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General RR module

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This commit is contained in:
Anthony Scemama 2018-01-18 23:42:48 +01:00
parent e3e16bd5bd
commit 932d5859fe
4 changed files with 266 additions and 259 deletions
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1
Basis/Basis.ml
View File

@ -37,3 +37,4 @@ Momentum X Y Z
|> String.concat line) |> String.concat line)
^ line ^ line

262
Basis/ERI.ml
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@ -1,9 +1,6 @@
open Util open Util
let cutoff = 1.e-20 (** (00|00)^m : Fundamental electron repulsion integral
let log_cutoff = -. (log cutoff)
(** (00|00)^m : Fundamental integral
$ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $ $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
maxm : Maximum total angular momentum maxm : Maximum total angular momentum
@ -24,260 +21,7 @@ let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
) )
(** In chop f g, evaluate g only if f is non zero, and return f *. (g ()) *)
let chop f g =
if (abs_float f) < cutoff then 0.
else f *. (g ())
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let ghvrr m (angMom_a, angMom_b, angMom_c, angMom_d)
(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
(maxm, zero_m_array)
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq)
map
=
let totAngMom_a = Angular_momentum.to_int totAngMom_a
and totAngMom_b = Angular_momentum.to_int totAngMom_b
and totAngMom_c = Angular_momentum.to_int totAngMom_c
and totAngMom_d = Angular_momentum.to_int totAngMom_d
in
(** Vertical recurrence relations *)
let rec gvrr m angMom_a angMom_c totAngMom_a totAngMom_c =
if angMom_a.(0) < 0 || angMom_a.(1) < 0 || angMom_a.(2) < 0
|| angMom_c.(0) < 0 || angMom_c.(1) < 0 || angMom_c.(2) < 0 then 0.
else
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; |]
|> Zkey.(of_int_array ~kind:Kind_3)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and xyz =
match angMom_a with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
am.(xyz) <- am.(xyz) - 1;
amm.(xyz) <- amm.(xyz) - 2;
chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
(fun () -> gvrr m am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
(fun () -> gvrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
(fun () -> gvrr m amm angMom_c (totAngMom_a-2) totAngMom_c
+. chop expo_inv_p (fun () ->
gvrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) )
in
if not found then
Zmap.add map.(m) key result;
result
| (_,_) ->
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; |]
|> Zkey.(of_int_array ~kind:Kind_6)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and xyz =
match angMom_c with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
am.(xyz) <- am.(xyz) - 1;
cm.(xyz) <- cm.(xyz) - 1;
cmm.(xyz) <- cmm.(xyz) - 2;
chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
(fun () -> gvrr m angMom_a cm totAngMom_a (totAngMom_c-1) )
-. chop (expo_inv_q *. (Coordinate.coord center_pq xyz))
(fun () -> gvrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) )
+. chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
(fun () -> gvrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
+. chop expo_inv_q
(fun () -> gvrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) )
-. chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
(fun () -> gvrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) )
in
if not found then
Zmap.add map.(m) key result;
result
(** Horizontal recurrence relations *)
and ghrr m angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
if angMom_b.(0) < 0 || angMom_b.(1) < 0 || angMom_b.(2) < 0
|| angMom_d.(0) < 0 || angMom_d.(1) < 0 || angMom_d.(2) < 0 then 0.
else
match (totAngMom_b, totAngMom_d) with
| (0,0) -> gvrr m angMom_a angMom_c totAngMom_a totAngMom_c
| (_,_) ->
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_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1;
angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |]
|> Zkey.(of_int_array ~kind:Kind_12)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
begin
match totAngMom_d with
| 0 ->
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz =
match angMom_b with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1;
ghrr m ap bm angMom_c angMom_d (totAngMom_a+1) (totAngMom_b-1)
totAngMom_c totAngMom_d
+. chop (Coordinate.coord center_ab xyz) (fun () ->
ghrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
totAngMom_c totAngMom_d )
| _ ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
and xyz =
match angMom_d with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
cp.(xyz) <- cp.(xyz) + 1;
dm.(xyz) <- dm.(xyz) - 1;
ghrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
(totAngMom_c+1) (totAngMom_d-1)
+. chop (Coordinate.coord center_cd xyz) (fun () ->
ghrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
totAngMom_c (totAngMom_d-1) )
end)
in
if not found then
Zmap.add map.(m) key result;
result
in
ghrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
totAngMom_c totAngMom_d
(** Electron-electron repulsion integral *) (** Electron-electron repulsion integral *)
let erint_contracted_class shell_a shell_b shell_c shell_d : float Zmap.t = let contracted_class shell_a shell_b shell_c shell_d : float Zmap.t =
TwoElectronRR.contracted_class ~zero_m shell_a shell_b shell_c shell_d
let shell_p = Shell_pair.create_array shell_a shell_b
and shell_q = Shell_pair.create_array shell_c shell_d
and maxm =
let open Angular_momentum in
(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Kind_4
Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d))
in
let contracted_class =
Array.make (Array.length class_indices) 0.;
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
for ab=0 to (Array.length shell_p - 1)
do
let b = shell_p.(ab).Shell_pair.j in
for cd=0 to (Array.length shell_q - 1)
do
let d = shell_q.(cd).Shell_pair.j in
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 =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
let map = Array.init maxm (fun _ -> Zmap.create 129) 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
let integral =
ghvrr 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
let norm =
shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD
in
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef *. norm
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
) class_indices
done
done;
let result =
Zmap.create (Array.length contracted_class)
in
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
result

