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Anthony Scemama 2018-02-23 15:49:27 +01:00
parent 738da438ea
commit d7d018b3ea
16 changed files with 446 additions and 508 deletions
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20
Basis/Basis.ml
View File

@ -4,8 +4,8 @@ type t =
contracted_shells : Contracted_shell.t array;
}
let size b = b.size
let contracted_shells b = b.contracted_shells
module Cs = Contracted_shell
module Gb = General_basis
(** Returns an array of the basis set per atom *)
let of_nuclei_and_general_basis n b =
@ -13,27 +13,27 @@ let of_nuclei_and_general_basis n b =
Array.map (fun (e, center) ->
List.assoc e b
|> Array.map (fun (totAngMom, shell) ->
let expo = Array.map (fun General_basis.{exponent ; coefficient} ->
let expo = Array.map (fun Gb.{exponent ; coefficient} ->
exponent) shell
and coef = Array.map (fun General_basis.{exponent ; coefficient} ->
and coef = Array.map (fun Gb.{exponent ; coefficient} ->
coefficient) shell
in
Contracted_shell.make ~expo ~coef ~totAngMom ~center ~index:0)
Cs.make ~expo ~coef ~totAngMom ~center ~index:0)
) n
|> Array.to_list
|> Array.concat
in
Array.iteri (fun i x ->
if (i > 0) then
result.(i) <- Contracted_shell.with_index x (
(Contracted_shell.index result.(i-1)) +
(Array.length (Contracted_shell.powers result.(i-1))))
result.(i) <- Cs.with_index x (
result.(i-1).index +
(Array.length result.(i-1).powers ))
) result ;
let size =
let n = ref 0 in
for i=0 to (Array.length result) - 1 do
n := !n + (Array.length (Contracted_shell.powers (result.(i))))
n := !n + (Array.length (result.(i).powers ))
done; !n
in
{ contracted_shells = result ; size }
@ -56,7 +56,7 @@ let to_string b =
"
^
( Array.map (fun i ->
Contracted_shell.to_string i) b
Cs.to_string i) b
|> Array.to_list
|> String.concat line
)

13
Basis/Basis.mli
View File

@ -1,10 +1,11 @@
type t
type t = private
{
(** Number of contracted Gaussians *)
size : int;
(** Number of contracted Gaussians *)
val size : t -> int
(** Array of contracted shells *)
val contracted_shells : t -> Contracted_shell.t array
(** Array of contracted shells *)
contracted_shells : Contracted_shell.t array;
}
(** Returns an array of the basis set per atom *)

