mirror of https://gitlab.com/scemama/QCaml.git
397 lines
16 KiB
OCaml
397 lines
16 KiB
OCaml
open Util
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let cutoff2 = cutoff *. cutoff
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exception NullQuartet
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(** Horizontal and Vertical Recurrence Relations (HVRR) *)
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let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
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(maxm, zero_m_array)
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(expo_b, expo_d)
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(expo_inv_p, expo_inv_q)
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(center_ab, center_cd, center_pq)
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coef_prod map
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=
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let ncoef = (Array.length coef_prod) in
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let empty =
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Array.make ncoef 0.
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in
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let totAngMom_a = Angular_momentum.to_int totAngMom_a
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and totAngMom_b = Angular_momentum.to_int totAngMom_b
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and totAngMom_c = Angular_momentum.to_int totAngMom_c
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and totAngMom_d = Angular_momentum.to_int totAngMom_d
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in
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(** Vertical recurrence relations *)
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let rec vrr0_v m angMom_a = function
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| 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
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in
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let f = expo_b *. (Coordinate.coord center_ab i) in
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Array.mapi (fun k c -> c *. expo_inv_p *.
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( (Coordinate.coord center_pq.(k) i) *. zero_m_array.(k).(m+1)
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-. f *. zero_m_array.(k).(m) ) ) coef_prod
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| 0 -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
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| totAngMom_a ->
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let key = Zkey.of_int_tuple (Zkey.Three
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(angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
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in
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let (found, result) =
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try (true, Zmap.find map.(m) key) with
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| Not_found -> (false,
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let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and xyz =
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match angMom_a with
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| [|0;0;_|] -> 2
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| [|0;_;_|] -> 1
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| _ -> 0
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in
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am.(xyz) <- am.(xyz) - 1;
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amm.(xyz) <- amm.(xyz) - 2;
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if am.(xyz) < 0 then empty else
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let v1 =
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let f =
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-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
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in
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if (abs_float f < cutoff) then empty else
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Array.mapi (fun k v1k -> f *. v1k) (vrr0_v m am (totAngMom_a-1) )
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in
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let p1 =
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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))
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in
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if amm.(xyz) < 0 then p1 else
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let f = (float_of_int am.(xyz)) *. expo_inv_p *. 0.5
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in
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if (abs_float f < cutoff) then empty else
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let v1 = vrr0_v m amm (totAngMom_a-2)
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and v2 = vrr0_v (m+1) amm (totAngMom_a-2)
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in
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Array.mapi (fun k _ -> p1.(k) +.
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f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) coef_prod
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)
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in
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if not found then
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Zmap.add map.(m) key result;
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result
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and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
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| (_,0) -> vrr0_v m angMom_a totAngMom_a
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| (_,_) ->
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let key = Zkey.of_int_tuple (Zkey.Six
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((angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1),
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(angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1)) )
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in
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let (found, result) =
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try (true, Zmap.find map.(m) key) with
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| Not_found -> (false,
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let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
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and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
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and xyz =
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match angMom_c with
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| [|0;0;_|] -> 2
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| [|0;_;_|] -> 1
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| _ -> 0
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in
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am.(xyz) <- am.(xyz) - 1;
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cm.(xyz) <- cm.(xyz) - 1;
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cmm.(xyz) <- cmm.(xyz) - 2;
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if cm.(xyz) < 0 then
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empty
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else
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let v1 =
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vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1)
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and v2 =
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vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
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in
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let p1 =
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Array.mapi (fun k _ ->
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-. v1.(k) *. expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz)
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-. v2.(k) *. (expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz))
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) coef_prod
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in
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let p2 =
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if cmm.(xyz) < 0 then p1 else
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let v1 =
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vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
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and v2 =
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vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
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and fcm =
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(float_of_int cm.(xyz)) *. 0.5
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in
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Array.mapi (fun k _ -> p1.(k) +. fcm *. expo_inv_q.(k)
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*. (v1.(k) +. expo_inv_q.(k) *. v2.(k))
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) coef_prod
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in
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if (am.(xyz) < 0) || (cm.(xyz) < 0) then p2 else
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let fa =
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(float_of_int angMom_a.(xyz)) *. expo_inv_p *. 0.5
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in
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(*
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if (abs_float fa < cutoff) then empty else
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*)
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let v =
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vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
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in
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Array.mapi (fun k _ ->
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p2.(k) -. fa *. expo_inv_q.(k) *. v.(k)
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) coef_prod
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)
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in
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if not found then
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Zmap.add map.(m) key result;
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result
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(** Horizontal recurrence relations *)
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and hrr0_v m angMom_a angMom_b angMom_c
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totAngMom_a totAngMom_b totAngMom_c =
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match totAngMom_b with
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| 0 ->
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begin
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
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| (_,0) -> vrr0_v m angMom_a totAngMom_a
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| (_,_) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
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end
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| 1 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
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let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
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ap.(xyz) <- ap.(xyz) + 1;
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let f = Coordinate.coord center_ab xyz in
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let v1 =
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vrr_v m ap angMom_c (totAngMom_a+1) totAngMom_c
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in
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if (abs_float f < cutoff) then v1 else
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let v2 =
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vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
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in
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Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2
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| _ ->
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let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
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and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
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and xyz =
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match angMom_b with
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| [|0;0;_|] -> 2
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| [|0;_;_|] -> 1