260
Basis/TwoElectronRR.ml Normal file
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@ -0,0 +1,260 @@
open Util
(** In chop f g, evaluate g only if f is non zero, and return f *. (g ()) *)
let chop f g =
if (abs_float f) < cutoff then 0.
else f *. (g ())
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let ghvrr m (angMom_a, angMom_b, angMom_c, angMom_d)
(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
(maxm, zero_m_array)
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq)
map
=
let totAngMom_a = Angular_momentum.to_int totAngMom_a
and totAngMom_b = Angular_momentum.to_int totAngMom_b
and totAngMom_c = Angular_momentum.to_int totAngMom_c
and totAngMom_d = Angular_momentum.to_int totAngMom_d
in
(** Vertical recurrence relations *)
let rec gvrr m angMom_a angMom_c totAngMom_a totAngMom_c =
if angMom_a.(0) < 0 || angMom_a.(1) < 0 || angMom_a.(2) < 0
|| angMom_c.(0) < 0 || angMom_c.(1) < 0 || angMom_c.(2) < 0 then 0.
else
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; |]
|> Zkey.(of_int_array ~kind:Kind_3)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and xyz =
match angMom_a with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
am.(xyz) <- am.(xyz) - 1;
amm.(xyz) <- amm.(xyz) - 2;
chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
(fun () -> gvrr m am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
(fun () -> gvrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c )
+. chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
(fun () -> gvrr m amm angMom_c (totAngMom_a-2) totAngMom_c
+. chop expo_inv_p (fun () ->
gvrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) )
in
if not found then
Zmap.add map.(m) key result;
result
| (_,_) ->
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; |]
|> Zkey.(of_int_array ~kind:Kind_6)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and xyz =
match angMom_c with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
am.(xyz) <- am.(xyz) - 1;
cm.(xyz) <- cm.(xyz) - 1;
cmm.(xyz) <- cmm.(xyz) - 2;
chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) )
(fun () -> gvrr m angMom_a cm totAngMom_a (totAngMom_c-1) )
-. chop (expo_inv_q *. (Coordinate.coord center_pq xyz))
(fun () -> gvrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) )
+. chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 )
(fun () -> gvrr m angMom_a cmm totAngMom_a (totAngMom_c-2)
+. chop expo_inv_q
(fun () -> gvrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) )
-. chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 )
(fun () -> gvrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) )
in
if not found then
Zmap.add map.(m) key result;
result
(** Horizontal recurrence relations *)
and ghrr m angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
if angMom_b.(0) < 0 || angMom_b.(1) < 0 || angMom_b.(2) < 0
|| angMom_d.(0) < 0 || angMom_d.(1) < 0 || angMom_d.(2) < 0 then 0.
else
match (totAngMom_b, totAngMom_d) with
| (0,0) -> gvrr m angMom_a angMom_c totAngMom_a totAngMom_c
| (_,_) ->
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_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1;
angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |]
|> Zkey.(of_int_array ~kind:Kind_12)
in
let (found, result) =
try (true, Zmap.find map.(m) key) with
| Not_found -> (false,
begin
match totAngMom_d with
| 0 ->
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz =
match angMom_b with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1;
ghrr m ap bm angMom_c angMom_d (totAngMom_a+1) (totAngMom_b-1)
totAngMom_c totAngMom_d
+. chop (Coordinate.coord center_ab xyz) (fun () ->
ghrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
totAngMom_c totAngMom_d )
| _ ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
and xyz =
match angMom_d with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
cp.(xyz) <- cp.(xyz) + 1;
dm.(xyz) <- dm.(xyz) - 1;
ghrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
(totAngMom_c+1) (totAngMom_d-1)
+. chop (Coordinate.coord center_cd xyz) (fun () ->
ghrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
totAngMom_c (totAngMom_d-1) )
end)
in
if not found then
Zmap.add map.(m) key result;
result
in
ghrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
totAngMom_c totAngMom_d
(** Computes all the two-electron integrals of the contracted shell quartet *)
let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
let shell_p = Shell_pair.create_array shell_a shell_b
and shell_q = Shell_pair.create_array shell_c shell_d
and maxm =
let open Angular_momentum in
(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Kind_4
Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d))
in
let contracted_class =
Array.make (Array.length class_indices) 0.;
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
for ab=0 to (Array.length shell_p - 1)
do
let b = shell_p.(ab).Shell_pair.j in
for cd=0 to (Array.length shell_q - 1)
do
let d = shell_q.(cd).Shell_pair.j in
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 =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
let map = Array.init maxm (fun _ -> Zmap.create 129) 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
let integral =
ghvrr 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
let norm =
shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD
in
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef *. norm
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
) class_indices
done
done;
let result =
Zmap.create (Array.length contracted_class)
in
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
result

2
Utils/Util.ml
View File

@ -1,3 +1,5 @@
let cutoff = 1.e-20
(** Constants *) (** Constants *)
let pi = acos (-1.) let pi = acos (-1.)
let pi_inv = 1. /. pi let pi_inv = 1. /. pi