mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-11-13 01:23:41 +01:00
730 lines
25 KiB
OCaml
730 lines
25 KiB
OCaml
open Util
|
|
open Lacaml.D
|
|
open Bigarray
|
|
|
|
let cutoff = Constants.cutoff
|
|
let cutoff2 = cutoff *. cutoff
|
|
|
|
exception NullQuartet
|
|
exception Found
|
|
|
|
let at_least_one_valid arr =
|
|
try
|
|
Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
|
|
with Found -> true
|
|
|
|
|
|
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
|
|
let hvrr_two_e_vector (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_1d map_2d np nq
|
|
=
|
|
|
|
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_v m angMom_a = function
|
|
| 0 -> Some zero_m_array.(m)
|
|
| totAngMom_a ->
|
|
let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
|
|
in
|
|
|
|
try Zmap.find map_1d.(m) key with
|
|
| Not_found ->
|
|
let result =
|
|
let am, amm, amxyz, xyz =
|
|
match angMom_a with
|
|
| (x,0,0) -> (x-1,0,0),(x-2,0,0), x-1, 0
|
|
| (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
|
|
| (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
|
|
in
|
|
if amxyz < 0 then
|
|
None
|
|
else
|
|
begin
|
|
let cab = Coordinate.coord center_ab xyz in
|
|
let v1_top, p1_top =
|
|
if abs_float cab < cutoff then
|
|
None,
|
|
vrr0_v (m+1) am (totAngMom_a-1)
|
|
else
|
|
vrr0_v m am (totAngMom_a-1),
|
|
vrr0_v (m+1) am (totAngMom_a-1)
|
|
in
|
|
let v1_top2, p1_top2 =
|
|
if amxyz < 1 then (None,None) else
|
|
vrr0_v m amm (totAngMom_a-2),
|
|
vrr0_v (m+1) amm (totAngMom_a-2)
|
|
in
|
|
|
|
let result = Array.make_matrix np nq 0. in
|
|
if amxyz < 1 then
|
|
begin
|
|
let p0 =
|
|
match p1_top with
|
|
| Some p1_top -> p1_top
|
|
| _ -> assert false
|
|
in
|
|
begin
|
|
match v1_top with
|
|
| None -> ()
|
|
| Some v0 ->
|
|
for l=0 to np-1 do
|
|
let f0 =
|
|
-. expo_b.(l) *. expo_inv_p.(l) *. cab
|
|
in
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- v0.(l).(k) *. f0
|
|
done
|
|
done
|
|
end;
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- result.(l).(k)
|
|
+. expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(l).(k)
|
|
done
|
|
done
|
|
end
|
|
else
|
|
begin
|
|
let p0 =
|
|
match p1_top with
|
|
| Some p1_top -> p1_top
|
|
| _ -> assert false
|
|
in
|
|
begin
|
|
match v1_top with
|
|
| None -> ()
|
|
| Some v0 ->
|
|
for l=0 to np-1 do
|
|
let f0 = -. expo_b.(l) *. expo_inv_p.(l) *. cab in
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- v0.(l).(k) *. f0
|
|
done
|
|
done
|
|
end;
|
|
let v1 =
|
|
match v1_top2 with
|
|
| Some v1_top2 -> v1_top2
|
|
| None -> assert false
|
|
in
|
|
let v2 =
|
|
match p1_top2 with
|
|
| Some p1_top2 -> p1_top2
|
|
| None -> assert false
|
|
in
|
|
for l=0 to np-1 do
|
|
let f = (float_of_int amxyz) *. expo_inv_p.(l) *. 0.5 in
|
|
for k=0 to nq-1
|
|
do
|
|
result.(l).(k) <- result.(l).(k) +.
|
|
expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(l).(k) +.