79
Basis/ContractedShellPair.ml
View File

@ -18,6 +18,11 @@ type t =
}
module Am = Angular_momentum
module Co = Coordinate
module Cs = Contracted_shell
module Sp = ShellPair
(** Creates an contracted shell pair : an array of pairs of primitive shells.
A contracted shell with N functions combined with a contracted
shell with M functions generates a NxM array of shell pairs.
@ -29,16 +34,15 @@ let create ?cutoff p_a p_b =
| Some cutoff -> cutoff, -. (log cutoff)
in
let center_ab = Coordinate.(
Contracted_shell.center p_a |- Contracted_shell.center p_b )
let center_ab = Co.( p_a.Cs.center |- p_b.Cs.center )
in
let norm_sq =
Coordinate.dot center_ab center_ab
Co.dot center_ab center_ab
in
let norm_coef_scale_a =
Contracted_shell.norm_coef_scale p_a
p_a.norm_coef_scale
and norm_coef_scale_b =
Contracted_shell.norm_coef_scale p_b
p_b.norm_coef_scale
in
let norm_coef_scale =
Array.map (fun v1 ->
@ -48,56 +52,53 @@ let create ?cutoff p_a p_b =
|> Array.concat
in
let shell_pairs =
Array.init (Contracted_shell.size p_a) (fun i ->
let p_a_expo_center = Coordinate.(
Contracted_shell.expo p_a i |. Contracted_shell.center p_a )
in
let norm_coef_a =
Contracted_shell.norm_coef p_a i
in
Array.init p_a.size (fun i ->
let p_a_expo_center = Co.(p_a.Cs.expo.(i) |. p_a.Cs.center) in
let norm_coef_a = p_a.norm_coef.(i) in
Array.init (Contracted_shell.size p_b) (fun j ->
Array.init p_b.size (fun j ->
try
let norm_coef_b =
Contracted_shell.norm_coef p_b j
let norm_coef_b = p_b.norm_coef.(j) in
let norm_coef = norm_coef_a *. norm_coef_b
in
let norm_coef =
norm_coef_a *. norm_coef_b
in
if (norm_coef < cutoff) then
if norm_coef < cutoff then
raise Null_contribution;
let p_b_expo_center = Coordinate.(
Contracted_shell.expo p_b j |. Contracted_shell.center p_b )
in
let expo = Contracted_shell.(expo p_a i +. expo p_b j) in
let p_b_expo_center = Co.(p_b.expo.(j) |. p_b.center) in
let expo = p_a.expo.(i) +. p_b.expo.(j) in
let expo_inv = 1. /. expo in
let center = Coordinate.(
expo_inv |. (p_a_expo_center |+ p_b_expo_center ) )
let center = Co.(expo_inv |. (p_a_expo_center |+ p_b_expo_center ) )
in
let argexpo =
Contracted_shell.(expo p_a i *. expo p_b j) *. norm_sq *. expo_inv
p_a.Cs.expo.(i) *. p_b.Cs.expo.(j) *. norm_sq *. expo_inv
in
if (argexpo > log_cutoff) then
raise Null_contribution;
let g =
(pi *. expo_inv)**(1.5) *. exp(-. argexpo)
(pi *. expo_inv)**(1.5) *. exp (-. argexpo)
in
let coef =
norm_coef *. Contracted_shell.(coef p_a i *. coef p_b j) *. g
norm_coef *. p_a.coef.(i) *. p_b.coef.(j) *. g
in
if (abs_float coef < cutoff) then
if abs_float coef < cutoff then
raise Null_contribution;
let center_a =
Coordinate.(center |- Contracted_shell.center p_a)
Co.(center |- p_a.center)
in
let monocentric =
Contracted_shell.center p_a = Contracted_shell.center p_b
p_a.center = p_b.center
in
let totAngMomInt =
(Angular_momentum.to_int (Contracted_shell.totAngMom p_a))
+ (Angular_momentum.to_int (Contracted_shell.totAngMom p_b))
Am.to_int p_a.totAngMom +
Am.to_int p_b.totAngMom
in
Some ShellPair.{ i ; j ; shell_a=p_a ; shell_b=p_b ; norm_coef ; coef ; expo ; expo_inv ; center ; center_a ; center_ab ; norm_sq ; monocentric ; totAngMomInt}
Some {
Sp.i ; j ;
shell_a=p_a ; shell_b=p_b ;
norm_coef ; coef ;
expo ; expo_inv ;
center ; center_a ; center_ab ;
norm_sq ; monocentric ; totAngMomInt
}
with
| Null_contribution -> None
)
@ -109,15 +110,15 @@ let create ?cutoff p_a p_b =
|> List.map (function Some x -> x | None -> assert false)
|> Array.of_list
in
let coef = Array.map (fun x -> (fun y -> y.ShellPair.coef) x) shell_pairs
and expo_inv = Array.map (fun x -> (fun y -> y.ShellPair.expo_inv) x) shell_pairs
let coef = Array.map (fun x -> (fun y -> y.Sp.coef) x) shell_pairs
and expo_inv = Array.map (fun x -> (fun y -> y.Sp.expo_inv) x) shell_pairs
in
{
shell_a = p_a ; shell_b = p_b ; coef ; expo_inv ;
shell_pairs ; center_ab=shell_pairs.(0).center_ab;
norm_coef_scale ; norm_sq=shell_pairs.(0).norm_sq;
totAngMomInt = shell_pairs.(0).ShellPair.totAngMomInt;
monocentric = shell_pairs.(0).ShellPair.monocentric;
totAngMomInt = shell_pairs.(0).Sp.totAngMomInt;
monocentric = shell_pairs.(0).Sp.monocentric;
}
@ -159,7 +160,7 @@ let shell_pairs basis =
let equivalent x y =
(Array.length x = Array.length y) &&
(Array.init (Array.length x) (fun k -> ShellPair.equivalent x.(k) y.(k))
(Array.init (Array.length x) (fun k -> Sp.equivalent x.(k) y.(k))
|> Array.fold_left (fun accu x -> x && accu) true)

