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Cleaning
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@ -1,5 +1,4 @@
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(** General basis set read from a file *)
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(** General basis set read from a file *)
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type primitive = {
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type primitive = {
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exponent: float ;
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exponent: float ;
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coefficient: float
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coefficient: float
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@ -9,6 +9,12 @@ type t = {
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norm_coef : (int array -> float) array;
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norm_coef : (int array -> float) array;
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}
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}
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let size a = a.size
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let expo a i = a.expo.(i)
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let coef a i = a.coef.(i)
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let center a = a.center
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let totAngMom a = a.totAngMom
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let norm_coef a i = a.norm_coef.(i)
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(** Normalization coefficient of contracted function i, which depends on the
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(** Normalization coefficient of contracted function i, which depends on the
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283
Basis/ERI.ml
Normal file
283
Basis/ERI.ml
Normal file
@ -0,0 +1,283 @@
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open Util
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let cutoff = 1.e-20
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let log_cutoff = -. (log cutoff)
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(** (00|00)^m : Fundamental integral
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$ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
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maxm : Maximum total angular momentum
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expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of $\phi_p$ and $\phi_q$
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norm_pq_sq : square of the distance between the centers of $\phi_p$ and $\phi_q$
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*)
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let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
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let exp_pq =
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1. /. expo_pq_inv
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in
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let t =
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norm_pq_sq *. exp_pq
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in
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boys_function ~maxm t
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|> Array.mapi (fun m fm ->
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two_over_sq_pi *. (if m mod 2 = 0 then fm else -.fm) *.
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(pow exp_pq m) *. (sqrt exp_pq)
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)
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(** In chop f g, evaluate g only if f is non zero, and return f *. (g ()) *)
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let chop f g =
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if (abs_float f) < cutoff then 0.
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else f *. (g ())
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(** Horizontal and Vertical Recurrence Relations (HVRR) *)
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let ghvrr 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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map
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=
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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 gvrr 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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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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chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
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(fun () -> gvrr 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 () -> gvrr (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 () -> gvrr m amm angMom_c (totAngMom_a-2) totAngMom_c
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+. chop expo_inv_p (fun () ->
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gvrr (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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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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chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
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(fun () -> gvrr 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 () -> gvrr (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 () -> gvrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
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+. chop expo_inv_q
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(fun () -> gvrr (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 () -> gvrr (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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(** Horizontal recurrence relations *)
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and ghrr 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) -> gvrr 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 (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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ghrr 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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+. chop (Coordinate.coord center_ab xyz) (fun () ->
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ghrr 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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ghrr 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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ghrr 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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ghrr 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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(** Electron-electron repulsion integral *)
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let erint_contracted_class 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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and 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.Kind_4
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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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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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for ab=0 to (Array.length shell_p - 1)
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do
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let b = shell_p.(ab).Shell_pair.j in
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for cd=0 to (Array.length shell_q - 1)
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do
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let d = shell_q.(cd).Shell_pair.j 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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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 map = Array.init maxm (fun _ -> Zmap.create 129) 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 integral =
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ghvrr 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, Contracted_shell.expo shell_d d)
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(shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv)