|
|
f *. (v1.(l).(k) +. v2.(l).(k) *. expo_inv_p.(l))
|
|
done
|
|
done
|
|
end;
|
|
Some result
|
|
end
|
|
in
|
|
Zmap.add map_1d.(m) key result;
|
|
result
|
|
|
|
and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
|
|
|
|
match (totAngMom_a, totAngMom_c) with
|
|
| (i,0) -> vrr0_v m angMom_a totAngMom_a
|
|
| (_,_) ->
|
|
|
|
let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
|
|
in
|
|
|
|
try Zmap.find map_2d.(m) key with
|
|
| Not_found ->
|
|
let result =
|
|
begin
|
|
let am, cm, cmm, axyz, cxyz, xyz =
|
|
let (aax, aay, aaz) = angMom_a
|
|
and (acx, acy, acz) = angMom_c in
|
|
if (acz > 0) then
|
|
(aax, aay, aaz-1),
|
|
(acx, acy, acz-1),
|
|
(acx, acy, acz-2),
|
|
aaz, acz, 2
|
|
else if (acy > 0) then
|
|
(aax, aay-1,aaz),
|
|
(acx, acy-1,acz),
|
|
(acx, acy-2,acz),
|
|
aay,acy, 1
|
|
else
|
|
(aax-1,aay,aaz),
|
|
(acx-1,acy,acz),
|
|
(acx-2,acy,acz),
|
|
aax,acx, 0
|
|
in
|
|
(*
|
|
let result = Array.make_matrix np nq 0. in
|
|
*)
|
|
let do_compute = ref false in
|
|
let v1 =
|
|
let f = -. (Coordinate.coord center_cd xyz) in
|
|
|
|
let f1 =
|
|
Array.init nq (fun k ->
|
|
let x = expo_d.(k) *. expo_inv_q.(k) *. f in
|
|
if ( (not !do_compute) && (abs_float x > cutoff) ) then
|
|
do_compute := true;
|
|
x)
|
|
in
|
|
if (!do_compute) then
|
|
match vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1) with
|
|
| None -> None
|
|
| Some v1 ->
|
|
begin
|
|
let result = Array.make_matrix np nq 0. in
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- v1.(l).(k) *. f1.(k)
|
|
done
|
|
done;
|
|
Some result
|
|
end
|
|
else None
|
|
in
|
|
|
|
let v2 =
|
|
let f2 =
|
|
Array.init np (fun l ->
|
|
Array.init nq (fun k ->
|
|
let x = expo_inv_q.(k) *. center_pq.(xyz).(l).(k) in
|
|
if (!do_compute) then x
|
|
else (if abs_float x > cutoff then do_compute := true ; x)
|
|
) )
|
|
in
|
|
if (!do_compute) then
|
|
match vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) with
|
|
| None -> None
|
|
| Some v2 ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
f2.(l).(k) <- -. v2.(l).(k) *. f2.(l).(k)
|
|
done
|
|
done;
|
|
Some f2
|
|
end
|
|
else
|
|
None
|
|
in
|
|
|
|
let p1 =
|
|
match v1, v2 with
|
|
| None, None -> None
|
|
| None, Some v2 -> Some v2
|
|
| Some v1, None -> Some v1
|
|
| Some v1, Some v2 ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
v2.(l).(k) <- v2.(l).(k) +. v1.(l).(k)
|
|
done
|
|
done;
|
|
Some v2
|
|
end
|
|
in
|
|
|
|
let p2 =
|
|
if cxyz < 2 then p1 else
|
|
let fcm = (float_of_int (cxyz-1)) *. 0.5 in
|
|
let f1 =
|
|
Array.init nq (fun k ->
|
|
let x = fcm *. expo_inv_q.(k) in
|
|
if (!do_compute) then x
|
|
else (if abs_float x > cutoff then do_compute := true ; x)
|
|
)
|
|
in
|
|
let v1 =
|
|
if (!do_compute) then
|
|
match vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2) with
|
|
| None -> None
|
|
| Some v1 ->
|
|
begin
|
|
let result = Array.make_matrix np nq 0. in
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- v1.(l).(k) *. f1.(k)