114
Basis/Contracted_shell.ml
View File

@ -1,32 +1,26 @@
open Util
open Constants
open Contracted_shell_type
open Coordinate
type t = Contracted_shell_type.t
type shell_contracted = {
expo : float array; (* Gaussian exponents *)
coef : float array; (* Contraction coefficients *)
center : Coordinate.t; (* Center of all the Gaussians *)
totAngMom : Angular_momentum.t; (* Total angular momentum *)
size : int; (* Number of contracted Gaussians *)
norm_coef : float array; (* Normalization coefficient of the class
corresponding to the i-th contraction *)
norm_coef_scale : float array; (* Inside a class, the norm is the norm
of the function with (totAngMom,0,0) *.
this scaling factor *)
index : int; (* Index in the array of contracted shells *)
powers : Zkey.t array; (* Array of Zkeys corresponding to the
powers of (x,y,z) in the class *)
}
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)
let norm_coef_scale a = a.norm_coef_scale
let index a = a.index
let with_index = Contracted_shell_type.with_index
let powers a = a.powers
type t = shell_contracted
let to_string s =
let coord = s.center in
let open Printf in
(match s.totAngMom with
| Angular_momentum.S -> sprintf "%3d " (s.index+1)
| _ -> sprintf "%3d-%-3d" (s.index+1) (s.index+(Array.length s.powers))
) ^
( sprintf "%1s %8.3f %8.3f %8.3f " (Angular_momentum.to_string s.totAngMom)
(get X coord) (get Y coord) (get Z coord) ) ^
(Array.map2 (fun e c -> sprintf "%16.8e %16.8e" e c) s.expo s.coef
|> Array.to_list |> String.concat (sprintf "\n%36s" " ") )
module Am = Angular_momentum
(** Normalization coefficient of contracted function i, which depends on the
exponent and the angular momentum. Two conventions can be chosen : a single
@ -37,7 +31,7 @@ let to_string s =
*)
let compute_norm_coef expo totAngMom =
let atot =
Angular_momentum.to_int totAngMom
Am.to_int totAngMom
in
let factor int_array =
let dfa = Array.map (fun j ->
@ -61,5 +55,75 @@ let compute_norm_coef expo totAngMom =
Array.map (fun x -> let f a = x *. (factor a) in f) expo
let make = Contracted_shell_type.make
let make ~index ~expo ~coef ~center ~totAngMom =
assert (Array.length expo = Array.length coef);
assert (Array.length expo > 0);
let norm_coef_func =
compute_norm_coef expo totAngMom
in
let powers =
Am.zkey_array (Am.Singlet totAngMom)
in
let norm_coef =
Array.map (fun f -> f [| Am.to_int totAngMom ; 0 ; 0 |]) norm_coef_func
in
let norm_coef_scale =
Array.map (fun a ->
(norm_coef_func.(0) (Zkey.to_int_array ~kind:Zkey.Kind_3 a)) /. norm_coef.(0)
) powers
in
{ index ; expo ; coef ; center ; totAngMom ; size=Array.length expo ; norm_coef ;
norm_coef_scale ; powers }
let with_index a i =
{ a with index = i }
let to_string s =
let coord = s.center in
let open Printf in
(match s.totAngMom with
| Am.S -> sprintf "%3d " (s.index+1)
| _ -> sprintf "%3d-%-3d" (s.index+1) (s.index+(Array.length s.powers))
) ^
( sprintf "%1s %8.3f %8.3f %8.3f " (Am.to_string s.totAngMom)
(get X coord) (get Y coord) (get Z coord) ) ^
(Array.map2 (fun e c -> sprintf "%16.8e %16.8e" e c) s.expo s.coef
|> Array.to_list |> String.concat (sprintf "\n%36s" " ") )
(** Normalization coefficient of contracted function i, which depends on the
exponent and the angular momentum. Two conventions can be chosen : a single
normalisation factor for all functions of the class, or a coefficient which
depends on the powers of x,y and z.
Returns, for each contracted function, an array of functions taking as
argument the [|x;y;z|] powers.
*)
let compute_norm_coef expo totAngMom =
let atot =
Am.to_int totAngMom
in
let factor int_array =
let dfa = Array.map (fun j ->
(float_of_int (1 lsl j) *. fact j) /. fact (j+j)
) int_array
in
sqrt (dfa.(0) *.dfa.(1) *. dfa.(2))
in
let expo =
if atot mod 2 = 0 then
Array.map (fun alpha ->
let alpha_2 = alpha +. alpha in
(alpha_2 *. pi_inv)**(0.75) *. (pow (alpha_2 +. alpha_2) (atot/2))
) expo
else
Array.map (fun alpha ->
let alpha_2 = alpha +. alpha in
(alpha_2 *. pi_inv)**(0.75) *. sqrt (pow (alpha_2 +. alpha_2) atot)
) expo
in
Array.map (fun x -> let f a = x *. factor a in f) expo

