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Preparation of Schwartz screening

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Anthony Scemama 2018-01-23 00:48:45 +01:00
parent 4a4809fc7e
commit a20b22dab7
3 changed files with 207 additions and 176 deletions
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4
Basis/Overlap.ml
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@ -1,10 +1,10 @@
open Util open Util
(** Computes all the overlap integrals of the contracted shell pair *) (** Computes all the overlap integrals of the contracted shell pair *)
let contracted_class shell_a shell_b : float Zmap.t = let contracted_class shell_a shell_b : float Zmap.t =
let shell_p = let shell_p =
Shell_pair.create_array shell_a shell_b Shell_pair.create_array shell_a shell_b
in in
(* Pre-computation of integral class indices *) (* Pre-computation of integral class indices *)

6
Basis/Shell_pair.ml
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@ -39,12 +39,6 @@ let create_array ?cutoff p_a p_b =
Array.init (Contracted_shell.size p_b) (fun j -> Array.init (Contracted_shell.size p_b) (fun j ->
try try
if Contracted_shell.center p_a = Contracted_shell.center p_b &&
((Angular_momentum.to_int @@ Contracted_shell.totAngMom p_a) +
(Angular_momentum.to_int @@ Contracted_shell.totAngMom p_b)) land 1 = 1
then
raise Null_contribution;
let f2 = let f2 =
Contracted_shell.norm_coef p_b j Contracted_shell.norm_coef p_b j
in in

373
Basis/TwoElectronRR.ml
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@ -1,5 +1,8 @@
open Util open Util
let cutoff2 = cutoff *. cutoff
exception NullQuartet
(** Horizontal and Vertical Recurrence Relations (HVRR) *) (** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d) let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
@ -20,79 +23,81 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
(** Vertical recurrence relations *) (** Vertical recurrence relations *)
let rec vrr m angMom_a angMom_c totAngMom_a totAngMom_c = let rec vrr m angMom_a angMom_c totAngMom_a totAngMom_c =
if angMom_a.(0) < 0 || angMom_a.(1) < 0 || angMom_a.(2) < 0 match (totAngMom_a, totAngMom_c) with
|| angMom_c.(0) < 0 || angMom_c.(1) < 0 || angMom_c.(2) < 0 then 0. | (0,0) -> zero_m_array.(m)
else | (_,0) ->
match (totAngMom_a, totAngMom_c) with
| (0,0) -> zero_m_array.(m)
| (_,0) ->
let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; |] let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; |]
|> Zkey.(of_int_array ~kind:Kind_3) |> Zkey.(of_int_array ~kind:Kind_3)
in in
let (found, result) = let (found, result) =
try (true, Zmap.find map.(m) key) with try (true, Zmap.find map.(m) key) with
| Not_found -> (false, | Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and xyz = and xyz =
match angMom_a with match angMom_a with
| [|0;0;_|] -> 2 | [|0;0;_|] -> 2
| [|0;_;_|] -> 1 | [|0;_;_|] -> 1
| _ -> 0 | _ -> 0
in in
am.(xyz) <- am.(xyz) - 1; am.(xyz) <- am.(xyz) - 1;
amm.(xyz) <- amm.(xyz) - 2; amm.(xyz) <- amm.(xyz) - 2;
if am.(xyz) < 0 then 0. else
chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)) chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
(fun () -> vrr m am angMom_c (totAngMom_a-1) totAngMom_c ) (fun () -> vrr m am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz)) +. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
(fun () -> vrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c ) (fun () -> vrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5) +. (if amm.(xyz) < 0 then 0. else
(fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
+. chop expo_inv_p (fun () -> (fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c
vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) +. chop expo_inv_p (fun () ->
in vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) )
if not found then in
Zmap.add map.(m) key result; if not found then
result Zmap.add map.(m) key result;
result
| (_,_) -> | (_,_) ->
let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1;
angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1; |] angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1; |]
|> Zkey.(of_int_array ~kind:Kind_6) |> Zkey.(of_int_array ~kind:Kind_6)
in in
let (found, result) = let (found, result) =