|
|
done;
|
|
done;
|
|
Some result
|
|
end
|
|
else None
|
|
in
|
|
|
|
let v3 =
|
|
let f2 =
|
|
Array.init nq (fun k ->
|
|
let x = expo_inv_q.(k) *. f1.(k) in
|
|
if (!do_compute) then x
|
|
else (if abs_float x > cutoff then do_compute := true ; x)
|
|
)
|
|
in
|
|
if (!do_compute) then
|
|
match vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) with
|
|
| None -> None
|
|
| Some v3 ->
|
|
begin
|
|
let result = Array.make_matrix np nq 0. in
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
result.(l).(k) <- v3.(l).(k) *. f2.(k)
|
|
done
|
|
done;
|
|
Some result
|
|
end
|
|
else None
|
|
in
|
|
match p1, v1, v3 with
|
|
| None, None, None -> None
|
|
| Some p1, None, None -> Some p1
|
|
| None, Some v1, None -> Some v1
|
|
| None, None, Some v3 -> Some v3
|
|
| Some p1, Some v1, Some v3 ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
v3.(l).(k) <- p1.(l).(k) +. v1.(l).(k) +. v3.(l).(k)
|
|
done
|
|
done;
|
|
Some v3
|
|
end
|
|
| Some p1, Some v1, None ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
p1.(l).(k) <- v1.(l).(k) +. p1.(l).(k)
|
|
done
|
|
done;
|
|
Some p1
|
|
end
|
|
| Some p1, None, Some v3 ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
p1.(l).(k) <- p1.(l).(k) +. v3.(l).(k)
|
|
done
|
|
done;
|
|
Some p1
|
|
end
|
|
| None , Some v1, Some v3 ->
|
|
begin
|
|
for l=0 to np-1 do
|
|
for k=0 to nq-1 do
|
|
v3.(l).(k) <- v1.(l).(k) +. v3.(l).(k)
|
|
done
|
|
done;
|
|
Some v3
|
|
end
|
|
in
|
|
if (axyz < 1) || (cxyz < 1) then p2 else
|
|
let v =
|
|
vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
|
|
in
|
|
match (p2, v) with
|
|
| None, None -> None
|
|
| Some p2, None -> Some p2
|
|
| _, Some v ->
|
|
begin
|
|
let p2 =
|
|
match p2 with
|
|
| None -> Array.make_matrix np nq 0.
|
|
| Some p2 -> p2
|
|
in
|
|
for l=0 to np-1 do
|
|
let fa = (float_of_int axyz) *. expo_inv_p.(l) *. 0.5 in
|
|
for k=0 to nq-1 do
|
|
p2.(l).(k) <- p2.(l).(k) -. fa *. expo_inv_q.(k) *. v.(l).(k)
|
|
done
|
|
done;
|
|
Some p2
|
|
end
|
|
end
|
|
in Zmap.add map_2d.(m) key result;
|
|
result
|
|
|
|
|
|
|
|
|
|
(** Horizontal recurrence relations *)
|
|
and hrr0_v angMom_a angMom_b angMom_c
|
|
totAngMom_a totAngMom_b totAngMom_c =
|
|
|
|
match totAngMom_b with
|
|
| 0 ->
|
|
begin
|
|
match (totAngMom_a, totAngMom_c) with
|
|
| (0,0) -> Array.fold_left (fun accu c ->
|
|
accu +. Array.fold_left (+.) 0. c) 0. zero_m_array.(0)
|
|
| (_,_) ->
|
|
begin
|
|
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
|
| None -> 0.
|
|
end
|
|
end
|
|
| 1 ->
|
|
let (aax, aay, aaz) = angMom_a in
|
|
let ap, xyz =
|
|
match angMom_b with
|
|
| (_,_,1) -> (aax,aay,aaz+1), 2
|
|
| (_,1,_) -> (aax,aay+1,aaz), 1
|
|
| (_,_,_) -> (aax+1,aay,aaz), 0
|
|
in
|
|
let f = Coordinate.coord center_ab xyz in
|
|
let v1 =
|
|
match vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c with
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
|
| None -> 0.
