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Anthony Scemama 2018-01-17 19:09:57 +01:00
parent 6437c5503a
commit 97e4a09664
5 changed files with 359 additions and 80 deletions
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1
Basis/Basis.ml
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@ -1,5 +1,4 @@
(** General basis set read from a file *)
type primitive = {
exponent: float ;
coefficient: float

6
Basis/Contracted_shell.ml
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@ -9,6 +9,12 @@ type t = {
norm_coef : (int array -> float) array;
}
let size a = a.size
let expo a i = a.expo.(i)
let coef a i = a.coef.(i)
let center a = a.center
let totAngMom a = a.totAngMom
let norm_coef a i = a.norm_coef.(i)
(** Normalization coefficient of contracted function i, which depends on the

283
Basis/ERI.ml Normal file
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@ -0,0 +1,283 @@
open Util
let cutoff = 1.e-20
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 $
maxm : Maximum total angular momentum
expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of $\phi_p$ and $\phi_q$
norm_pq_sq : square of the distance between the centers of $\phi_p$ and $\phi_q$
*)
let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
let exp_pq =
1. /. expo_pq_inv
in
let t =
norm_pq_sq *. exp_pq
in
boys_function ~maxm t
|> Array.mapi (fun m fm ->
two_over_sq_pi *. (if m mod 2 = 0 then fm else -.fm) *.
(pow exp_pq m) *. (sqrt exp_pq)
)
(** 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 *)
let erint_contracted_class 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, Contracted_shell.totAngMom shell_b,
Contracted_shell.totAngMom shell_c, Contracted_shell.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

50
Basis/Shell_pair.ml
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@ -3,8 +3,8 @@ open Util
type t = {
expo : float;
expo_inv : float;
center_ab: float array;
center : float array;
center_ab: Coordinate.t;
center : Coordinate.t;
norm_sq : float;
norm : float;
coef : float;
@ -21,59 +21,45 @@ let create_array ?(cutoff=0.) p_a p_b =
else -. (log cutoff)
in
let x_a = Coordinate.x p_a.Contracted_shell.center
and y_a = Coordinate.y p_a.Contracted_shell.center
and z_a = Coordinate.z p_a.Contracted_shell.center
and x_b = Coordinate.x p_b.Contracted_shell.center
and y_b = Coordinate.y p_b.Contracted_shell.center
and z_b = Coordinate.z p_b.Contracted_shell.center
in
(*
match p_a.Contracted_shell.center, p_b.Contracted_shell.center with
| [|x_a; y_a; z_a|], [|x_b; y_b; z_b|] ->
*)
let center_ab =
Coordinate.(p_a.Contracted_shell.center |- p_b.Contracted_shell.center)
Coordinate.(Contracted_shell.center p_a |- Contracted_shell.center p_b)
in
let norm_sq =
Coordinate.dot center_ab center_ab
in
Array.init p_a.Contracted_shell.size (fun i ->
Array.init (Contracted_shell.size p_a) (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 |]
Coordinate.(Contracted_shell.expo p_a i |. Contracted_shell.center p_a)
in
let f1 =
Contracted_shell.norm_coef p_a i
in
Array.init p_b.Contracted_shell.size (fun j ->
Array.init (Contracted_shell.size p_b) (fun j ->
try
let f1 =
p_a.Contracted_shell.norm_coef.(i)
in
let f2 =
p_b.Contracted_shell.norm_coef.(j)
Contracted_shell.norm_coef p_b j
in
let norm_fun a b =
f1 a *. f2 b
in
let norm =
norm_fun
[| Angular_momentum.to_int p_a.Contracted_shell.totAngMom ; 0 ; 0 |]
[| Angular_momentum.to_int p_b.Contracted_shell.totAngMom ; 0 ; 0 |]
[| Angular_momentum.to_int @@ Contracted_shell.totAngMom p_a ; 0 ; 0 |]
[| Angular_momentum.to_int @@ Contracted_shell.totAngMom p_b ; 0 ; 0 |]
in
if (norm < cutoff) then
raise Null_contribution;
let p_b_expo_center =
[| p_b.Contracted_shell.expo.(j) *. x_b ; p_b.Contracted_shell.expo.(j) *. y_b ; p_b.Contracted_shell.expo.(j) *. z_b |]
Coordinate.(Contracted_shell.expo p_b j |. Contracted_shell.center p_b)
in
let expo = p_a.Contracted_shell.expo.(i) +. p_b.Contracted_shell.expo.(j) in
let expo = Contracted_shell.(expo p_a i +. expo p_b j) in
let expo_inv = 1. /. expo in
let center =
[| (p_a_expo_center.(0) +. p_b_expo_center.(0)) *. expo_inv;
(p_a_expo_center.(1) +. p_b_expo_center.(1)) *. expo_inv;
(p_a_expo_center.(2) +. p_b_expo_center.(2)) *. expo_inv |]
Coordinate.( expo_inv |. (p_a_expo_center |+ p_b_expo_center ) )
in
let argexpo =
p_a.Contracted_shell.expo.(i) *. p_b.Contracted_shell.expo.(j)
*. norm_sq *. expo_inv
Contracted_shell.(expo p_a i *. expo p_b j) *. norm_sq *. expo_inv
in
if (argexpo > log_cutoff) then
raise Null_contribution;
@ -85,11 +71,11 @@ let create_array ?(cutoff=0.) p_a p_b =
norm_inv *. norm_fun a b
in
let coef =
norm *. p_a.Contracted_shell.coef.(i) *. p_b.Contracted_shell.coef.(j) *. g
norm *. Contracted_shell.(coef p_a i *. coef p_b j) *. g
in
if (abs_float coef < cutoff) then
raise Null_contribution;
Some { i ; j ; norm_fun ; norm ; coef ; expo ; expo_inv ; center ; center_ab=(Coordinate.to_float_array center_ab) ; norm_sq }
Some { i ; j ; norm_fun ; norm ; coef ; expo ; expo_inv ; center ; center_ab ; norm_sq }
with
| Null_contribution -> None
)

5
Utils/Angular_momentum.mli
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@ -2,3 +2,8 @@ exception AngularMomentumError of string
type t = S | P | D | F | G | H | I | J | K | L | M | N | O
val of_char : char -> t
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