31 +01:00
end
2018-02-20 23:54:48 +01:00
else
2018-02-21 17:27:31 +01:00
begin
2018-02-23 15:49:27 +01:00
let amm = Po.decr xyz am in
2018-02-21 17:27:31 +01:00
let v3 = vrr0 amm in
let v1 = vrr0 am in
let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
2018-02-23 02:02:53 +01:00
Array.iteri (fun m _ ->
2018-02-21 17:27:31 +01:00
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)
2018-02-23 02:02:53 +01:00
+. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1)) ) result
2018-02-21 17:27:31 +01:00
end;
result
2018-02-09 10:49:27 +01:00
in Zmap.add map_1d key result;
result
2018-01-18 23:42:48 +01:00
2018-02-01 16:09:04 +01:00
2018-02-19 16:01:13 +01:00
and vrr angMom_a angMom_c =
2018-01-24 16:29:48 +01:00
2018-02-23 15:49:27 +01:00
match angMom_a.Po.tot, angMom_c.Po.tot with
2018-02-20 23:54:48 +01:00
| (i,0) -> if (i>0) then vrr0 angMom_a
else zero_m_array
2018-02-09 10:49:27 +01:00
| (_,_) ->
2018-02-22 01:38:47 +01:00
let key = Zkey.of_powers_six angMom_a angMom_c in
2018-02-09 10:49:27 +01:00
try Zmap.find map_2d key with
| Not_found ->
let result =
2018-02-23 15:49:27 +01:00
(* angMom_c.Po.tot > 0 so cm.Po.tot >= 0 *)
2018-02-21 20:21:45 +01:00
let xyz = get_xyz angMom_c in
2018-02-23 15:49:27 +01:00
let cm = Po.decr xyz angMom_c in
let cmxyz = Po.get xyz cm in
let axyz = Po.get xyz angMom_a in
2018-02-19 16:01:13 +01:00
2018-02-21 17:27:31 +01:00
let f1 =
2018-02-23 15:49:27 +01:00
-. expo_d *. expo_inv_q *. Co.get xyz center_cd
2018-02-21 17:27:31 +01:00
and f2 =
2018-02-23 15:49:27 +01:00
expo_inv_q *. Co.get xyz center_pq
2018-02-21 17:27:31 +01:00
in
2018-02-23 15:49:27 +01:00
let result = Array.make (maxsze - angMom_a.Po.tot - angMom_c.Po.tot) 0. in
2018-02-22 01:38:47 +01:00
if axyz > 0 then
2018-02-21 17:27:31 +01:00
begin
2018-02-23 15:49:27 +01:00
let am = Po.decr xyz angMom_a in
2018-02-22 01:38:47 +01:00
let f5 =
(float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5
2018-02-21 17:27:31 +01:00
in
2018-02-22 01:38:47 +01:00
if (abs_float f5 > cutoff) then
let v5 =
vrr am cm
in
2018-02-23 02:02:53 +01:00
Array.iteri (fun m _ ->
result.(m) <- result.(m) -. f5 *. v5.(m+1)) result
2018-02-21 17:27:31 +01:00
end;
if cmxyz > 0 then
begin
let f3 =
(float_of_int cmxyz) *. expo_inv_q *. 0.5
in
if (abs_float f3 > cutoff) ||
(abs_float (f3 *. expo_inv_q) > cutoff) then
2018-02-11 23:41:18 +01:00
begin
2018-02-21 17:27:31 +01:00
let v3 =
2018-02-23 15:49:27 +01:00
let cmm = Po.decr xyz cm in
2018-02-21 17:27:31 +01:00
vrr angMom_a cmm
2018-02-09 10:49:27 +01:00
in
2018-02-23 02:02:53 +01:00
Array.iteri (fun m _ ->
2018-02-21 17:27:31 +01:00
result.(m) <- result.(m) +.