|
|
in
|
|
if (abs_float f < cutoff) then v1 else
|
|
let v2 =
|
|
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
|
| None -> 0.
|
|
in
|
|
v1 +. v2 *. f
|
|
| _ ->
|
|
let (aax, aay, aaz) = angMom_a
|
|
and (abx, aby, abz) = angMom_b in
|
|
let bxyz, xyz =
|
|
match angMom_b with
|
|
| (0,0,_) -> abz, 2
|
|
| (0,_,_) -> aby, 1
|
|
| _ -> abx, 0
|
|
in
|
|
if (bxyz < 1) then 0. else
|
|
let ap, bm =
|
|
match xyz with
|
|
| 0 -> (aax+1,aay,aaz),(abx-1,aby,abz)
|
|
| 1 -> (aax,aay+1,aaz),(abx,aby-1,abz)
|
|
| _ -> (aax,aay,aaz+1),(abx,aby,abz-1)
|
|
in
|
|
|
|
let h1 =
|
|
hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
|
|
in
|
|
let f = (Coordinate.coord center_ab xyz) in
|
|
if (abs_float f < cutoff) then h1 else
|
|
let h2 =
|
|
hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
|
|
in
|
|
h1 +. h2 *. f
|
|
|
|
and hrr_v angMom_a angMom_b angMom_c angMom_d
|
|
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
|
|
|
|
match (totAngMom_b, totAngMom_d) with
|
|
| (_,0) -> if (totAngMom_b = 0) then
|
|
begin
|
|
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
|
| None -> 0.
|
|
end
|
|
else
|
|
hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
|
|
| (_,_) ->
|
|
let (acx, acy, acz) = angMom_c
|
|
and (adx, ady, adz) = angMom_d in
|
|
let cp, dm, xyz =
|
|
match angMom_d with
|
|
| (_,0,0) -> (acx+1, acy, acz), (adx-1, ady, adz), 0
|
|
| (_,_,0) -> (acx, acy+1, acz), (adx, ady-1, adz), 1
|
|
| _ -> (acx, acy, acz+1), (adx, ady, adz-1), 2
|
|
in
|
|
let h1 =
|
|
hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
|
|
in
|
|
let f = (Coordinate.coord center_cd xyz) in
|
|
if (abs_float f < cutoff) then
|
|
h1
|
|
else
|
|
let h2 =
|
|
hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
|
|
in h1 +. f *. h2
|
|
in
|
|
hrr_v
|
|
(angMom_a.(0),angMom_a.(1),angMom_a.(2))
|
|
(angMom_b.(0),angMom_b.(1),angMom_b.(2))
|
|
(angMom_c.(0),angMom_c.(1),angMom_c.(2))
|
|
(angMom_d.(0),angMom_d.(1),angMom_d.(2))
|
|
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.ContractedShellPair.shell_a
|
|
and shell_b = shell_p.ContractedShellPair.shell_b
|
|
and shell_c = shell_q.ContractedShellPair.shell_a
|
|
and shell_d = shell_q.ContractedShellPair.shell_b
|
|
and sp = shell_p.ContractedShellPair.shell_pairs
|
|
and sq = shell_q.ContractedShellPair.shell_pairs
|
|
in
|
|
let maxm =
|
|
shell_p.ContractedShellPair.totAngMomInt +
|
|
shell_q.ContractedShellPair.totAngMomInt
|
|
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
|
|
|
|
(** Screening on the product of coefficients *)
|
|
let coef_max_p =
|
|
Array.fold_left (fun accu x ->
|
|
if (abs_float x) > accu then (abs_float x) else accu)
|
|
0. shell_p.ContractedShellPair.coef
|
|
and coef_max_q =
|
|
Array.fold_left (fun accu x ->