56
Basis/Contracted_shell.mli
View File

@ -1,45 +1,16 @@
type t = Contracted_shell_type.t
type shell_contracted = private {
expo : float array;
coef : float array;
center : Coordinate.t;
totAngMom : Angular_momentum.t;
size : int;
norm_coef : float array;
norm_coef_scale : float array;
index : int;
powers : Zkey.t array;
}
(** Returns the number of contracted Gaussians *)
val size : t -> int
(** Returns the i-th exponent *)
val expo : t -> int -> float
(** Returns the i-th contraction coefficient *)
val coef : t -> int -> float
(** Point on which all the Gaussians are centered *)
val center : t -> Coordinate.t
(** Total angular momentum *)
val totAngMom : t -> Angular_momentum.t
(** Normalization coefficient of the class corresponding to the i-th contraction *)
val norm_coef : t -> int -> float
(** Inside a class, the norm is the norm of the function with (totAngMom,0,0) *.
this scaling factor *)
val norm_coef_scale : t -> float array
(** The index in the array of contracted shells *)
val index : t -> int
(** Returns a copy of the contracted shell with a modified index *)
val with_index : t -> int -> t
(** The array of Zkeys corresponding to the powers of (x,y,z) in the class *)
val powers : t -> Zkey.t array
type t = shell_contracted
(** Pretty-printing of the contracted shell in a string *)
@ -52,4 +23,5 @@ val make :
coef:float array ->
center:Coordinate.t -> totAngMom:Angular_momentum.t -> t
(** Returns a copy of the contracted shell with a modified index *)
val with_index : t -> int -> t

