mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-08-28 23:42:00 +02:00
439 lines
14 KiB
OCaml
439 lines
14 KiB
OCaml
open Util
|
|
open Constants
|
|
|
|
module Am = Angular_momentum
|
|
module Co = Coordinate
|
|
module Cs = Contracted_shell
|
|
module Csp = ContractedShellPair
|
|
module Sp = ShellPair
|
|
module Po = Powers
|
|
|
|
let debug=false
|
|
|
|
let cutoff2 = cutoff *. cutoff
|
|
|
|
exception NullQuartet
|
|
|
|
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
|
|
let rec hvrr_two_e
|
|
angMom_a angMom_b angMom_c angMom_d
|
|
zero_m_array
|
|
expo_b expo_d
|
|
expo_inv_p expo_inv_q
|
|
center_ab center_cd center_pq
|
|
center_pa center_qc
|
|
map_1d map_2d =
|
|
|
|
(* Swap electrons 1 and 2 so that the max angular momentum is on 1 *)
|
|
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
|
|
zero_m_array
|
|
expo_d expo_b
|
|
expo_inv_q expo_inv_p
|
|
center_cd center_ab (Co.neg center_pq)
|
|
center_qc center_pa
|
|
map_1d map_2d
|
|
|
|
else
|
|
|
|
let maxm = angMom_a.Po.tot + angMom_b.Po.tot + angMom_c.Po.tot + angMom_d.Po.tot in
|
|
let maxsze = maxm+1 in
|
|
|
|
|
|
let get_xyz angMom =
|
|
match angMom with
|
|
| { Po.y=0 ; z=0 ; _ } -> Co.X
|
|
| { z=0 ; _ } -> Co.Y
|
|
| _ -> Co.Z
|
|
in
|
|
|
|
|
|
(** Vertical recurrence relations *)
|
|
let rec vrr0 angMom_a =
|
|
|
|
match angMom_a.Po.tot with
|
|
| 0 -> zero_m_array
|
|
| _ ->
|
|
let key = Zkey.of_powers_three angMom_a in
|
|
|
|
try Zmap.find map_1d key with
|
|
| Not_found ->
|
|
let result =
|
|
let xyz = get_xyz angMom_a in
|
|
let am = Po.decr xyz angMom_a in
|
|
let amxyz = Po.get xyz am in
|
|
|
|
let f1 = expo_inv_p *. Co.get xyz center_pq
|
|
and f2 = expo_b *. expo_inv_p *. Co.get xyz center_ab
|
|
in
|
|
let result = Array.create_float (maxsze - angMom_a.Po.tot) in
|
|
if amxyz = 0 then
|
|
begin
|
|
let v1 = vrr0 am in
|
|
Array.iteri (fun m _ ->
|
|
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)) result
|
|
end
|
|
else
|
|
begin
|
|
let amm = Po.decr xyz am in
|
|
let v3 = vrr0 amm in
|
|
let v1 = vrr0 am in
|
|
let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
|
|
Array.iteri (fun m _ ->
|
|
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)
|
|
+. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1)) ) result
|
|
end;
|
|
result
|
|
in Zmap.add map_1d key result;
|
|
result
|
|
|
|
|
|
and vrr angMom_a angMom_c =
|
|
|
|
match angMom_a.Po.tot, angMom_c.Po.tot with
|
|
| (i,0) -> if (i>0) then vrr0 angMom_a
|
|
else zero_m_array
|
|
| (_,_) ->
|
|
let key = Zkey.of_powers_six angMom_a angMom_c in
|
|
|
|
try Zmap.find map_2d key with
|
|
| Not_found ->
|
|
let result =
|
|
(* angMom_c.Po.tot > 0 so cm.Po.tot >= 0 *)
|
|
let xyz = get_xyz angMom_c in
|
|
let cm = Po.decr xyz angMom_c in
|
|
let cmxyz = Po.get xyz cm in
|
|
let axyz = Po.get xyz angMom_a in
|
|
|
|
let f1 =
|
|
-. expo_d *. expo_inv_q *. Co.get xyz center_cd
|
|
and f2 =
|
|
expo_inv_q *. Co.get xyz center_pq
|
|
in
|
|
let result = Array.make (maxsze - angMom_a.Po.tot - angMom_c.Po.tot) 0. in
|
|
if axyz > 0 then
|
|
begin
|
|
let am = Po.decr xyz angMom_a in
|
|
let f5 =
|
|
(float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5
|
|
in
|
|
if (abs_float f5 > cutoff) then
|
|
let v5 =
|
|
vrr am cm
|
|
in
|
|
Array.iteri (fun m _ ->
|
|
result.(m) <- result.(m) -. f5 *. v5.(m+1)) result
|
|
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
|
|
begin
|
|
let v3 =
|
|
let cmm = Po.decr xyz cm in
|
|
vrr angMom_a cmm
|
|
in
|
|
Array.iteri (fun m _ ->
|
|
result.(m) <- result.(m) +.
