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QCaml/Basis/TwoElectronRR.ml

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OCaml
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open Util
open Constants
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)
(totAngMom_a_in, totAngMom_b_in, totAngMom_c_in, totAngMom_d_in)
(maxm, zero_m_array)
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq)
map_1d map_2d map_1d' map_2d'
=
let maxsze = maxm+1 in
let totAngMom_a = Angular_momentum.to_int totAngMom_a_in
and totAngMom_b = Angular_momentum.to_int totAngMom_b_in
and totAngMom_c = Angular_momentum.to_int totAngMom_c_in
and totAngMom_d = Angular_momentum.to_int totAngMom_d_in
in
(* Swap electrons 1 and 2 so that the max angular momentum is on 1 *)
if (totAngMom_a+totAngMom_b < totAngMom_c+totAngMom_d) then
hvrr_two_e (angMom_c, angMom_d, angMom_a, angMom_b)
(totAngMom_c_in, totAngMom_d_in, totAngMom_a_in, totAngMom_b_in)
(maxm, zero_m_array)
(expo_d, expo_b)
(expo_inv_q, expo_inv_p)
(center_cd, center_ab, (Coordinate.neg center_pq) )
map_1d' map_2d' map_1d map_2d
else
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;
let (x,y,z) = angMom_a in Printf.printf "%d %d %d\n" x y z;
let (x,y,z) = angMom_b in Printf.printf "%d %d %d\n" x y z;
let (x,y,z) = angMom_c in Printf.printf "%d %d %d\n" x y z;
let (x,y,z) = angMom_d in Printf.printf "%d %d %d\n" x y z;
Printf.printf "%f %f %f %f\n%f %f %f\n%f %f %f\n%f %f %f\n" expo_b expo_d
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)
end;
(** Vertical recurrence relations *)
let rec vrr0 angMom_a totAngMom_a =
if debug then
begin
let (x,y,z) = angMom_a in
Printf.printf "vrr0: %d : %d %d %d\n" totAngMom_a x y z
end;
match totAngMom_a with
| 0 -> zero_m_array
| _ ->
let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in
try Zmap.find map_1d 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 empty else
let f1 = expo_inv_p *. (Coordinate.coord center_pq xyz)
and f2 = expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
in
let result = Array.create_float maxsze in
if amxyz < 1 then
begin
let v1 =
vrr0 am (totAngMom_a-1)
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 v3 =
vrr0 amm (totAngMom_a-2)
in
let v1 =
vrr0 am (totAngMom_a-1)
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 totAngMom_a totAngMom_c =
if debug then
begin
let angMom_ax, angMom_ay, angMom_az = angMom_a in
let angMom_cx, angMom_cy, angMom_cz = angMom_c in
Printf.printf "vrr : %d %d : %d %d %d %d %d %d\n" totAngMom_a totAngMom_c
angMom_ax angMom_ay angMom_az angMom_cx angMom_cy angMom_cz
end;
match (totAngMom_a, totAngMom_c) with
| (i,0) -> if (i>0) then
vrr0 angMom_a totAngMom_a
(*
OneElectronRR.hvrr_one_e (angMom_a, angMom_b) (totAngMom_a_in, totAngMom_b_in)
(maxm, zero_m_array) (expo_b) (expo_inv_p) (center_ab, center_pq, center_ab)
map_1d
*)
else zero_m_array
| (_,_) ->
let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c) ) in
try Zmap.find map_2d key with
| Not_found ->
let result =
let am, cm, cmm, axyz, cmxyz, xyz =
let angMom_ax, angMom_ay, angMom_az = angMom_a
and angMom_cx, angMom_cy, angMom_cz = angMom_c in
match angMom_c with
| (_,0,0) ->
(angMom_ax-1, angMom_ay, angMom_az),
(angMom_cx-1, angMom_cy, angMom_cz),
(angMom_cx-2, angMom_cy, angMom_cz),
angMom_ax,angMom_cx-1, 0
| (_,_,0) ->
(angMom_ax, angMom_ay-1, angMom_az),
(angMom_cx, angMom_cy-1, angMom_cz),
(angMom_cx, angMom_cy-2, angMom_cz),
angMom_ay,angMom_cy-1, 1
| _ ->
(angMom_ax, angMom_ay, angMom_az-1),
(angMom_cx, angMom_cy, angMom_cz-1),
(angMom_cx, angMom_cy, angMom_cz-2),
angMom_az,angMom_cz-1, 2
in
if cmxyz < 0 then empty
else
let f1 =
-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz)
and f2 =
expo_inv_q *. (Coordinate.coord center_pq xyz)
in
let result = Array.make maxsze 0. in
if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then
begin
let v1 =
vrr angMom_a cm totAngMom_a (totAngMom_c-1)
in
for m=0 to maxm-1 do
result.(m) <- f1 *. v1.(m) -. f2 *. v1.(m+1) ;
done;
result.(maxm) <- f1 *. v1.(maxm) ;
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 =
vrr angMom_a cmm totAngMom_a (totAngMom_c-2)