73
Basis/Contracted_shell_type.ml
View File

@ -1,73 +0,0 @@
open Util
open Constants
type shell_contracted = {
expo : float array;
coef : float array;
center : Coordinate.t;
totAngMom : Angular_momentum.t;
size : int;
norm_coef : float array;
norm_coef_scale : float array;
index : int;
powers : Zkey.t array;
}
type t = shell_contracted
(** Normalization coefficient of contracted function i, which depends on the
exponent and the angular momentum. Two conventions can be chosen : a single
normalisation factor for all functions of the class, or a coefficient which
depends on the powers of x,y and z.
Returns, for each contracted function, an array of functions taking as
argument the [|x;y;z|] powers.
*)
let compute_norm_coef expo totAngMom =
let atot =
Angular_momentum.to_int totAngMom
in
let factor int_array =
let dfa = Array.map (fun j ->
( float_of_int (1 lsl j) *. fact j) /. fact (j+j)
) int_array
in
sqrt (dfa.(0) *.dfa.(1) *. dfa.(2))
in
let expo =
if atot mod 2 = 0 then
Array.map (fun alpha ->
let alpha_2 = alpha +. alpha in
(alpha_2 *. pi_inv)**(0.75) *. (pow (alpha_2 +. alpha_2) (atot/2))
) expo
else
Array.map (fun alpha ->
let alpha_2 = alpha +. alpha in
(alpha_2 *. pi_inv)**(0.75) *. sqrt (pow (alpha_2 +. alpha_2) atot)
) expo
in
Array.map (fun x -> let f a = x *. (factor a) in f) expo
let make ~index ~expo ~coef ~center ~totAngMom =
assert (Array.length expo = Array.length coef);
assert (Array.length expo > 0);
let norm_coef_func =
compute_norm_coef expo totAngMom
in
let powers =
Angular_momentum.zkey_array (Angular_momentum.Singlet totAngMom)
in
let norm_coef =
Array.map (fun f -> f [| Angular_momentum.to_int totAngMom ; 0 ; 0 |]) norm_coef_func
in
let norm_coef_scale =
Array.map (fun a ->
(norm_coef_func.(0) (Zkey.to_int_array ~kind:Zkey.Kind_3 a)) /. norm_coef.(0)
) powers
in
{ index ; expo ; coef ; center ; totAngMom ; size=Array.length expo ; norm_coef ;
norm_coef_scale ; powers }
let with_index a i = { a with index = i }

24
Basis/Contracted_shell_type.mli
View File

@ -1,24 +0,0 @@
type shell_contracted = private {
expo : float array;
coef : float array;
center : Coordinate.t;
totAngMom : Angular_momentum.t;
size : int;
norm_coef : float array;
norm_coef_scale : float array;
index : int;
powers : Zkey.t array;
}
type t = shell_contracted
val make :
index:int ->
expo:float array ->
coef:float array ->
center:Coordinate.t -> totAngMom:Angular_momentum.t -> t
(** Returns a copy of the contracted shell with a modified index *)
val with_index : t -> int -> t