2018-02-23 02:02:53 +01:00
f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1)) ) result
2018-02-21 17:27:31 +01:00
end
end;
2018-02-22 01:38:47 +01:00
if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then
2018-02-21 17:27:31 +01:00
begin
2018-02-22 01:38:47 +01:00
let v1 =
vrr angMom_a cm
2018-02-21 17:27:31 +01:00
in
2018-02-23 02:02:53 +01:00
Array.iteri (fun m _ ->
result.(m) <- result.(m) +. f1 *. v1.(m) -. f2 *. v1.(m+1) ) result
2018-02-21 17:27:31 +01:00
end;
result
2018-02-09 10:49:27 +01:00
in Zmap.add map_2d key result;
result
2018-01-18 23:42:48 +01:00
2018-02-23 03:25:25 +01:00
(*
2018-02-21 17:27:31 +01:00
and trr angMom_a angMom_c =
2018-02-23 15:49:27 +01:00
match (angMom_a.Po.tot, angMom_c.Po.tot) with
2018-02-21 20:21:45 +01:00
| (i,0) -> if (i>0) then (vrr0 angMom_a).(0)
else zero_m_array.(0)
2018-02-21 17:27:31 +01:00
| (_,_) ->
2018-02-22 01:38:47 +01:00
let key = Zkey.of_powers_six angMom_a angMom_c in
2018-02-21 17:27:31 +01:00
2018-02-22 01:38:47 +01:00
try (Zmap.find map_2d key).(0) with
2018-02-21 17:27:31 +01:00
| Not_found ->
let result =
2018-02-21 20:21:45 +01:00
let xyz = get_xyz angMom_c in
2018-02-23 15:49:27 +01:00
let axyz = Po.get xyz angMom_a in
let cm = Po.decr xyz angMom_c in
let cmxyz = Po.get xyz cm in
2018-02-21 20:21:45 +01:00
let expo_inv_q_over_p = expo_inv_q /. expo_inv_p in
let f =
2018-02-23 15:49:27 +01:00
Co.get xyz center_qc +. expo_inv_q_over_p *.
Co.get xyz center_pa
2018-02-21 20:21:45 +01:00
in
2018-02-22 01:38:47 +01:00
let result = 0. in
2018-02-21 20:21:45 +01:00
let result =
if cmxyz < 1 then result else
let f = 0.5 *. (float_of_int cmxyz) *. expo_inv_q in
if abs_float f < cutoff then 0. else
2018-02-23 15:49:27 +01:00
let cmm = Po.decr xyz cm in
2018-02-21 20:21:45 +01:00
let v3 = trr angMom_a cmm in
result +. f *. v3
in
2018-02-22 01:38:47 +01:00
let result =
if abs_float f < cutoff then result else
let v1 = trr angMom_a cm in
result +. f *. v1
in
2018-02-21 20:21:45 +01:00
let result =
if cmxyz < 0 then result else
let f = -. expo_inv_q_over_p in
2018-02-23 15:49:27 +01:00
let ap = Po.incr xyz angMom_a in
2018-02-21 20:21:45 +01:00
let v4 = trr ap cm in
result +. v4 *. f
in
2018-02-22 01:38:47 +01:00
let result =
if axyz < 1 then result else
let f = 0.5 *. (float_of_int axyz) *. expo_inv_q in
if abs_float f < cutoff then result else
2018-02-23 15:49:27 +01:00
let am = Po.decr xyz angMom_a in
2018-02-22 01:38:47 +01:00