try (true, Zmap.find map.(m) key) with try (true, Zmap.find map.(m) key) with
| Not_found -> (false, | Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and xyz = and xyz =
match angMom_c with match angMom_c with
| [|0;0;_|] -> 2 | [|0;0;_|] -> 2
| [|0;_;_|] -> 1 | [|0;_;_|] -> 1
| _ -> 0 | _ -> 0
in in
am.(xyz) <- am.(xyz) - 1; am.(xyz) <- am.(xyz) - 1;
cm.(xyz) <- cm.(xyz) - 1; cm.(xyz) <- cm.(xyz) - 1;
cmm.(xyz) <- cmm.(xyz) - 2; cmm.(xyz) <- cmm.(xyz) - 2;
if cm.(xyz) < 0 then 0. else
chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) ) chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
(fun () -> vrr m angMom_a cm totAngMom_a (totAngMom_c-1) ) (fun () -> vrr m angMom_a cm totAngMom_a (totAngMom_c-1) )
-. chop (expo_inv_q *. (Coordinate.coord center_pq xyz)) -. chop (expo_inv_q *. (Coordinate.coord center_pq xyz))
(fun () -> vrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) ) (fun () -> vrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) )
+. chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 ) +. (if cmm.(xyz) < 0 then 0. else
(fun () -> vrr m angMom_a cmm totAngMom_a (totAngMom_c-2) chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
+. chop expo_inv_q (fun () -> vrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
(fun () -> vrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) ) +. chop expo_inv_q
-. chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 ) (fun () -> vrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) ) )
(fun () -> vrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) ) -. (if am.(xyz) lor cm.(xyz) < 0 then 0. else
in chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
if not found then (fun () -> vrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) ))
Zmap.add map.(m) key result; in
result if not found then
Zmap.add map.(m) key result;
result
@ -101,62 +106,60 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
and hrr m angMom_a angMom_b angMom_c angMom_d and hrr m angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d = totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
if angMom_b.(0) < 0 || angMom_b.(1) < 0 || angMom_b.(2) < 0 match (totAngMom_b, totAngMom_d) with
|| angMom_d.(0) < 0 || angMom_d.(1) < 0 || angMom_d.(2) < 0 then 0. | (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
else | (_,_) ->
match (totAngMom_b, totAngMom_d) with
| (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
| (_,_) ->
let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1;
angMom_b.(0)+1; angMom_b.(1)+1; angMom_b.(2)+1; angMom_b.(0)+1; angMom_b.(1)+1; angMom_b.(2)+1;
angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1; angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1;
angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |] angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |]
|> Zkey.(of_int_array ~kind:Kind_12) |> Zkey.(of_int_array ~kind:Kind_12)
in in
let (found, result) = let (found, result) =
try (true, Zmap.find map.(m) key) with try (true, Zmap.find map.(m) key) with
| Not_found -> (false, | Not_found -> (false,
begin begin
match totAngMom_d with match totAngMom_d with
| 0 -> | 0 ->
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |] and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz = and xyz =
match angMom_b with match angMom_b with
| [|0;0;_|] -> 2 | [|0;0;_|] -> 2
| [|0;_;_|] -> 1 | [|0;_;_|] -> 1
| _ -> 0 | _ -> 0
in in
ap.(xyz) <- ap.(xyz) + 1; ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1; bm.(xyz) <- bm.(xyz) - 1;
hrr m ap bm angMom_c angMom_d (totAngMom_a+1) (totAngMom_b-1) if (bm.(xyz) < 0) then 0. else
totAngMom_c totAngMom_d hrr m ap bm angMom_c angMom_d
(totAngMom_a+1) (totAngMom_b-1) totAngMom_c totAngMom_d
+. chop (Coordinate.coord center_ab xyz) (fun () -> +. chop (Coordinate.coord center_ab xyz) (fun () ->
hrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1) hrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
totAngMom_c totAngMom_d ) totAngMom_c totAngMom_d )
| _ -> | _ ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |] and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
and xyz = and xyz =
match angMom_d with match angMom_d with
| [|0;0;_|] -> 2 | [|0;0;_|] -> 2
| [|0;_;_|] -> 1 | [|0;_;_|] -> 1
| _ -> 0 | _ -> 0
