mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-08-30 00:03:42 +02:00
445 lines
15 KiB
OCaml
445 lines
15 KiB
OCaml
open Util
|
|
open Constants
|
|
open Powers
|
|
open Coordinate
|
|
|
|
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.tot + angMom_b.tot < angMom_c.tot + angMom_d.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, (Coordinate.neg center_pq) )
|
|
(center_qc, center_pa)
|
|
map_1d map_2d
|
|
|
|
else
|
|
|
|
let maxm = angMom_a.tot + angMom_b.tot + angMom_c.tot + angMom_d.tot in
|
|
let maxsze = maxm+1 in
|
|
|
|
|
|
let get_xyz angMom =
|
|
match angMom with
|
|
| { y=0 ; z=0 ; _ } -> X
|
|
| { z=0 ; _ } -> Y
|
|
| _ -> Z
|
|
in
|
|
|
|
|
|
(** Vertical recurrence relations *)
|
|
let rec vrr0 angMom_a =
|
|
|
|
match angMom_a.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 = Powers.decr xyz angMom_a in
|
|
let amxyz = Powers.get xyz am in
|
|
|
|
let f1 = expo_inv_p *. (Coordinate.get xyz center_pq)
|
|
and f2 = expo_b *. expo_inv_p *. (Coordinate.get xyz center_ab)
|
|
in
|
|
let result = Array.create_float maxsze in
|
|
if amxyz = 0 then
|
|
begin
|
|
let v1 =
|
|
vrr0 am
|
|
in
|
|
for m=0 to maxm-1 do
|
|
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)
|
|
done;
|
|
result.(maxm) <- -. f2 *. v1.(maxm)
|
|
end
|
|
else
|
|
begin
|
|
let amm = Powers.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
|
|
for m=0 to maxm-1 do
|
|
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)
|
|
+. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1))
|
|
done;
|
|
result.(maxm) <- f3 *. v3.(maxm)
|
|
end;
|
|
result
|
|
in Zmap.add map_1d key result;
|
|
result
|
|
|
|
|
|
and vrr angMom_a angMom_c =
|
|
|
|
match angMom_a.tot, angMom_c.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.tot > 0 so cm.tot >= 0 *)
|
|
let xyz = get_xyz angMom_c in
|
|
let cm = Powers.decr xyz angMom_c in
|
|
let cmxyz = Powers.get xyz cm in
|
|
let axyz = Powers.get xyz angMom_a in
|
|
|
|
let f1 =
|
|
-. expo_d *. expo_inv_q *. (Coordinate.get xyz center_cd)
|
|
and f2 =
|
|
expo_inv_q *. (Coordinate.get xyz center_pq)
|
|
in
|
|
let result = Array.make maxsze 0. in
|
|
if axyz > 0 then
|
|
begin
|
|
let am = Powers.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
|
|
for m=0 to maxm-1 do
|
|
result.(m) <- result.(m) -. f5 *. v5.(m+1)
|
|
done
|
|
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 = Powers.decr xyz cm in
|
|
vrr angMom_a cmm
|
|
in
|
|
for m=0 to maxm-1 do
|
|
result.(m) <- result.(m) +.
|
|
f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1))
|
|
done;
|
|
result.(maxm) <- result.(maxm) +. f3 *. v3.(maxm)
|
|
end
|
|
end;
|
|
if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then
|
|
begin
|
|
let v1 =
|
|
vrr angMom_a cm
|
|
in
|
|
for m=0 to maxm-1 do
|
|
result.(m) <- result.(m) +. f1 *. v1.(m) -. f2 *. v1.(m+1) ;
|
|
done;
|
|
result.(maxm) <- result.(maxm) +. f1 *. v1.(maxm) ;
|
|
end;
|
|
result
|
|
in Zmap.add map_2d key result;
|
|
result
|
|
|
|
|
|
and trr angMom_a angMom_c =
|
|
|
|
match (angMom_a.tot, angMom_c.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 = Powers.get xyz angMom_a in
|
|
let cm = Powers.decr xyz angMom_c in
|
|
let cmxyz = Powers.get xyz cm in
|
|
|
|
let expo_inv_q_over_p = expo_inv_q /. expo_inv_p in
|
|
let f =
|
|
Coordinate.get xyz center_qc +. expo_inv_q_over_p *.