let v2 = trr am cm in
result +. f *. v2
in
2018-02-21 20:21:45 +01:00
result
in
2018-02-22 01:38:47 +01:00
Zmap.add map_2d key [|result|];
2018-02-21 20:21:45 +01:00
result
2018-02-22 09:57:43 +01:00
*)
2018-02-22 01:38:47 +01:00
in
2018-01-18 23:42:48 +01:00
2018-02-23 03:25:25 +01:00
2018-02-22 01:38:47 +01:00
let vrr a c =
2018-02-22 09:57:43 +01:00
(vrr a c).(0)
(*
2018-02-22 01:48:30 +01:00
if maxm < 10 then (vrr a c).(0) else trr a c
2018-02-22 09:57:43 +01:00
*)
2018-02-22 01:38:47 +01:00
in
2018-01-18 23:42:48 +01:00
2018-02-01 16:09:04 +01:00
2018-02-09 10:49:27 +01:00
(** Horizontal recurrence relations *)
2018-02-22 01:38:47 +01:00
let rec hrr0 angMom_a angMom_b angMom_c =
2018-01-24 16:29:48 +01:00
2018-02-23 15:49:27 +01:00
match angMom_b.Po.tot with
2018-02-09 10:49:27 +01:00
| 1 ->
2018-02-19 16:01:13 +01:00
let xyz = get_xyz angMom_b in
2018-02-23 15:49:27 +01:00
let ap = Po.incr xyz angMom_a in
2018-02-20 23:54:48 +01:00
let v1 = vrr ap angMom_c in
2018-02-23 15:49:27 +01:00
let f2 = Co.get xyz center_ab in
2018-02-22 01:38:47 +01:00
if (abs_float f2 < cutoff) then v1 else
2018-02-20 23:54:48 +01:00
let v2 = vrr angMom_a angMom_c in
2018-02-22 01:38:47 +01:00
v1 +. f2 *. v2
2018-02-22 09:57:43 +01:00
| 0 -> vrr angMom_a angMom_c
2018-02-09 10:49:27 +01:00
| _ ->
2018-02-19 16:01:13 +01:00
let xyz = get_xyz angMom_b in
2018-02-23 15:49:27 +01:00
let bxyz = Po.get xyz angMom_b in
2018-02-20 23:54:48 +01:00
if bxyz > 0 then
2018-02-23 15:49:27 +01:00
let ap = Po.incr xyz angMom_a in
let bm = Po.decr xyz angMom_b in
2018-02-20 23:54:48 +01:00
let h1 = hrr0 ap bm angMom_c in
2018-02-23 15:49:27 +01:00
let f2 = Co.get xyz center_ab in
2018-02-20 23:54:48 +01:00
if abs_float f2 < cutoff then h1 else
let h2 = hrr0 angMom_a bm angMom_c in
h1 +. f2 *. h2
else 0.
2018-01-24 16:29:48 +01:00
2018-02-13 17:36:25 +01:00
2018-02-19 16:01:13 +01:00
and hrr angMom_a angMom_b angMom_c angMom_d =
2018-01-18 23:42:48 +01:00
2018-02-23 15:49:27 +01:00
match (angMom_b.Po.tot, angMom_d.Po.tot) with
2018-02-20 23:54:48 +01:00
| (_,0) ->
2018-02-23 15:49:27 +01:00
if (angMom_b.Po.tot = 0) then
2018-02-22 01:38:47 +01:00
vrr angMom_a angMom_c
2018-02-09 10:49:27 +01:00
else
2018-02-20 23:54:48 +01:00
hrr0 angMom_a angMom_b angMom_c
2018-02-09 10:49:27 +01:00
| (_,_) ->
2018-02-19 16:01:13 +01:00
let xyz = get_xyz angMom_d in
2018-02-23 15:49:27 +01:00
let cp = Po.incr xyz angMom_c in
let dm = Po.decr xyz angMom_d in