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(shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq)
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map
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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 coef_prod =
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shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef *. norm
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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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done
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done;
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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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@ -3,8 +3,8 @@ open Util
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type t = {
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type t = {
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expo : float;
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expo : float;
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expo_inv : float;
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expo_inv : float;
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center_ab: float array;
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center_ab: Coordinate.t;
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center : float array;
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center : Coordinate.t;
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norm_sq : float;
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norm_sq : float;
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norm : float;
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norm : float;
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coef : float;
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coef : float;
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@ -21,83 +21,69 @@ let create_array ?(cutoff=0.) p_a p_b =
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else -. (log cutoff)
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else -. (log cutoff)
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in
|
in
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let x_a = Coordinate.x p_a.Contracted_shell.center
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let center_ab =
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and y_a = Coordinate.y p_a.Contracted_shell.center
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Coordinate.(Contracted_shell.center p_a |- Contracted_shell.center p_b)
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and z_a = Coordinate.z p_a.Contracted_shell.center
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and x_b = Coordinate.x p_b.Contracted_shell.center
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and y_b = Coordinate.y p_b.Contracted_shell.center
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and z_b = Coordinate.z p_b.Contracted_shell.center
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in
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in
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(*
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let norm_sq =
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match p_a.Contracted_shell.center, p_b.Contracted_shell.center with
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Coordinate.dot center_ab center_ab
|
||||||
| [|x_a; y_a; z_a|], [|x_b; y_b; z_b|] ->
|
in
|
||||||
*)
|
Array.init (Contracted_shell.size p_a) (fun i ->
|
||||||
let center_ab =
|
let p_a_expo_center =
|
||||||
Coordinate.(p_a.Contracted_shell.center |- p_b.Contracted_shell.center)
|
Coordinate.(Contracted_shell.expo p_a i |. Contracted_shell.center p_a)
|
||||||
in
|
in
|
||||||
let norm_sq =
|
let f1 =
|
||||||
Coordinate.dot center_ab center_ab
|
Contracted_shell.norm_coef p_a i
|
||||||
in
|
in
|
||||||
Array.init p_a.Contracted_shell.size (fun i ->
|
|
||||||
let p_a_expo_center =
|
|
||||||
[| p_a.Contracted_shell.expo.(i) *. x_a ; p_a.Contracted_shell.expo.(i) *. y_a ; p_a.Contracted_shell.expo.(i) *. z_a |]
|
|
||||||
in
|
|
||||||
|
|
||||||
Array.init p_b.Contracted_shell.size (fun j ->
|
Array.init (Contracted_shell.size p_b) (fun j ->
|
||||||
try
|
try
|
||||||
let f1 =
|
let f2 =
|
||||||
p_a.Contracted_shell.norm_coef.(i)
|
Contracted_shell.norm_coef p_b j
|
||||||
in
|
in
|
||||||
let f2 =
|
let norm_fun a b =
|
||||||
p_b.Contracted_shell.norm_coef.(j)
|
f1 a *. f2 b
|
||||||
in
|
in
|
||||||
let norm_fun a b =
|
let norm =
|
||||||
f1 a *. f2 b
|
norm_fun
|
||||||
in
|
[| Angular_momentum.to_int @@ Contracted_shell.totAngMom p_a ; 0 ; 0 |]
|
||||||
let norm =
|
[| Angular_momentum.to_int @@ Contracted_shell.totAngMom p_b ; 0 ; 0 |]
|
||||||
norm_fun
|
in
|
||||||
[| Angular_momentum.to_int p_a.Contracted_shell.totAngMom ; 0 ; 0 |]
|
if (norm < cutoff) then
|
||||||
[| Angular_momentum.to_int p_b.Contracted_shell.totAngMom ; 0 ; 0 |]
|
raise Null_contribution;
|
||||||
in
|
let p_b_expo_center =
|
||||||
if (norm < cutoff) then
|
Coordinate.(Contracted_shell.expo p_b j |. Contracted_shell.center p_b)
|
||||||
raise Null_contribution;
|
in
|
||||||
let p_b_expo_center =
|
let expo = Contracted_shell.(expo p_a i +. expo p_b j) in
|
||||||
[| p_b.Contracted_shell.expo.(j) *. x_b ; p_b.Contracted_shell.expo.(j) *. y_b ; p_b.Contracted_shell.expo.(j) *. z_b |]
|
let expo_inv = 1. /. expo in
|
||||||
in
|
let center =
|
||||||
let expo = p_a.Contracted_shell.expo.(i) +. p_b.Contracted_shell.expo.(j) in
|
Coordinate.( expo_inv |. (p_a_expo_center |+ p_b_expo_center ) )
|
||||||
let expo_inv = 1. /. expo in
|
in
|
||||||
let center =
|
let argexpo =
|
||||||
[| (p_a_expo_center.(0) +. p_b_expo_center.(0)) *. expo_inv;
|
Contracted_shell.(expo p_a i *. expo p_b j) *. norm_sq *. expo_inv
|
||||||
(p_a_expo_center.(1) +. p_b_expo_center.(1)) *. expo_inv;
|
in
|
||||||
(p_a_expo_center.(2) +. p_b_expo_center.(2)) *. expo_inv |]
|
if (argexpo > log_cutoff) then
|
||||||
in
|
raise Null_contribution;
|
||||||
let argexpo =
|
let g =
|
||||||
p_a.Contracted_shell.expo.(i) *. p_b.Contracted_shell.expo.(j)
|
(pi *. expo_inv)**(1.5) *. exp(-. argexpo)
|
||||||
*. norm_sq *. expo_inv
|
in
|
||||||
in
|
let norm_inv = 1./.norm in
|
||||||
if (argexpo > log_cutoff) then
|
let norm_fun a b =
|
||||||
raise Null_contribution;
|
norm_inv *. norm_fun a b
|
||||||
let g =
|
in
|
||||||
(pi *. expo_inv)**(1.5) *. exp(-. argexpo)
|
let coef =
|
||||||
in
|
norm *. Contracted_shell.(coef p_a i *. coef p_b j) *. g
|
||||||
let norm_inv = 1./.norm in
|
in
|
||||||
let norm_fun a b =
|
if (abs_float coef < cutoff) then
|
||||||
norm_inv *. norm_fun a b
|
raise Null_contribution;
|
||||||
in
|
Some { i ; j ; norm_fun ; norm ; coef ; expo ; expo_inv ; center ; center_ab ; norm_sq }
|
||||||
let coef =
|
with
|
||||||
norm *. p_a.Contracted_shell.coef.(i) *. p_b.Contracted_shell.coef.(j) *. g
|
| Null_contribution -> None
|
||||||
in
|
)
|
||||||
if (abs_float coef < cutoff) then
|
)
|
||||||
raise Null_contribution;
|
|> Array.to_list
|
||||||
Some { i ; j ; norm_fun ; norm ; coef ; expo ; expo_inv ; center ; center_ab=(Coordinate.to_float_array center_ab) ; norm_sq }
|
|> Array.concat
|
||||||
with
|
|> Array.to_list
|
||||||
| Null_contribution -> None
|
|> List.filter (function Some _ -> true | None -> false)
|
||||||
)
|
|> List.map (function Some x -> x | None -> assert false)
|
||||||
)
|
|> Array.of_list
|
||||||
|> Array.to_list
|
|
||||||
|> Array.concat
|
|
||||||
|> Array.to_list
|
|
||||||
|> List.filter (function Some _ -> true | None -> false)
|
|
||||||
|> List.map (function Some x -> x | None -> assert false)
|
|
||||||
|> Array.of_list
|
|
||||||
|
|
||||||
|
|||||||
@ -2,3 +2,8 @@ exception AngularMomentumError of string
|
|||||||
type t = S | P | D | F | G | H | I | J | K | L | M | N | O
|
type t = S | P | D | F | G | H | I | J | K | L | M | N | O
|
||||||
val of_char : char -> t
|
val of_char : char -> t
|
||||||
val to_string : t -> string
|
val to_string : t -> string
|
||||||
|
val to_char : t -> char
|
||||||
|
val to_int : t -> int
|
||||||
|
val of_int : int -> t
|
||||||
|
type kind = Kind_2 of (t * t) | Kind_4 of (t * t * t * t)
|
||||||
|
val zkey_array : kind -> Z.t array
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user