|
|
(Coordinate.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 = Powers.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 = Powers.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 = Powers.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 =
|
|
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.tot with
|
|
| 1 ->
|
|
let xyz = get_xyz angMom_b in
|
|
let ap = Powers.incr xyz angMom_a in
|
|
let v1 = vrr ap angMom_c in
|
|
let f2 = Coordinate.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 -> trr angMom_a angMom_c
|
|
| _ ->
|
|
let xyz = get_xyz angMom_b in
|
|
let bxyz = Powers.get xyz angMom_b in
|
|
if bxyz > 0 then
|
|
let ap = Powers.incr xyz angMom_a in
|
|
let bm = Powers.decr xyz angMom_b in
|
|
let h1 = hrr0 ap bm angMom_c in
|
|
let f2 = Coordinate.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.tot, angMom_d.tot) with
|
|
| (_,0) ->
|
|
if (angMom_b.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 = Powers.incr xyz angMom_c in
|
|
let dm = Powers.decr xyz angMom_d in
|
|
let h1 = hrr angMom_a angMom_b cp dm in
|
|
let f2 = Coordinate.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.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
|
|
|
|
let monocentric =
|
|
shell_p.ContractedShellPair.monocentric &&
|
|
shell_q.ContractedShellPair.monocentric &&
|
|
Contracted_shell.center shell_p.ContractedShellPair.shell_a =
|
|
Contracted_shell.center shell_q.ContractedShellPair.shell_a
|
|
in
|
|
|
|
(* Compute all integrals in the shell for each pair of significant shell pairs *)
|
|
|
|
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
|
|
let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
|
|
for ab=0 to (Array.length sp - 1) do
|
|
let cab = shell_p.ContractedShellPair.coef.(ab) in
|
|
let b = sp.(ab).ShellPair.j in
|
|
for cd=0 to (Array.length shell_q.ContractedShellPair.shell_pairs - 1) do
|
|
let coef_prod =
|
|
cab *. shell_q.ContractedShellPair.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 =
|
|
sp.(ab).ShellPair.center |- sq.(cd).ShellPair.center
|
|
in
|
|
let norm_pq_sq =
|
|
Coordinate.dot center_pq center_pq
|
|
in
|
|
|
|
let expo_pq_inv =
|
|
shell_p.ContractedShellPair.expo_inv.(ab) +.
|
|
shell_q.ContractedShellPair.expo_inv.(cd)
|
|
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.ContractedShellPair.shell_pairs.(cd).ShellPair.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.x+angMom_b.x+angMom_c.x+angMom_d.x)=1) ||
|
|
((1 land angMom_a.y+angMom_b.y+angMom_c.y+angMom_d.y)=1) ||
|
|
((1 land angMom_a.z+angMom_b.z+angMom_c.z+angMom_d.z)=1)
|
|
) then
|
|
raise NullQuartet
|
|
end;
|
|
|
|
(*
|
|
(* Schwartz screening *)
|
|
if (maxm > 2) then
|
|
(
|
|
let schwartz_p =
|
|
let key = Zkey.of_int_tuple (Zkey.Twelve
|
|
(angMomA, angMomB, angMomA, angMomB) )
|
|
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_tuple (Zkey.Twelve
|
|
(angMomC, angMomD, angMomC, angMomD) )
|
|
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
|
|
(Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d)
|
|
(shell_p.ContractedShellPair.expo_inv.(ab),
|
|
shell_q.ContractedShellPair.expo_inv.(cd) )
|
|
(sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq)
|
|
(sp.(ab).ShellPair.center_a , sq.(cd).ShellPair.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 = 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
|
|
|
|
|