2018-02-20 23:54:48 +01:00
let h1 = hrr angMom_a angMom_b cp dm in
2018-02-23 15:49:27 +01:00
let f2 = Co.get xyz center_cd in
2018-02-20 23:54:48 +01:00
if abs_float f2 < cutoff then h1 else
let h2 = hrr angMom_a angMom_b angMom_c dm in
h1 +. f2 *. h2
2018-02-01 16:09:04 +01:00
2018-02-09 10:49:27 +01:00
in
hrr angMom_a angMom_b angMom_c angMom_d
2018-01-18 23:42:48 +01:00
2018-01-23 19:26:28 +01:00
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
2018-01-18 23:42:48 +01:00
2018-02-23 15:49:27 +01:00
let shell_a = shell_p.Csp.shell_a
and shell_b = shell_p.Csp.shell_b
and shell_c = shell_q.Csp.shell_a
and shell_d = shell_q.Csp.shell_b
and sp = shell_p.Csp.shell_pairs
and sq = shell_q.Csp.shell_pairs
2018-01-18 23:42:48 +01:00
in
2018-02-23 15:49:27 +01:00
let maxm = shell_p.Csp.totAngMomInt + shell_q.Csp.totAngMomInt in
2018-01-18 23:42:48 +01:00
(* Pre-computation of integral class indices *)
let class_indices =
2018-02-23 15:49:27 +01:00
Am.zkey_array (Am.Quartet
(shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom ))
2018-01-18 23:42:48 +01:00
in
let contracted_class =
Array.make (Array.length class_indices) 0.;
in
2018-02-11 23:41:18 +01:00
let monocentric =
2018-02-23 15:49:27 +01:00
shell_p.Csp.monocentric &&
shell_q.Csp.monocentric &&
shell_p.Csp.shell_a.Cs.center =
shell_q.Csp.shell_a.Cs.center
2018-02-11 23:41:18 +01:00
in
2018-01-18 23:42:48 +01:00
(* Compute all integrals in the shell for each pair of significant shell pairs *)
2018-02-23 15:49:27 +01:00
let norm_coef_scale_p = shell_p.Csp.norm_coef_scale in
let norm_coef_scale_q = shell_q.Csp.norm_coef_scale in
2018-02-09 19:41:22 +01:00
for ab=0 to (Array.length sp - 1) do
2018-02-23 15:49:27 +01:00
let cab = shell_p.Csp.coef.(ab) in
let b = sp.(ab).Sp.j in
for cd=0 to (Array.length shell_q.Csp.shell_pairs - 1) do
2018-01-30 14:51:37 +01:00
let coef_prod =
2018-02-23 15:49:27 +01:00
cab *. shell_q.Csp.coef.(cd)
2018-01-30 14:51:37 +01:00
in
(** Screening on the product of coefficients *)
try
2018-02-23 15:49:27 +01:00
if (abs_float coef_prod) < 1.e-3 *. cutoff then
2018-01-30 14:51:37 +01:00
raise NullQuartet;
let center_pq =
2018-02-23 15:49:27 +01:00
Co.(sp.(ab).Sp.center |- sq.(cd).Sp.center)
2018-01-30 14:51:37 +01:00
in
let norm_pq_sq =
2018-02-23 15:49:27 +01:00
Co.dot center_pq center_pq
2018-01-30 14:51:37 +01:00
in
2018-02-12 00:56:32 +01:00
let expo_pq_inv =
2018-02-23 15:49:27 +01:00
shell_p.Csp.expo_inv.(ab) +.
