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QCaml/Basis/TwoElectronRR.ml

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OCaml
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open Util
let cutoff2 = cutoff *. cutoff
let debug = false
exception NullQuartet
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_two_e (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
=
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
let maxm = totAngMom_a + totAngMom_b + totAngMom_c + totAngMom_d in
let empty = Array.make (maxm+1) 0.
in
if debug then begin
Printf.printf "\n---- %d %d %d %d ----\n" totAngMom_a totAngMom_b totAngMom_c totAngMom_d;
Printf.printf "%d %d %d\n" angMom_a.(0) angMom_a.(1) angMom_a.(2) ;
Printf.printf "%d %d %d\n" angMom_b.(0) angMom_b.(1) angMom_b.(2) ;
Printf.printf "%d %d %d\n" angMom_c.(0) angMom_c.(1) angMom_c.(2) ;
Printf.printf "%d %d %d\n" angMom_d.(0) angMom_d.(1) angMom_d.(2) ;
Printf.printf "%f %f %f %f\n%f %f %f\n%f %f %f\n%f %f %f\n" expo_b expo_d
end
expo_inv_p expo_inv_q
(Coordinate.coord center_ab 0) (Coordinate.coord center_ab 1) (Coordinate.coord center_ab 2)
(Coordinate.coord center_cd 0) (Coordinate.coord center_cd 1) (Coordinate.coord center_cd 2)
(Coordinate.coord center_pq 0) (Coordinate.coord center_pq 1) (Coordinate.coord center_pq 2);
(** Vertical recurrence relations *)
let rec vrr0 angMom_a totAngMom_a =
if debug then
Printf.printf "vrr0: %d : %d %d %d\n" totAngMom_a angMom_a.(0) angMom_a.(1) angMom_a.(2);
match totAngMom_a with
| 0 -> zero_m_array
| _ ->
let maxsze = maxm+1 in
let key = Zkey.of_int_tuple (Zkey.Three
(angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
in
try Zmap.find map key with
| Not_found ->
let result =
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
in
let xyz =
match angMom_a with
| [|_;0;0|] -> 0
| [|_;_;0|] -> 1
| _ -> 2
in
am.(xyz) <- am.(xyz) - 1;
amm.(xyz) <- amm.(xyz) - 2;
if am.(xyz) < 0 then empty else
let v1 =
vrr0 am (totAngMom_a-1)
in
let f1 = expo_inv_p *. (Coordinate.coord center_pq xyz)
and f2 = expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
in
if amm.(xyz) < 0 then
Array.init (maxsze) (fun m ->
if m = maxm then 0. else (f1 *. v1.(m+1) ) -. f2 *. v1.(m) )
else
let f3 = (float_of_int am.(xyz)) *. expo_inv_p *. 0.5 in
let v3 =
vrr0 amm (totAngMom_a-2)
in
Array.init (maxsze) (fun m ->
(if m = maxm then 0. else (f1 *. v1.(m+1) ) -. f2 *. v1.(m) )
+. f3 *. (v3.(m) +. if m = maxm then 0. else
expo_inv_p *. v3.(m+1))
)
in Zmap.add map key result;
result
and vrr angMom_a angMom_c totAngMom_a totAngMom_c =
if debug then
Printf.printf "vrr : %d %d : %d %d %d %d %d %d\n" totAngMom_a totAngMom_c angMom_a.(0) angMom_a.(1) angMom_a.(2) angMom_c.(0) angMom_c.(1) angMom_c.(2);
match (totAngMom_a, totAngMom_c) with
| (0,0) -> zero_m_array
| (_,0) -> vrr0 angMom_a totAngMom_a
| (_,_) ->
let maxsze = maxm+1 in
let key = Zkey.of_int_tuple (Zkey.Six
((angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1),
(angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1)) )
in
try Zmap.find map key with
| Not_found ->
let result =
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and xyz =
match angMom_c with
| [|_;0;0|] -> 0
| [|_;_;0|] -> 1
| _ -> 2
in
am.(xyz) <- am.(xyz) - 1;
cm.(xyz) <- cm.(xyz) - 1;
cmm.(xyz) <- cmm.(xyz) - 2;
if cm.(xyz) < 0 then empty else
let f1 =
-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz)
in
let f2 =
expo_inv_q *. (Coordinate.coord center_pq xyz)
in
let result =
if ( (abs_float f1 < cutoff) && (abs_float f2 < cutoff) ) then empty else
let v1 =
vrr angMom_a cm totAngMom_a (totAngMom_c-1)
in
Array.init (maxsze) (fun m ->
f1 *. v1.(m) -. (if m = maxm then 0. else f2 *. v1.(m+1)) )
in
let result =
if cmm.(xyz) < 0 then result else
let f3 =
(float_of_int cm.(xyz)) *. expo_inv_q *. 0.5
in
if (abs_float f3 < cutoff) && (abs_float (f3 *. expo_inv_q) < cutoff) then result else
let v3 =
vrr angMom_a cmm totAngMom_a (totAngMom_c-2)
in
Array.init (maxsze) (fun m -> result.(m) +.