|
|
if (abs_float x) > accu then (abs_float x) else accu)
|
|
0. shell_q.ContractedShellPair.coef
|
|
in
|
|
|
|
let rec build_list cutoff vec accu = function
|
|
| -1 -> Array.of_list accu
|
|
| k -> build_list cutoff vec (
|
|
if (abs_float vec.(k) > cutoff) then (k::accu)
|
|
else accu ) (k-1)
|
|
in
|
|
let p_list =
|
|
let vec = shell_p.ContractedShellPair.coef in
|
|
build_list (cutoff /. coef_max_q) vec [] (Array.length vec - 1)
|
|
and q_list =
|
|
let vec = shell_q.ContractedShellPair.coef in
|
|
build_list (cutoff /. coef_max_p) vec [] (Array.length vec - 1)
|
|
in
|
|
|
|
(*
|
|
if (Array.length p_list) < (Array.length shell_p.ContractedShellPair.coef) then
|
|
begin
|
|
Printf.printf "Reduced p from %d to %d:\n" (Array.length
|
|
shell_p.ContractedShellPair.coef) (Array.length p_list);
|
|
Array.iter (fun k -> Printf.printf "%d " k) p_list; print_newline ();
|
|
Printf.printf "\n%!"
|
|
end;
|
|
|
|
if (Array.length q_list) < (Array.length shell_q.ContractedShellPair.coef) then
|
|
begin
|
|
Printf.printf "Reduced q from %d to %d:\n" (Array.length
|
|
shell_q.ContractedShellPair.coef) (Array.length q_list);
|
|
Array.iter (fun k -> Printf.printf "%d " k) q_list; print_newline ();
|
|
Printf.printf "\n%!"
|
|
end;
|
|
*)
|
|
|
|
let np, nq =
|
|
Array.length p_list,
|
|
Array.length q_list
|
|
in
|
|
let filter_p vec = Array.init np (fun k -> vec.(p_list.(k)))
|
|
and filter_q vec = Array.init nq (fun k -> vec.(q_list.(k)))
|
|
in
|
|
let sp = filter_p sp
|
|
and sq = filter_q sq
|
|
in
|
|
|
|
|
|
(* Compute all integrals in the shell for each pair of significant shell pairs *)
|
|
|
|
begin
|
|
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
|
|
totAngMom shell_c, totAngMom shell_d) with
|
|
| Angular_momentum.(S,S,S,S) ->
|
|
contracted_class.(0) <-
|
|
begin
|
|
try
|
|
let expo_inv_p =
|
|
Vec.init np (fun ab -> sp.(ab-1).ShellPair.expo_inv)
|
|
and expo_inv_q =
|
|
Vec.init nq (fun cd -> sq.(cd-1).ShellPair.expo_inv)
|
|
in
|
|
|
|
let coef =
|
|
let result = Mat.make0 nq np in
|
|
Lacaml.D.ger
|
|
(Vec.of_array @@ filter_q shell_q.ContractedShellPair.coef)
|
|
(Vec.of_array @@ filter_p shell_p.ContractedShellPair.coef)
|
|
result;
|
|
result
|
|
in
|
|
let zm_array = Mat.init_cols np nq (fun i j ->
|
|
try
|
|
if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
|
|
raise NullQuartet;
|
|
|
|
let expo_pq_inv =
|
|
expo_inv_p.{i} +. expo_inv_q.{j}
|
|
in
|
|
let center_pq =
|
|
Coordinate.(sp.(i-1).ShellPair.center |- sq.(j-1).ShellPair.center)
|
|
in
|
|
let norm_pq_sq =
|
|
Coordinate.dot center_pq center_pq
|
|
in
|
|
|
|
let zero_m_array =
|
|
zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
|
|
in
|
|
zero_m_array.(0)
|
|
with NullQuartet -> 0.