shell_q.Csp.expo_inv.(cd)
2018-02-12 00:56:32 +01:00
in
2018-01-30 14:51:37 +01:00
let zero_m_array =
2018-02-03 19:01:30 +01:00
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
2018-01-30 14:51:37 +01:00
in
begin
2018-02-23 15:49:27 +01:00
match (shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom) with
| Am.(S,S,S,S) ->
2018-02-03 19:01:30 +01:00
let integral =
zero_m_array.(0)
in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
2018-01-30 14:51:37 +01:00
| _ ->
2018-02-23 15:49:27 +01:00
let d = shell_q.Csp.shell_pairs.(cd).Sp.j in
2018-02-03 19:01:30 +01:00
let map_1d = Zmap.create (4*maxm) in
let map_2d = Zmap.create (Array.length class_indices) in
let norm_coef_scale =
2018-02-11 23:41:18 +01:00
Array.to_list norm_coef_scale_p
|> List.map (fun v1 ->
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q)
2018-02-03 19:01:30 +01:00
|> Array.concat
in
2018-02-12 00:56:32 +01:00
2018-02-03 19:01:30 +01:00
(* Compute the integral class from the primitive shell quartet *)
class_indices
|> Array.iteri (fun i key ->
2018-02-19 16:01:13 +01:00
let (angMom_a,angMom_b,angMom_c,angMom_d) =
match Zkey.to_powers ~kind:Zkey.Kind_12 key with
2018-02-06 17:13:25 +01:00
| Zkey.Twelve x -> x
| _ -> assert false
2018-02-03 19:01:30 +01:00
in
try
2018-02-12 00:56:32 +01:00
if monocentric then
begin
2018-02-23 15:49:27 +01:00
if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) ||
((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) ||
((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1)
2018-02-12 00:56:32 +01:00
) then
raise NullQuartet
end;
2018-02-19 16:01:13 +01:00
2018-02-12 00:56:32 +01:00
(* Schwartz screening *)
2018-02-23 15:49:27 +01:00
(*
if (maxm > 8) then
2018-02-12 00:56:32 +01:00
(
let schwartz_p =
2018-02-23 15:49:27 +01:00
let key =
Zkey.of_powers_twelve angMom_a angMom_b angMom_a angMom_b
2018-02-12 00:56:32 +01:00
in
match schwartz_p with
| None -> 1.
| Some schwartz_p -> Zmap.find schwartz_p key
2018-01-24 16:29:48 +01:00
in
2018-02-12 00:56:32 +01:00
if schwartz_p < cutoff then raise NullQuartet;
let schwartz_q =
2018-02-23 15:49:27 +01:00
let key =
Zkey.of_powers_twelve angMom_c angMom_d angMom_c angMom_d
2018-02-12 00:56:32 +01:00
in
match schwartz_q with
| None -> 1.
| Some schwartz_q -> Zmap.find schwartz_q key
2018-01-24 16:29:48 +01:00
in
2018-02-12 00:56:32 +01:00
if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
2018-02-23 15:49:27 +01:00
);
2018-01-24 16:29:48 +01:00
*)
2018-02-12 00:56:32 +01:00
2018-02-03 19:01:30 +01:00
let norm = norm_coef_scale.(i) in
let coef_prod = coef_prod *. norm in
2018-02-21 20:21:45 +01:00
2018-02-03 19:01:30 +01:00
let integral =
2018-02-23 15:49:27 +01:00
hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
2018-02-19 16:01:13 +01:00
zero_m_array
2018-02-23 15:49:27 +01:00
shell_b.expo.(b) shell_d.expo.(d)
shell_p.Csp.expo_inv.(ab)
shell_q.Csp.expo_inv.(cd)
sp.(ab).Sp.center_ab sq.(cd).Sp.center_ab center_pq
sp.(ab).Sp.center_a sq.(cd).Sp.center_a
2018-02-21 20:21:45 +01:00
map_1d map_2d
2018-02-03 19:01:30 +01:00
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
with NullQuartet -> ()
)
2018-01-30 14:51:37 +01:00
end
2018-02-03 19:01:30 +01:00
with NullQuartet -> ()
2018-01-30 14:51:37 +01:00
done
done;
2018-01-24 16:29:48 +01:00
2018-01-18 23:42:48 +01:00
let result =
Zmap.create (Array.length contracted_class)
in
2018-02-02 22:43:56 +01:00
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
2018-01-18 23:42:48 +01:00
result
2018-01-23 19:26:28 +01:00
(** 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 =
2018-02-23 15:49:27 +01:00
let shell_p = Csp.create ~cutoff shell_a shell_b
and shell_q = Csp.create ~cutoff shell_c shell_d
2018-01-23 19:26:28 +01:00
in
contracted_class_shell_pairs ~zero_m shell_p shell_q