|
|
f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1)) ) result
|
|
end
|
|
end;
|
|
if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then
|
|
begin
|
|
let v1 =
|
|
vrr angMom_a cm
|
|
in
|
|
Array.iteri (fun m _ ->
|
|
result.(m) <- result.(m) +. f1 *. v1.(m) -. f2 *. v1.(m+1) ) result
|
|
end;
|
|
result
|
|
in Zmap.add map_2d key result;
|
|
result
|
|
|
|
(*
|
|
and trr angMom_a angMom_c =
|
|
|
|
match (angMom_a.Po.tot, angMom_c.Po.tot) with
|
|
| (i,0) -> if (i>0) then (vrr0 angMom_a).(0)
|
|
else zero_m_array.(0)
|
|
| (_,_) ->
|
|
let key = Zkey.of_powers_six angMom_a angMom_c in
|
|
|
|
try (Zmap.find map_2d key).(0) with
|
|
| Not_found ->
|
|
let result =
|
|
let xyz = get_xyz angMom_c in
|
|
let axyz = Po.get xyz angMom_a in
|
|
let cm = Po.decr xyz angMom_c in
|
|
let cmxyz = Po.get xyz cm in
|
|
|
|
let expo_inv_q_over_p = expo_inv_q /. expo_inv_p in
|
|
let f =
|
|
Co.get xyz center_qc +. expo_inv_q_over_p *.
|
|
Co.get xyz center_pa
|
|
in
|
|
let result = 0. in
|
|
|
|
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
|
|
let cmm = Po.decr xyz cm in
|
|
let v3 = trr angMom_a cmm in
|
|
result +. f *. v3
|
|
in
|
|
let result =
|
|
if abs_float f < cutoff then result else
|
|
let v1 = trr angMom_a cm in
|
|
result +. f *. v1
|
|
in
|
|
let result =
|
|
if cmxyz < 0 then result else
|
|
let f = -. expo_inv_q_over_p in
|
|
let ap = Po.incr xyz angMom_a in
|
|
let v4 = trr ap cm in
|
|
result +. v4 *. f
|
|
in
|
|
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
|
|
let am = Po.decr xyz angMom_a in
|
|
let v2 = trr am cm in
|
|
result +. f *. v2
|
|
in
|
|
result
|
|
in
|
|
Zmap.add map_2d key [|result|];
|
|
result
|
|
|
|
*)
|
|
in
|
|
|
|
|
|
let vrr a c =
|
|
(vrr a c).(0)
|
|
(*
|
|
if maxm < 10 then (vrr a c).(0) else trr a c
|
|
*)
|
|
in
|
|
|
|
|
|
(** Horizontal recurrence relations *)
|
|
let rec hrr0 angMom_a angMom_b angMom_c =
|
|
|
|
match angMom_b.Po.tot with
|
|
| 1 ->
|
|
let xyz = get_xyz angMom_b in
|
|
let ap = Po.incr xyz angMom_a in
|
|
let v1 = vrr ap angMom_c in
|
|
let f2 = Co.get xyz center_ab in
|
|
if (abs_float f2 < cutoff) then v1 else
|
|
let v2 = vrr angMom_a angMom_c in
|
|
v1 +. f2 *. v2
|
|
| 0 -> vrr angMom_a angMom_c
|
|
| _ ->
|
|
let xyz = get_xyz angMom_b in
|
|
let bxyz = Po.get xyz angMom_b in
|
|
if bxyz > 0 then
|
|
let ap = Po.incr xyz angMom_a in
|
|
let bm = Po.decr xyz angMom_b in
|
|
let h1 = hrr0 ap bm angMom_c in
|
|
let f2 = Co.get xyz center_ab in
|
|
if abs_float f2 < cutoff then h1 else
|
|
let h2 = hrr0 angMom_a bm angMom_c in
|
|
h1 +. f2 *. h2
|
|
else 0.