in in
cp.(xyz) <- cp.(xyz) + 1; cp.(xyz) <- cp.(xyz) + 1;
dm.(xyz) <- dm.(xyz) - 1; dm.(xyz) <- dm.(xyz) - 1;
hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
(totAngMom_c+1) (totAngMom_d-1) (totAngMom_c+1) (totAngMom_d-1)
+. chop (Coordinate.coord center_cd xyz) (fun () -> +. chop (Coordinate.coord center_cd xyz) (fun () ->
hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
totAngMom_c (totAngMom_d-1) ) totAngMom_c (totAngMom_d-1) )
end) end)
in in
if not found then if not found then
Zmap.add map.(m) key result; Zmap.add map.(m) key result;
result result
in in
hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
@ -185,6 +188,15 @@ let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
totAngMom shell_c, totAngMom shell_d)) totAngMom shell_c, totAngMom shell_d))
in in
(*
(* Precomputation of overlaps *)
let overlaps_p =
Overlap.contracted_class shell_a shell_b
and overlaps_q =
Overlap.contracted_class shell_c shell_d
in
*)
let contracted_class = let contracted_class =
Array.make (Array.length class_indices) 0.; Array.make (Array.length class_indices) 0.;
in in
@ -197,66 +209,91 @@ let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
for cd=0 to (Array.length shell_q - 1) for cd=0 to (Array.length shell_q - 1)
do do
let coef_prod = try
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef let coef_prod =
in shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
(** Screening on thr product of coefficients *) in
if (abs_float coef_prod) > 1.e-4*.cutoff then (** Screening on the product of coefficients *)
begin if (abs_float coef_prod) < 1.e-4*.cutoff then
raise NullQuartet;
let expo_pq_inv =
shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
in
let center_pq =
Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
in
let zero_m_array = let expo_pq_inv =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
in in
let center_pq =
Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
in
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b, let zero_m_array =
totAngMom shell_c, totAngMom shell_d) with zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
| Angular_momentum.(S,S,S,S) -> Array.iteri (fun i key -> in
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
in totAngMom shell_c, totAngMom shell_d) with
let integral = | Angular_momentum.(S,S,S,S) -> Array.iteri (fun i key ->
zero_m_array.(0) let coef_prod =
in shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral in
) class_indices let integral =
| _ -> zero_m_array.(0)
let d = shell_q.(cd).Shell_pair.j in in
let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
(* Compute the integral class from the primitive shell quartet *) ) class_indices
Array.iteri (fun i key -> | _ ->
let (angMomA,angMomB,angMomC,angMomD) = let d = shell_q.(cd).Shell_pair.j in
let a = Zkey.to_int_array Zkey.Kind_12 key in let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
( [| a.(0) ; a.(1) ; a.(2) |], (* Compute the integral class from the primitive shell quartet *)
[| a.(3) ; a.(4) ; a.(5) |], Array.iteri (fun i key ->
[| a.(6) ; a.(7) ; a.(8) |], let (angMomA,angMomB,angMomC,angMomD) =
[| a.(9) ; a.(10) ; a.(11) |] ) let a = Zkey.to_int_array Zkey.Kind_12 key in
in ( [| a.(0) ; a.(1) ; a.(2) |],
let norm = [| a.(3) ; a.(4) ; a.(5) |],
shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD [| a.(6) ; a.(7) ; a.(8) |],
in [| a.(9) ; a.(10) ; a.(11) |] )
let integral = chop norm (fun () -> in
hvrr_two_e 0 (angMomA, angMomB, angMomC, angMomD) try
(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b, (*
Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d) (* Schwartz screening *)
(maxm, zero_m_array) let schwartz_p =
(Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d) Zmap.find overlaps_p @@ Zkey.of_int_array ~kind:Zkey.Kind_6
(shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv) [| angMomA.(0) ; angMomA.(1) ; angMomA.(2) ;
(shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq) angMomB.(0) ; angMomB.(1) ; angMomB.(2) |]
map ) |> abs_float
in in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral let schwartz_q =
) class_indices Zmap.find overlaps_q @@ Zkey.of_int_array ~kind:Zkey.Kind_6
end [| 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
done; done;
let result = let result =