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QCaml/Basis/TwoElectronRR.ml

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OCaml
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open Util
module Am = AngularMomentum
module Asp = AtomicShellPair
module Aspc = AtomicShellPairCouple
module Co = Coordinate
module Cs = ContractedShell
module Csp = ContractedShellPair
module Cspc = ContractedShellPairCouple
module Po = Powers
module Psp = PrimitiveShellPair
module Pspc = PrimitiveShellPairCouple
module Ps = PrimitiveShell
module Zp = Zero_m_parameters
let cutoff = Constants.integrals_cutoff
let cutoff2 = cutoff *. cutoff
exception NullQuartet
type four_idx_intermediates =
{
expo_b : float ;
expo_d : float ;
expo_p_inv : float ;
expo_q_inv : float ;
center_ab : Co.t ;
center_cd : Co.t ;
center_pq : Co.t ;
center_pa : Co.t ;
center_qc : Co.t ;
zero_m_array : float array ;
}
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let rec hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
abcd 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
let abcd = {
expo_b = abcd.expo_d ;
expo_d = abcd.expo_b ;
expo_p_inv = abcd.expo_q_inv ;
expo_q_inv = abcd.expo_p_inv ;
center_ab = abcd.center_cd ;
center_cd = abcd.center_ab ;
center_pq = Co.neg abcd.center_pq ;
center_pa = abcd.center_qc ;
center_qc = abcd.center_pa ;
zero_m_array = abcd.zero_m_array ;
} in
hvrr_two_e
angMom_c angMom_d angMom_a angMom_b
abcd 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
let expo_p_inv = abcd.expo_p_inv
and expo_q_inv = abcd.expo_q_inv
and center_ab = abcd.center_ab
and center_cd = abcd.center_cd
and center_pq = abcd.center_pq
in
(** Vertical recurrence relations *)
let rec vrr0 angMom_a =
match angMom_a.Po.tot with
| 0 -> abcd.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_p_inv *. Co.get xyz center_pq
and f2 = abcd.expo_b *. expo_p_inv *. 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_p_inv *. 0.5 in
Array.iteri (fun m _ ->
result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)
+. f3 *. (v3.(m) +. expo_p_inv *. 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 abcd.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 =
-. abcd.expo_d *. expo_q_inv *. Co.get xyz center_cd
and f2 =
expo_q_inv *. 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_p_inv *. expo_q_inv *. 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_q_inv *. 0.5
in
if (abs_float f3 > cutoff) ||
(abs_float (f3 *. expo_q_inv) > 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_q_inv *. 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 abcd.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_q_inv /. expo_p_inv 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_q_inv 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_q_inv 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_pair_couple ~zero_m shell_pair_couple : float Zmap.t =
let maxm = Am.to_int (Cspc.ang_mom shell_pair_couple) in
(* Pre-computation of integral class indices *)
let class_indices = Cspc.zkey_array shell_pair_couple in
let contracted_class =
Array.make (Array.length class_indices) 0.;
in
let monocentric =
Cspc.monocentric shell_pair_couple
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
let shell_p = Cspc.shell_pair_p shell_pair_couple
and shell_q = Cspc.shell_pair_q shell_pair_couple
in
let center_ab = Csp.a_minus_b shell_p
and center_cd = Csp.a_minus_b shell_q
in
let norm_scales = Cspc.norm_scales shell_pair_couple in
List.iter (fun (coef_prod, spc) ->
let sp_ab = Pspc.shell_pair_p spc
and sp_cd = Pspc.shell_pair_q spc
in
let expo_p_inv = Psp.exponent_inv sp_ab
in
let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in
let center_pa = Psp.center_minus_a sp_ab in
let center_qc = Psp.center_minus_a sp_cd in
let norm_pq_sq = Co.dot center_pq center_pq in
let expo_q_inv = Psp.exponent_inv sp_cd in
let normalization = Psp.normalization sp_ab *. Psp.normalization sp_cd in
let zero_m_array =
zero_m Zp.{
maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ;
center_pq ; center_pa ; center_qc ; normalization ;
}
in
begin
match Cspc.ang_mom shell_pair_couple with
| Am.S ->
let integral = zero_m_array.(0) in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
| _ ->
let expo_b = Ps.exponent (Psp.shell_b sp_ab)
and expo_d = Ps.exponent (Psp.shell_b sp_cd)
in
let map_1d = Zmap.create (4*maxm)
and map_2d = Zmap.create (Array.length class_indices)
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 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;
let norm = norm_scales.(i) in
let coef_prod = coef_prod *. norm in
let abcd = {
expo_b ; expo_d ; expo_p_inv ; expo_q_inv ;
center_ab ; center_cd ; center_pq ;
center_pa ; center_qc ; zero_m_array ;
} in
let integral =
hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
abcd map_1d map_2d
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
with NullQuartet -> ()
)
end
) (Cspc.coefs_and_shell_pair_couples shell_pair_couple);
let result =
Zmap.create (Array.length contracted_class)
in
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
result
let contracted_class_atomic_shell_pair_couple ~zero_m atomic_shell_pair_couple : float Zmap.t =
let maxm = Am.to_int (Aspc.ang_mom atomic_shell_pair_couple) in
(* Pre-computation of integral class indices *)
let class_indices = Aspc.zkey_array atomic_shell_pair_couple in
let contracted_class =
Array.make (Array.length class_indices) 0.;
in
let monocentric =
Aspc.monocentric atomic_shell_pair_couple
in
let shell_p = Aspc.atomic_shell_pair_p atomic_shell_pair_couple
and shell_q = Aspc.atomic_shell_pair_q atomic_shell_pair_couple
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
let center_ab = Asp.a_minus_b shell_p
and center_cd = Asp.a_minus_b shell_q
in
let norm_scales = Aspc.norm_scales atomic_shell_pair_couple in
List.iter (fun cspc ->
List.iter (fun (coef_prod, spc) ->
let sp_ab = Pspc.shell_pair_p spc
and sp_cd = Pspc.shell_pair_q spc
in
let expo_p_inv = Psp.exponent_inv sp_ab
in
let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in
let center_qc = Psp.center_minus_a sp_cd in
let center_pa = Psp.center_minus_a sp_ab in
let norm_pq_sq = Co.dot center_pq center_pq in
let expo_q_inv = Psp.exponent_inv sp_cd in
let normalization = Psp.normalization sp_ab *. Psp.normalization sp_cd in
let zero_m_array =
zero_m Zp.{
maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ;
center_pq ; center_pa ; center_qc ; normalization ;
}
in
begin
match Aspc.ang_mom atomic_shell_pair_couple with
| Am.S ->
let integral = zero_m_array.(0) in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
| _ ->
let expo_b = Ps.exponent (Psp.shell_b sp_ab)
and expo_d = Ps.exponent (Psp.shell_b sp_cd)
in
let map_1d = Zmap.create (4*maxm)
and map_2d = Zmap.create (Array.length class_indices)
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 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;
let norm = norm_scales.(i) in
let coef_prod = coef_prod *. norm in
let abcd = {
expo_b ; expo_d ; expo_p_inv ; expo_q_inv ;
center_ab ; center_cd ; center_pq ;
center_pa ; center_qc ; zero_m_array ;
} in
let integral =
hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
abcd
map_1d map_2d
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
with NullQuartet -> ()
)
end
) (Cspc.coefs_and_shell_pair_couples cspc)
) (Aspc.contracted_shell_pair_couples atomic_shell_pair_couple);
let result =
Zmap.create (Array.length contracted_class)
in
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
result
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