|
|
|
|
|
|
and hrr angMom_a angMom_b angMom_c angMom_d =
|
|
|
|
match (angMom_b.Po.tot, angMom_d.Po.tot) with
|
|
| (_,0) ->
|
|
if (angMom_b.Po.tot = 0) then
|
|
vrr angMom_a angMom_c
|
|
else
|
|
hrr0 angMom_a angMom_b angMom_c
|
|
| (_,_) ->
|
|
let xyz = get_xyz angMom_d in
|
|
let cp = Po.incr xyz angMom_c in
|
|
let dm = Po.decr xyz angMom_d in
|
|
let h1 = hrr angMom_a angMom_b cp dm in
|
|
let f2 = Co.get xyz center_cd in
|
|
if abs_float f2 < cutoff then h1 else
|
|
let h2 = hrr angMom_a angMom_b angMom_c dm in
|
|
h1 +. f2 *. h2
|
|
|
|
in
|
|
hrr angMom_a angMom_b angMom_c angMom_d
|
|
|
|
|
|
|
|
|
|
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
|
|
|
|
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
|
|
in
|
|
let maxm = shell_p.Csp.totAngMomInt + shell_q.Csp.totAngMomInt in
|
|
|
|
(* Pre-computation of integral class indices *)
|
|
let class_indices =
|
|
Am.zkey_array (Am.Quartet
|
|
(shell_a.totAngMom, shell_b.totAngMom,
|
|
shell_c.totAngMom, shell_d.totAngMom ))
|
|
in
|
|
|
|
let contracted_class =
|
|
Array.make (Array.length class_indices) 0.;
|
|
in
|
|
|
|
let monocentric =
|
|
shell_p.Csp.monocentric &&
|
|
shell_q.Csp.monocentric &&
|
|
shell_p.Csp.shell_a.Cs.center =
|
|
shell_q.Csp.shell_a.Cs.center
|
|
in
|
|
|
|
(* Compute all integrals in the shell for each pair of significant shell pairs *)
|
|
|
|
let norm_coef_scale_p = shell_p.Csp.norm_coef_scale in
|
|
let norm_coef_scale_q = shell_q.Csp.norm_coef_scale in
|
|
for ab=0 to (Array.length sp - 1) do
|
|
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
|
|
let coef_prod =
|
|
cab *. shell_q.Csp.coef.(cd)
|
|
in
|
|
(** Screening on the product of coefficients *)
|
|
try
|
|
if (abs_float coef_prod) < 1.e-3 *. cutoff then
|
|
raise NullQuartet;
|
|
|
|
let center_pq =
|
|
Co.(sp.(ab).Sp.center |- sq.(cd).Sp.center)
|
|
in
|
|
let norm_pq_sq =
|
|
Co.dot center_pq center_pq
|
|
in
|
|
|
|
let expo_pq_inv =
|
|
shell_p.Csp.expo_inv.(ab) +.
|
|
shell_q.Csp.expo_inv.(cd)
|
|
in
|
|
|
|
let zero_m_array =
|
|
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
|
|
in
|
|
begin
|
|
match (shell_a.totAngMom, shell_b.totAngMom,
|
|
shell_c.totAngMom, shell_d.totAngMom) with
|
|
| Am.(S,S,S,S) ->
|
|
let integral =
|
|
zero_m_array.(0)
|
|
in
|
|
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
|
|
| _ ->
|
|
let d = shell_q.Csp.shell_pairs.(cd).Sp.j in
|
|
let map_1d = Zmap.create (4*maxm) in
|
|
let map_2d = Zmap.create (Array.length class_indices) in
|
|
let norm_coef_scale =
|
|
Array.to_list norm_coef_scale_p
|
|
|> List.map (fun v1 ->
|
|
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q)
|
|
|> Array.concat
|
|
in
|
|
|
|
(* Compute the integral class from the primitive shell quartet *)
|
|
class_indices
|
|
|> Array.iteri (fun i key ->
|
|
let (angMom_a,angMom_b,angMom_c,angMom_d) =
|
|
match Zkey.to_powers ~kind:Zkey.Kind_12 key with
|
|
| Zkey.Twelve x -> x
|
|
| _ -> assert false
|
|
in
|
|
try
|
|
if monocentric then
|
|
begin
|
|
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)
|
|
) then
|
|
raise NullQuartet
|
|
end;
|
|
|
|
(* Schwartz screening *)
|
|
(*
|
|
if (maxm > 8) then
|
|
(
|
|
let schwartz_p =
|
|
let key =
|
|
Zkey.of_powers_twelve angMom_a angMom_b angMom_a angMom_b
|
|
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_powers_twelve angMom_c angMom_d angMom_c angMom_d
|
|
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
|
|
angMom_a angMom_b angMom_c angMom_d
|
|
zero_m_array
|
|
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
|
|
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 = Csp.create ~cutoff shell_a shell_b
|
|
and shell_q = Csp.create ~cutoff shell_c shell_d
|
|
in
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
|
|
|