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| _ -> 0
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in
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ap.(xyz) <- ap.(xyz) + 1;
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bm.(xyz) <- bm.(xyz) - 1;
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if (bm.(xyz) < 0) then empty else
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let h1 =
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hrr0_v m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
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in
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let f = (Coordinate.coord center_ab xyz) in
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if (abs_float f < cutoff) then h1 else
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let h2 =
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hrr0_v m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
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in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2
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and hrr_v m angMom_a angMom_b angMom_c angMom_d
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
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match (totAngMom_b, totAngMom_d) with
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| (0,0) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,0) -> hrr0_v m angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
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and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
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and xyz =
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match angMom_d with
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| [|0;0;_|] -> 2
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| [|0;_;_|] -> 1
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| _ -> 0
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in
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cp.(xyz) <- cp.(xyz) + 1;
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dm.(xyz) <- dm.(xyz) - 1;
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let h1 =
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hrr_v m angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
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and h2 =
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hrr_v m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
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in
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Array.mapi (fun k center_cd -> h1.(k) +. h2.(k) *. (Coordinate.coord center_cd xyz)) center_cd
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in
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hrr_v m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
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totAngMom_c totAngMom_d
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let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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let shell_a = shell_p.(0).Shell_pair.shell_a
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and shell_b = shell_p.(0).Shell_pair.shell_b
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and shell_c = shell_q.(0).Shell_pair.shell_a
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and shell_d = shell_q.(0).Shell_pair.shell_b
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in
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let maxm =
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let open Angular_momentum in
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(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
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+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
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in
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(* Pre-computation of integral class indices *)
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let class_indices =
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Angular_momentum.zkey_array
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(Angular_momentum.Quartet
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Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d))
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in
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let contracted_class =
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Array.make (Array.length class_indices) 0.;
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in
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(* Compute all integrals in the shell for each pair of significant shell pairs *)
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begin
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match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d) with
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| Angular_momentum.(S,S,S,S) ->
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contracted_class.(0) <-
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Array.fold_left
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(fun accu shell_ab -> accu +.
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Array.fold_left (fun accu shell_cd ->
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let coef_prod =
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shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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try
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if (abs_float coef_prod) < 1.e-3*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.center)
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in
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let norm_pq_sq =
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Coordinate.dot center_pq center_pq
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in
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let zero_m_array =
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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in
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accu +. coef_prod *. zero_m_array.(0)
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with NullQuartet -> accu
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) 0. shell_q
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) 0. shell_p
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| _ ->
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Array.iter (fun shell_ab ->
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let b = shell_ab.Shell_pair.j in
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let common =
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Array.mapi (fun idx shell_cd ->
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let coef_prod =
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shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
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in
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let expo_pq_inv =
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shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.center)
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in
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let norm_pq_sq =
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Coordinate.dot center_pq center_pq
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in
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let zero_m_array =
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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in
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let d = shell_cd.Shell_pair.j in
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(zero_m_array, shell_cd.Shell_pair.expo_inv,
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Contracted_shell.expo shell_d d, shell_cd.Shell_pair.center_ab,
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center_pq,coef_prod,idx)
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) shell_q
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|> Array.to_list
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|> List.filter (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> abs_float coef_prod >= 1.e-4 *. cutoff)
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|> Array.of_list
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in
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let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> zero_m_array) common
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and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> expo_inv ) common
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and d = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> d) common
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and center_cd = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> center_cd) common
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and center_pq = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> center_pq) common
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and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> coef_prod) common
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and idx = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod,idx) -> idx) common
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in
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(* Compute the integral class from the primitive shell quartet *)
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let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
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Array.iteri (fun i key ->
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let a = Zkey.to_int_array Zkey.Kind_12 key in
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let (angMomA,angMomB,angMomC,angMomD) =
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( [| a.(0) ; a.(1) ; a.(2) |],
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[| a.(3) ; a.(4) ; a.(5) |],
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[| a.(6) ; a.(7) ; a.(8) |],
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[| a.(9) ; a.(10) ; a.(11) |] )
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in
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let norm =
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Array.map (fun shell_cd ->
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shell_ab.Shell_pair.norm_fun angMomA angMomB *. shell_cd.Shell_pair.norm_fun angMomC angMomD
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) shell_q
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in
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let integral =
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hvrr_two_e_vector 0 (angMomA, angMomB, angMomC, angMomD)
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(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
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Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
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(maxm, zero_m_array)
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(Contracted_shell.expo shell_b b, d)
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(shell_ab.Shell_pair.expo_inv, expo_inv)
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(shell_ab.Shell_pair.center_ab, center_cd, center_pq)
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coef_prod map
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|> Array.mapi (fun i x -> x *. norm.(idx.(i)) )
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in
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let x = Array.fold_left (+.) 0. integral in
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contracted_class.(i) <- contracted_class.(i) +. x
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) class_indices
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) shell_p
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end;
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let result =
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Zmap.create (Array.length contracted_class)
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in
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Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
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result
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(** Computes all the two-electron integrals of the contracted shell quartet *)
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let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
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let shell_p = Shell_pair.create_array shell_a shell_b
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and shell_q = Shell_pair.create_array shell_c shell_d
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in
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contracted_class_shell_pairs ~zero_m shell_p shell_q
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