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 (axyz > 0) && (cmxyz >= 0) then
begin
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 (totAngMom_a-1) (totAngMom_c-1)
in
for m=0 to maxm-1 do
result.(m) <- result.(m) -. f5 *. v5.(m+1)
done
end;
result
in Zmap.add map_2d key result;
result
(** Horizontal recurrence relations *)
and hrr0 angMom_a angMom_b angMom_c
totAngMom_a totAngMom_b totAngMom_c =
if debug then
begin
let angMom_ax, angMom_ay, angMom_az = angMom_a
and angMom_bx, angMom_by, angMom_bz = angMom_b
and angMom_cx, angMom_cy, angMom_cz = angMom_c in
Printf.printf "hrr0: %d %d %d : %d %d %d %d %d %d %d %d %d\n"
totAngMom_a totAngMom_b totAngMom_c
angMom_ax angMom_ay angMom_az
angMom_bx angMom_by angMom_bz
angMom_cx angMom_cy angMom_cz
end;
match totAngMom_b with
| 0 -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
| 1 ->
let angMom_ax, angMom_ay, angMom_az = angMom_a in
let ap, xyz =
match angMom_b with
| (1,_,_) -> (angMom_ax+1,angMom_ay,angMom_az), 0
| (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), 1
| _ -> (angMom_ax,angMom_ay,angMom_az+1), 2
in
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 angMom_ax, angMom_ay, angMom_az = angMom_a
and angMom_bx, angMom_by, angMom_bz = angMom_b in
let bxyz, xyz =
match angMom_b with
| (_,0,0) -> angMom_bx, 0
| (_,_,0) -> angMom_by, 1
| (_,_,_) -> angMom_bz, 2
in
if (bxyz < 1) then 0. else
let ap, bm =
match xyz with
| 0 -> (angMom_ax+1,angMom_ay,angMom_az),(angMom_bx-1,angMom_by,angMom_bz)
| 1 -> (angMom_ax,angMom_ay+1,angMom_az),(angMom_bx,angMom_by-1,angMom_bz)
| _ -> (angMom_ax,angMom_ay,angMom_az+1),(angMom_bx,angMom_by,angMom_bz-1)
in
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
begin
let angMom_ax, angMom_ay, angMom_az = angMom_a in
let angMom_bx, angMom_by, angMom_bz = angMom_b in
let angMom_cx, angMom_cy, angMom_cz = angMom_c in
let angMom_dx, angMom_dy, angMom_dz = angMom_d in
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_ax angMom_ay angMom_az
angMom_bx angMom_by angMom_bz
angMom_cx angMom_cy angMom_cz
angMom_dx angMom_dy angMom_dz
end;
match (totAngMom_b, totAngMom_d) with
| (_,0) -> if (totAngMom_b = 0) then
(vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
else
hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
| (_,_) ->
let (angMom_cx, angMom_cy, angMom_cz) = angMom_c
and (angMom_dx, angMom_dy, angMom_dz) = angMom_d in
let cp, dm, xyz =
match angMom_d with
| (_,0,0) -> (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), 0
| (_,_,0) -> (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), 1
| _ -> (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), 2
in
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.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
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 expo_pq_inv =
shell_p.ContractedShellPair.expo_inv.(ab) +.
shell_q.ContractedShellPair.expo_inv.(cd)
in
let center_pq =
Coordinate.(sp.(ab).ShellPair.center |- sq.(cd).ShellPair.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.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 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
let () =
if debug then (
if monocentric then
Printf.printf "Mono-centric\n"
else
Printf.printf "Multi-centric\n"
)
in
(* Compute the integral class from the primitive shell quartet *)
class_indices
|> Array.iteri (fun i key ->
let (angMomA,angMomB,angMomC,angMomD) =
match Zkey.to_int_tuple ~kind:Zkey.Kind_12 key with
| Zkey.Twelve x -> x
| _ -> assert false
in
try
if monocentric then
begin
let ax,ay,az = angMomA
and bx,by,bz = angMomB
and cx,cy,cz = angMomC
and dx,dy,dz = angMomD
in
if ( ((1 land ax+bx+cx+dx)=1) ||
((1 land ay+by+cy+dy)=1) ||
((1 land az+bz+cz+dz)=1)
) then
raise NullQuartet
end;
(* 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 coef_prod = coef_prod *. norm in
let integral =
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.ContractedShellPair.expo_inv.(ab),
shell_q.ContractedShellPair.expo_inv.(cd) )
(sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq)
map_1d map_2d 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
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