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Preparation of Schwartz screening
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@ -1,10 +1,10 @@
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open Util
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(** Computes all the overlap integrals of the contracted shell pair *)
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let contracted_class shell_a shell_b : float Zmap.t =
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let contracted_class shell_a shell_b : float Zmap.t =
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let shell_p =
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Shell_pair.create_array shell_a shell_b
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Shell_pair.create_array shell_a shell_b
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in
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(* Pre-computation of integral class indices *)
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@ -39,12 +39,6 @@ let create_array ?cutoff p_a p_b =
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Array.init (Contracted_shell.size p_b) (fun j ->
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try
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if Contracted_shell.center p_a = Contracted_shell.center p_b &&
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((Angular_momentum.to_int @@ Contracted_shell.totAngMom p_a) +
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(Angular_momentum.to_int @@ Contracted_shell.totAngMom p_b)) land 1 = 1
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then
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raise Null_contribution;
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let f2 =
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Contracted_shell.norm_coef p_b j
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in
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@ -1,5 +1,8 @@
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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 m (angMom_a, angMom_b, angMom_c, angMom_d)
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@ -20,79 +23,81 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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(** Vertical recurrence relations *)
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let rec vrr m angMom_a angMom_c totAngMom_a totAngMom_c =
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if angMom_a.(0) < 0 || angMom_a.(1) < 0 || angMom_a.(2) < 0
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|| angMom_c.(0) < 0 || angMom_c.(1) < 0 || angMom_c.(2) < 0 then 0.
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else
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> zero_m_array.(m)
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| (_,0) ->
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match (totAngMom_a, totAngMom_c) with
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| (0,0) -> zero_m_array.(m)
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| (_,0) ->
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let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; |]
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|> Zkey.(of_int_array ~kind:Kind_3)
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in
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let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; |]
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|> Zkey.(of_int_array ~kind:Kind_3)
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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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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 0. else
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chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
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(fun () -> vrr m am angMom_c (totAngMom_a-1) totAngMom_c )
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+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
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(fun () -> vrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c )
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+. chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
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(fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c
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+. chop expo_inv_p (fun () ->
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vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) )
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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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+. (if amm.(xyz) < 0 then 0. else
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chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
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(fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c
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+. chop expo_inv_p (fun () ->
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vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) )
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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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| (_,_) ->
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| (_,_) ->
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let key = [| 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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|> Zkey.(of_int_array ~kind:Kind_6)
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in
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let key = [| 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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|> Zkey.(of_int_array ~kind:Kind_6)
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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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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 0. else
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chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
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(fun () -> vrr m angMom_a cm totAngMom_a (totAngMom_c-1) )
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-. chop (expo_inv_q *. (Coordinate.coord center_pq xyz))
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(fun () -> vrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) )
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+. chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
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(fun () -> vrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
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+. chop expo_inv_q
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(fun () -> vrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) )
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-. chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
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(fun () -> vrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) )
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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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+. (if cmm.(xyz) < 0 then 0. else
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chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
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(fun () -> vrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
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+. chop expo_inv_q
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(fun () -> vrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) ) )
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-. (if am.(xyz) lor cm.(xyz) < 0 then 0. else
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chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
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(fun () -> vrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) ))
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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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@ -101,62 +106,60 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
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and hrr 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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if angMom_b.(0) < 0 || angMom_b.(1) < 0 || angMom_b.(2) < 0
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|| angMom_d.(0) < 0 || angMom_d.(1) < 0 || angMom_d.(2) < 0 then 0.