f3 *. (v3.(m) +. (if m=maxm then 0. else expo_inv_q *. v3.(m+1)) ))
in
let result =
if am.(xyz) lor cm.(xyz) < 0 then result else
let f5 =
(float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5
in
if (abs_float f5 < cutoff) then result else
let v5 =
vrr am cm (totAngMom_a-1) (totAngMom_c-1)
in
Array.init (maxsze) (fun m ->
result.(m) -. (if m = maxm then 0. else f5 *. v5.(m+1)))
in
result
in Zmap.add map key result;
result
(** Horizontal recurrence relations *)
and hrr0 angMom_a angMom_b angMom_c
totAngMom_a totAngMom_b totAngMom_c =
if debug then
Printf.printf "hrr0: %d %d %d : %d %d %d %d %d %d %d %d %d\n" totAngMom_a totAngMom_b totAngMom_c 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);
match totAngMom_b with
| 0 -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
| 1 ->
let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
ap.(xyz) <- ap.(xyz) + 1;
let v1 =
vrr ap angMom_c (totAngMom_a+1) totAngMom_c
in
let f2 =
(Coordinate.coord center_ab xyz)
in
if (abs_float f2 < cutoff) then v1.(0) else
let v2 =
vrr angMom_a angMom_c totAngMom_a totAngMom_c
in
v1.(0) +. f2 *. v2.(0)
| _ ->
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz =
match angMom_b with
| [|_;0;0|] -> 0
| [|_;_;0|] -> 1
| _ -> 2
in
ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1;
if (bm.(xyz) < 0) then 0. else
let h1 =
hrr0 ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
in
let f2 =
(Coordinate.coord center_ab xyz)
in
if (abs_float f2 < cutoff) then h1 else
let h2 =
hrr0 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
in
h1 +. f2 *. h2
and hrr angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
if debug then
Printf.printf "hrr : %d %d %d %d : %d %d %d %d %d %d %d %d %d %d %d %d\n" totAngMom_a totAngMom_b totAngMom_c totAngMom_d 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);
match (totAngMom_b, totAngMom_d) with
| (0,0) -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
| (_,0) -> hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
| (_,_) ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
and xyz =
match angMom_d with
| [|_;0;0|] -> 0
| [|_;_;0|] -> 1
| _ -> 2
in
cp.(xyz) <- cp.(xyz) + 1;
dm.(xyz) <- dm.(xyz) - 1;
let h1 =
hrr angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
in
let f2 = Coordinate.coord center_cd xyz in
if (abs_float f2 < cutoff) then h1 else
let h2 =
hrr angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
in
h1 +. f2 *. h2
in
hrr angMom_a angMom_b angMom_c angMom_d 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.(0).Shell_pair.shell_a
and shell_b = shell_p.(0).Shell_pair.shell_b
and shell_c = shell_q.(0).Shell_pair.shell_a
and shell_d = shell_q.(0).Shell_pair.shell_b
in
let maxm =
let open Angular_momentum in
(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
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
(* Compute all integrals in the shell for each pair of significant shell pairs *)
for ab=0 to (Array.length shell_p - 1) do
let cab = shell_p.(ab).Shell_pair.coef in
let b = shell_p.(ab).Shell_pair.j in
let norm_coef_scale_p = shell_p.(ab).Shell_pair.norm_coef_scale in
for cd=0 to (Array.length shell_q - 1) do
let coef_prod =
cab *. shell_q.(cd).Shell_pair.coef
in
(** Screening on the product of coefficients *)
try
if (abs_float coef_prod) < 1.e-4*.cutoff then
raise NullQuartet;
let expo_pq_inv =
shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
in
let center_pq =
Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
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.(cd).Shell_pair.j in
let map = Zmap.create (Array.length class_indices) in
let norm_coef_scale_q = shell_q.(cd).Shell_pair.norm_coef_scale in
let norm_coef_scale =
Array.map (fun v1 ->
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
) norm_coef_scale_p
|> Array.to_list
|> Array.concat
in
(* Compute the integral class from the primitive shell quartet *)
class_indices
|> 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
try
(* Schwartz screening *)
(*
let schwartz_p =
let key =
Zkey.of_int_array Zkey.Kind_12
[| a.(0) ; a.(1) ; a.(2) ;
a.(3) ; a.(4) ; a.(5) ;
a.(0) ; a.(1) ; a.(2) ;
a.(3) ; a.(4) ; a.(5) |]
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_array Zkey.Kind_12
[| a.(6) ; a.(7) ; a.(8) ;
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 integral = chop norm (fun () ->
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 )
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
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