mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-11-19 04:22:21 +01:00
388 lines
16 KiB
OCaml
388 lines
16 KiB
OCaml
open Util
|
|
|
|
let cutoff2 = cutoff *. cutoff
|
|
|
|
exception NullQuartet
|
|
|
|
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
|
|
let hvrr_two_e_vector m (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)
|
|
coef_prod map
|
|
=
|
|
|
|
let ncoef = (Array.length coef_prod) in
|
|
let empty =
|
|
Array.make ncoef 0.
|
|
in
|
|
|
|
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 -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
|
|
| 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
|
|
in
|
|
let f = expo_b *. (Coordinate.coord center_ab i) in
|
|
Array.mapi (fun k c -> c *. expo_inv_p *.
|
|
( (Coordinate.coord center_pq.(k) i) *. zero_m_array.(k).(m+1)
|
|
-. f *. zero_m_array.(k).(m) ) ) coef_prod
|
|
|
|
| totAngMom_a ->
|
|
let key = Zkey.of_int_tuple (Zkey.Three
|
|
(angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
|
|
in
|
|
|
|
let (found, result) =
|
|
try (true, Zmap.find map.(m) key) with
|
|
| Not_found -> (false,
|
|
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
|
|
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
|
|
and xyz =
|
|
match angMom_a with
|
|
| [|0;0;_|] -> 2
|
|
| [|0;_;_|] -> 1
|
|
| _ -> 0
|
|
in
|
|
am.(xyz) <- am.(xyz) - 1;
|
|
amm.(xyz) <- amm.(xyz) - 2;
|
|
if am.(xyz) < 0 then
|
|
empty
|
|
else
|
|
let v1 =
|
|
let f =
|
|
-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
|
|
in
|
|
Array.mapi (fun k v1k -> f *. v1k) (vrr0_v m am (totAngMom_a-1) )
|
|
in
|
|
let p1 =
|
|
|
|
Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p *. (Coordinate.coord center_pq.(k) xyz) *. v2k) (vrr0_v (m+1) am (totAngMom_a-1))
|
|
in
|
|
if amm.(xyz) < 0 then p1 else
|
|
let v1 = vrr0_v m amm (totAngMom_a-2)
|
|
and v2 = vrr0_v (m+1) amm (totAngMom_a-2)
|
|
and f = (float_of_int am.(xyz)) *. expo_inv_p *. 0.5
|
|
in
|
|
Array.mapi (fun k _ -> p1.(k) +.
|
|
f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) coef_prod
|
|
)
|
|
in
|
|
if not found then
|
|
Zmap.add map.(m) key result;
|
|
result
|
|
|
|
and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
|
|
|
|
match (totAngMom_a, totAngMom_c) with
|
|
| (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
|
|
| (_,0) -> vrr0_v m angMom_a totAngMom_a
|
|
| (_,_) ->
|
|
|
|
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
|
|
|
|
let (found, result) =
|
|
try (true, Zmap.find map.(m) key) with
|
|
| Not_found -> (false,
|
|
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;_|] -> 2
|
|
| [|0;_;_|] -> 1
|
|
| _ -> 0
|
|
in
|
|
am.(xyz) <- am.(xyz) - 1;
|
|
cm.(xyz) <- cm.(xyz) - 1;
|
|
cmm.(xyz) <- cmm.(xyz) - 2;
|
|
if cm.(xyz) < 0 then
|
|
empty
|
|
else
|
|
let v1 =
|
|
vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1)
|
|
and v2 =
|
|
vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
|
|
in
|
|
let p1 =
|
|
Array.mapi (fun k _ ->
|
|
-. v1.(k) *. expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz)
|
|
-. v2.(k) *. (expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz))
|
|
) coef_prod
|
|
in
|
|
let p2 =
|
|
if cmm.(xyz) < 0 then p1 else
|
|
let v1 =
|
|
vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
|
|
and v2 =
|
|
vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
|
|
and fcm =
|
|
(float_of_int cm.(xyz)) *. 0.5
|
|
in
|
|
Array.mapi (fun k _ -> p1.(k) +. fcm *. expo_inv_q.(k)
|
|
*. (v1.(k) +. expo_inv_q.(k) *. v2.(k))
|
|
) coef_prod
|
|
in
|
|
if (am.(xyz) < 0) || (cm.(xyz) < 0) then p2 else
|
|
let v =
|
|
vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
|
|
and fa =
|
|
(float_of_int angMom_a.(xyz)) *. expo_inv_p *. 0.5
|
|
in
|
|
Array.mapi (fun k _ ->
|
|
p2.(k) -. fa *. expo_inv_q.(k) *. v.(k)
|
|
) coef_prod
|
|
)
|
|
in
|
|
if not found then
|
|
Zmap.add map.(m) key result;
|
|
result
|
|
|
|
|
|
|
|
|
|
(** Horizontal recurrence relations *)
|
|
and hrr0_v m 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.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
|
|
| (_,0) -> vrr0_v m angMom_a totAngMom_a
|
|
| (_,_) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
|
|
end
|
|
| 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_v m ap angMom_c (totAngMom_a+1) totAngMom_c
|
|
and v2 =
|
|
vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
|
|
and f = Coordinate.coord center_ab xyz
|
|
in
|
|
Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2
|
|
| _ ->
|
|
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;_|] -> 2
|
|
| [|0;_;_|] -> 1
|
|
| _ -> 0
|
|
in
|
|
ap.(xyz) <- ap.(xyz) + 1;
|
|
bm.(xyz) <- bm.(xyz) - 1;
|
|
if (bm.(xyz) < 0) then empty else
|
|
let h1 =
|
|
hrr0_v m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
|
|
and h2 =
|
|
hrr0_v m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
|
|
and f = (Coordinate.coord center_ab xyz)
|
|
in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2
|
|
|
|
and hrr_v m angMom_a angMom_b angMom_c angMom_d
|
|
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
|
|
|
|
match (totAngMom_b, totAngMom_d) with
|
|
| (0,0) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
|
|
| (_,0) -> hrr0_v m 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;_|] -> 2
|
|
| [|0;_;_|] -> 1
|
|
| _ -> 0
|
|
in
|
|
cp.(xyz) <- cp.(xyz) + 1;
|
|
dm.(xyz) <- dm.(xyz) - 1;
|
|
let h1 =
|
|
hrr_v m angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
|
|
and h2 =
|
|
hrr_v m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
|
|
in
|
|
Array.mapi (fun k center_cd -> h1.(k) +. h2.(k) *. (Coordinate.coord center_cd xyz)) center_cd
|
|
in
|
|
hrr_v m 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 *)
|
|
|
|
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) <-
|
|
Array.fold_left
|
|
(fun accu shell_ab -> accu +.
|
|
Array.fold_left (fun accu shell_cd ->
|
|
let coef_prod =
|
|
shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
|
|
in
|
|
(** Screening on the product of coefficients *)
|
|
try
|
|
if (abs_float coef_prod) < 1.e-3*.cutoff then
|
|
raise NullQuartet;
|
|
|
|
let expo_pq_inv =
|
|
shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
|
|
in
|
|
let center_pq =
|
|
Coordinate.(shell_ab.Shell_pair.center |- shell_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
|
|
|
|
accu +. coef_prod *. zero_m_array.(0)
|
|
with NullQuartet -> accu
|
|
) 0. shell_q
|
|
) 0. shell_p
|
|
|
|
| _ ->
|
|
Array.iter (fun shell_ab ->
|
|
let b = shell_ab.Shell_pair.j in
|
|
let common =
|
|
Array.mapi (fun idx shell_cd ->
|
|
let coef_prod =
|
|
shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
|
|
in
|
|
let expo_pq_inv =
|
|
shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
|
|
in
|
|
let center_pq =
|
|
Coordinate.(shell_ab.Shell_pair.center |- shell_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
|
|
|
|
let d = shell_cd.Shell_pair.j in
|
|
|
|
(zero_m_array, shell_cd.Shell_pair.expo_inv,
|
|
Contracted_shell.expo shell_d d, shell_cd.Shell_pair.center_ab,
|
|
center_pq,coef_prod,idx)
|
|
) shell_q
|
|
|> Array.to_list
|
|
|> List.filter (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> abs_float coef_prod >= 1.e-4 *. cutoff)
|
|
|> Array.of_list
|
|
in
|
|
let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> zero_m_array) common
|
|
and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> expo_inv ) common
|
|
and d = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> d) common
|
|
and center_cd = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> center_cd) common
|
|
and center_pq = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> center_pq) common
|
|
and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> coef_prod) common
|
|
and idx = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
|
|
center_pq,coef_prod,idx) -> idx) common
|
|
in
|
|
(* Compute the integral class from the primitive shell quartet *)
|
|
let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
|
|
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 norm =
|
|
Array.map (fun shell_cd ->
|
|
shell_ab.Shell_pair.norm_fun angMomA angMomB *. shell_cd.Shell_pair.norm_fun angMomC angMomD
|
|
) shell_q
|
|
in
|
|
let integral =
|
|
hvrr_two_e_vector 0 (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, d)
|
|
(shell_ab.Shell_pair.expo_inv, expo_inv)
|
|
(shell_ab.Shell_pair.center_ab, center_cd, center_pq)
|
|
coef_prod map
|
|
|> Array.mapi (fun i x -> x *. norm.(idx.(i)) )
|
|
in
|
|
let x = Array.fold_left (+.) 0. integral in
|
|
contracted_class.(i) <- contracted_class.(i) +. x
|
|
) class_indices
|
|
) shell_p
|
|
|
|
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 = Shell_pair.create_array shell_a shell_b
|
|
and shell_q = Shell_pair.create_array shell_c shell_d
|
|
in
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
|