51
Basis/ERI.ml
View File

@ -6,6 +6,10 @@ open Bigarray
type t = (float, float32_elt, fortran_layout) Bigarray.Genarray.t
module Bs = Basis
module Cs = Contracted_shell
module Csp = ContractedShellPair
(** (00|00)^m : Fundamental electron repulsion integral
$ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
@ -77,16 +81,14 @@ let of_basis basis =
| _ -> assert false
in
let n =
Basis.size basis
and shell =
Basis.contracted_shells basis
let n = basis.Bs.size
and shell = basis.Bs.contracted_shells
in
(* Pre-compute all shell pairs *)
let shell_pairs =
ContractedShellPair.shell_pairs shell
Csp.shell_pairs shell
in
(* Pre-compute diagonal integrals for Schwartz *)
@ -103,7 +105,7 @@ let of_basis basis =
let icount = ref 0 in
for i=0 to (Array.length shell) - 1 do
print_int (Contracted_shell.index shell.(i)) ; print_newline ();
print_int shell.(i).index ; print_newline ();
for j=0 to i do
let schwartz_p, schwartz_p_max = schwartz.(i).(j) in
if (schwartz_p_max >= cutoff) then
@ -112,6 +114,9 @@ let of_basis basis =
done;
Printf.printf "%d shell pairs computed in %f seconds\n" !icount (Unix.gettimeofday () -. t0);
(* Group shell pairs by common pairs of atoms *)
(* 4D data initialization *)
let eri_array =
Genarray.create Float32 fortran_layout [| n ; n ; n ; n|]
@ -124,7 +129,7 @@ let of_basis basis =
let inn = ref 0 and out = ref 0 in
for i=0 to (Array.length shell) - 1 do
print_int (Contracted_shell.index shell.(i)) ; print_newline ();
print_int shell.(i).index ; print_newline ();
for j=0 to i do
let schwartz_p, schwartz_p_max = schwartz.(i).(j) in
try
@ -135,7 +140,7 @@ let of_basis basis =
in
let sp =
shell_p.ContractedShellPair.shell_pairs
shell_p.Csp.shell_pairs
in
for k=0 to i do
@ -148,7 +153,7 @@ let of_basis basis =
shell_q = shell_pairs.(k).(l)
in
let sq =
shell_q.ContractedShellPair.shell_pairs
shell_q.Csp.shell_pairs
in
let swap =
@ -172,16 +177,16 @@ let of_basis basis =
(* Write the data in the output file *)
Array.iteri (fun i_c powers_i ->
let i_c = (Contracted_shell.index shell.(i)) + i_c + 1 in
let i_c = shell.(i).index + i_c + 1 in
let xi = to_powers powers_i in
Array.iteri (fun j_c powers_j ->
let j_c = (Contracted_shell.index shell.(j)) + j_c + 1 in
let j_c = shell.(j).index + j_c + 1 in
let xj = to_powers powers_j in
Array.iteri (fun k_c powers_k ->
let k_c = (Contracted_shell.index shell.(k)) + k_c + 1 in
let k_c = shell.(k).index + k_c + 1 in
let xk = to_powers powers_k in
Array.iteri (fun l_c powers_l ->
let l_c = (Contracted_shell.index shell.(l)) + l_c + 1 in
let l_c = shell.(l).index + l_c + 1 in
let xl = to_powers powers_l in
let key =
if swap then
@ -205,10 +210,10 @@ let of_basis basis =
)
else
out := !out + 1;
) (Contracted_shell.powers shell.(l))
) (Contracted_shell.powers shell.(k))
) (Contracted_shell.powers shell.(j))
) (Contracted_shell.powers shell.(i));
) shell.(l).powers
) shell.(k).powers
) shell.(j).powers
) shell.(i).powers
with NullIntegral -> ()
done;
done;
@ -264,7 +269,7 @@ let to_file ~filename basis =
let oc = open_out filename in
let zkey = Array.map (fun b ->
let result =
Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
Angular_momentum.(zkey_array (Kind_1 b.totAngMom))
in
{ n=Array.length result ; cls=result }
) basis
@ -362,7 +367,7 @@ let to_file ~filename basis =
let xto_file ~filename basis =
let zkey = Array.map (fun b ->
let result =
Angular_momentum.(zkey_array (Kind_1 b.Contracted_shell.totAngMom))
Angular_momentum.(zkey_array (Kind_1 b.totAngMom))
in
{ n=Array.length result ; cls=result }
) basis
@ -373,10 +378,10 @@ let xto_file ~filename basis =
let (i,j,k,l) = (1,1,1,18) in
let (i,j,k,l) = (i-1,j-1,k-1,l-1) in
basis.(i) |> Contracted_shell.to_string |> print_endline;
basis.(j) |> Contracted_shell.to_string |> print_endline;
basis.(k) |> Contracted_shell.to_string |> print_endline;
basis.(l) |> Contracted_shell.to_string |> print_endline;
basis.(i) |> Cs.to_string |> print_endline;
basis.(j) |> Cs.to_string |> print_endline;
basis.(k) |> Cs.to_string |> print_endline;
basis.(l) |> Cs.to_string |> print_endline;
let bi, bj, bk, bl =
basis.(i), basis.(j), basis.(k), basis.(l)
in

4
Basis/General_basis.ml
View File

@ -9,6 +9,8 @@ type general_contracted_shell = Angular_momentum.t * (primitive array)
type t = Element.t * (general_contracted_shell array)
module Am = Angular_momentum
let string_of_primitive ?id prim =
match id with
| None -> (string_of_float prim.exponent)^" "^(string_of_float prim.coefficient)
@ -20,7 +22,7 @@ let string_of_contracted_shell (angular_momentum, prim_array) =
Array.length prim_array
in
Printf.sprintf "%s %d\n%s"
(Angular_momentum.to_string angular_momentum) n
(Am.to_string angular_momentum) n
(Array.init n (fun i -> string_of_primitive ~id:(i+1) prim_array.(i))
|> Array.to_list
|> String.concat "\n")