|
|
) in
|
|
Mat.gemm_trace zm_array coef
|
|
with (Invalid_argument _) -> 0.
|
|
end
|
|
| _ ->
|
|
|
|
let coef =
|
|
let cp = filter_p shell_p.ContractedShellPair.coef
|
|
and cq = filter_q shell_q.ContractedShellPair.coef
|
|
in
|
|
Array.init np (fun l -> Array.init nq (fun k -> cq.(k) *. cp.(l)) )
|
|
in
|
|
|
|
let expo_inv_p =
|
|
Array.map (fun shell_ab -> shell_ab.ShellPair.expo_inv) sp
|
|
and expo_inv_q =
|
|
Array.map (fun shell_cd -> shell_cd.ShellPair.expo_inv) sq
|
|
in
|
|
|
|
let expo_b =
|
|
Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
|
|
and expo_d =
|
|
Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
|
|
in
|
|
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
|
|
|
|
let center_pq =
|
|
Array.init 3 (fun xyz ->
|
|
Array.init np (fun ab ->
|
|
let shell_ab = sp.(ab) in
|
|
Array.init nq (fun cd ->
|
|
let shell_cd = sq.(cd)
|
|
in
|
|
let cpq =
|
|
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
|
|
in
|
|
match xyz with
|
|
| 0 -> Coordinate.x cpq;
|
|
| 1 -> Coordinate.y cpq;
|
|
| 2 -> Coordinate.z cpq;
|
|
| _ -> assert false
|
|
)
|
|
)
|
|
)
|
|
in
|
|
let zero_m_array =
|
|
let result =
|
|
Array.init (maxm+1) (fun _ ->
|
|
Array.init np (fun _ -> Array.make nq 0. ) )
|
|
in
|
|
let empty = Array.make (maxm+1) 0. in
|
|
Array.iteri (fun ab shell_ab ->
|
|
let zero_m_array_tmp =
|
|
Array.mapi (fun cd shell_cd ->
|
|
if (abs_float coef.(ab).(cd) < cutoff) then
|
|
empty
|
|
else
|
|
let expo_pq_inv =
|
|
expo_inv_p.(ab) +. expo_inv_q.(cd)
|
|
in
|
|
let norm_pq_sq =
|
|
center_pq.(0).(ab).(cd) *. center_pq.(0).(ab).(cd) +.
|
|
center_pq.(1).(ab).(cd) *. center_pq.(1).(ab).(cd) +.
|
|
center_pq.(2).(ab).(cd) *. center_pq.(2).(ab).(cd)
|
|
in
|
|
|
|
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
|
|
) sq
|
|
in
|
|
(* Transpose result *)
|
|
for m=0 to maxm do
|
|
for cd=0 to nq-1 do
|
|
result.(m).(ab).(cd) <- zero_m_array_tmp.(cd).(m) *. coef.(ab).(cd)
|
|
done
|
|
done
|
|
) sp;
|
|
result
|
|
in
|
|
|
|
let norm =
|
|
let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
|
|
Array.map (fun v1 ->
|
|
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
|
|
) norm_coef_scale_p
|
|
|> Array.to_list
|
|
|> Array.concat
|
|
in
|
|
|
|
let map_1d = Array.init (maxm+1) (fun _ -> Zmap.create (4*maxm))
|
|
and map_2d = Array.init (maxm+1) (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
|
|
let integral =
|
|
hvrr_two_e_vector (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)
|
|
(expo_b, expo_d)
|
|
(expo_inv_p, expo_inv_q)
|
|
(shell_p.ContractedShellPair.center_ab,
|
|
shell_q.ContractedShellPair.center_ab, center_pq)
|
|
map_1d map_2d np nq
|
|
in
|
|
contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i)
|
|
) class_indices
|
|
|
|
end;
|
|
|
|
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 = ContractedShellPair.create ~cutoff shell_a shell_b
|
|
and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
|
|
in
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
|