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else
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match (totAngMom_b, totAngMom_d) with
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| (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,_) ->
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match (totAngMom_b, totAngMom_d) with
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| (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,_) ->
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let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1;
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angMom_b.(0)+1; angMom_b.(1)+1; angMom_b.(2)+1;
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angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1;
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angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |]
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|> Zkey.(of_int_array ~kind:Kind_12)
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in
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let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1;
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angMom_b.(0)+1; angMom_b.(1)+1; angMom_b.(2)+1;
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angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1;
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angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |]
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|> Zkey.(of_int_array ~kind:Kind_12)
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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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begin
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match totAngMom_d with
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| 0 ->
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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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hrr m ap bm angMom_c angMom_d (totAngMom_a+1) (totAngMom_b-1)
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totAngMom_c totAngMom_d
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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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begin
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match totAngMom_d with
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| 0 ->
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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 0. else
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hrr m ap bm angMom_c angMom_d
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(totAngMom_a+1) (totAngMom_b-1) totAngMom_c totAngMom_d
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+. chop (Coordinate.coord center_ab xyz) (fun () ->
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hrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
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totAngMom_c totAngMom_d )
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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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hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
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(totAngMom_c+1) (totAngMom_d-1)
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+. chop (Coordinate.coord center_cd xyz) (fun () ->
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hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
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totAngMom_c (totAngMom_d-1) )
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end)
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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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| _ ->
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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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hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
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(totAngMom_c+1) (totAngMom_d-1)
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+. chop (Coordinate.coord center_cd xyz) (fun () ->
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hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
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totAngMom_c (totAngMom_d-1) )
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end)
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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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in
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hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
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@ -185,6 +188,15 @@ let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
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totAngMom shell_c, totAngMom shell_d))
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in
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(*
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(* Precomputation of overlaps *)
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let overlaps_p =
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Overlap.contracted_class shell_a shell_b
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and overlaps_q =
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Overlap.contracted_class shell_c shell_d
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in
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*)
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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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@ -197,66 +209,91 @@ let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
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for cd=0 to (Array.length shell_q - 1)
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do
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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(** Screening on thr product of coefficients *)
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if (abs_float coef_prod) > 1.e-4*.cutoff then
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begin
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try
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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if (abs_float coef_prod) < 1.e-4*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(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 expo_pq_inv =
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shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(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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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) -> Array.iteri (fun i key ->
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let coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
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in
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let integral =
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zero_m_array.(0)
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in
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contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
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) class_indices
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| _ ->
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let d = shell_q.(cd).Shell_pair.j in
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let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
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(* Compute the integral class from the primitive shell quartet *)
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Array.iteri (fun i key ->
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let (angMomA,angMomB,angMomC,angMomD) =
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let a = Zkey.to_int_array Zkey.Kind_12 key in
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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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shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD
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in
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let integral = chop norm (fun () ->
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hvrr_two_e 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)
|
||||
(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
|
||||
) class_indices
|
||||
end
|
||||
let zero_m_array =
|
||||
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
|
||||
in
|
||||
|
||||
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
|
||||
totAngMom shell_c, totAngMom shell_d) with
|
||||
| Angular_momentum.(S,S,S,S) -> Array.iteri (fun i key ->
|
||||
let coef_prod =
|
||||
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
|
||||
in
|
||||
let integral =
|
||||
zero_m_array.(0)
|
||||
in
|
||||
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
|
||||
) class_indices
|
||||
| _ ->
|
||||
let d = shell_q.(cd).Shell_pair.j in
|
||||
let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
|
||||
(* Compute the integral class from the primitive shell quartet *)
|
||||
Array.iteri (fun i key ->
|
||||
let (angMomA,angMomB,angMomC,angMomD) =
|
||||
let a = Zkey.to_int_array Zkey.Kind_12 key in
|
||||
( [| 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 =
|
||||
Zmap.find overlaps_p @@ Zkey.of_int_array ~kind:Zkey.Kind_6
|
||||
[| angMomA.(0) ; angMomA.(1) ; angMomA.(2) ;
|
||||
angMomB.(0) ; angMomB.(1) ; angMomB.(2) |]
|
||||
|> abs_float
|
||||
in
|
||||
let schwartz_q =
|
||||
Zmap.find overlaps_q @@ Zkey.of_int_array ~kind:Zkey.Kind_6
|
||||
[| angMomC.(0) ; angMomC.(1) ; angMomC.(2) ;
|
||||
angMomD.(0) ; angMomD.(1) ; angMomD.(2) |]
|
||||
|> abs_float
|
||||
in
|
||||
if schwartz_p*.schwartz_q = 0. then
|
||||
() ; (*raise NullQuartet; *)
|
||||
*)
|
||||
|
||||
let norm =
|
||||
shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD
|
||||
in
|
||||
let integral = chop norm (fun () ->
|
||||
hvrr_two_e 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, 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
|
||||
(*
|
||||
;if (schwartz_p*.schwartz_q < cutoff2) then Printf.printf "%e %e\n" (schwartz_p*.schwartz_q) integral;
|
||||
*)
|
||||
with NullQuartet -> ()
|
||||
) class_indices
|
||||
with NullQuartet -> ()
|
||||
done
|
||||
done;
|
||||
let result =
|
||||
|
||||
Loading…
Reference in New Issue
Block a user