56
Basis/KinInt.ml
View File

@ -1,8 +1,13 @@
open Util
open Constants
open Lacaml.D
open Powers
open Coordinate
module Am = Angular_momentum
module Bs = Basis
module Co = Coordinate
module Cs = Contracted_shell
module Csp = ContractedShellPair
module Sp = ShellPair
type t = Mat.t
@ -11,13 +16,12 @@ type t = Mat.t
let contracted_class shell_a shell_b : float Zmap.t =
let shell_p =
ContractedShellPair.create shell_a shell_b
Csp.create shell_a shell_b
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array (Angular_momentum.Doublet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b))
Am.zkey_array (Am.Doublet (shell_a.totAngMom, shell_b.totAngMom))
in
let contracted_class =
@ -26,35 +30,35 @@ let contracted_class shell_a shell_b : float Zmap.t =
(* Compute all integrals in the shell for each pair of significant shell pairs *)
let sp = shell_p.ContractedShellPair.shell_pairs in
let sp = shell_p.Csp.shell_pairs in
let center_ab =
shell_p.ContractedShellPair.center_ab
shell_p.Csp.center_ab
in
let norm_coef_scale =
shell_p.ContractedShellPair.norm_coef_scale
shell_p.Csp.norm_coef_scale
in
for ab=0 to (Array.length sp - 1)
do
let coef_prod =
shell_p.ContractedShellPair.coef.(ab)
shell_p.Csp.coef.(ab)
in
(** Screening on thr product of coefficients *)
if (abs_float coef_prod) > 1.e-4*.cutoff then
begin
let center_pa =
sp.(ab).ShellPair.center_a
sp.(ab).Sp.center_a
in
let expo_inv =
shell_p.ContractedShellPair.expo_inv.(ab)
shell_p.Csp.expo_inv.(ab)
in
let i, j =
sp.(ab).ShellPair.i, sp.(ab).ShellPair.j
sp.(ab).Sp.i, sp.(ab).Sp.j
in
let expo_a =
Contracted_shell.expo sp.(ab).ShellPair.shell_a i
sp.(ab).Sp.shell_a.expo.(i)
and expo_b =
Contracted_shell.expo sp.(ab).ShellPair.shell_b j
sp.(ab).Sp.shell_b.expo.(j)
in
Array.iteri (fun i key ->
@ -65,14 +69,14 @@ let contracted_class shell_a shell_b : float Zmap.t =
in
let ov a b k =
let xyz = match k with
| 0 -> X
| 1 -> Y
| _ -> Z
| 0 -> Co.X
| 1 -> Co.Y
| _ -> Co.Z
in
Overlap_primitives.hvrr (a, b)
expo_inv
(Coordinate.get xyz center_ab,
Coordinate.get xyz center_pa)
(Co.get xyz center_ab,
Co.get xyz center_pa)
in
let f k =
ov angMomA.(k) angMomB.(k) k
@ -116,10 +120,8 @@ let of_basis basis =
| _ -> assert false
in
let n =
Basis.size basis
and shell =
Basis.contracted_shells basis
let n = basis.Bs.size
and shell = basis.Bs.contracted_shells
in
let result = Mat.create n n in
@ -131,10 +133,10 @@ let of_basis basis =
in
Array.iteri (fun j_c powers_j ->
let j_c = Contracted_shell.index shell.(j) + j_c + 1 in
let j_c = shell.(j).index + j_c + 1 in
let xj = to_powers powers_j in
Array.iteri (fun i_c powers_i ->
let i_c = Contracted_shell.index shell.(i) + i_c + 1 in
let i_c = shell.(i).index + i_c + 1 in
let xi = to_powers powers_i in
let key =
Zkey.of_powers (Zkey.Six (xi,xj))
@ -145,8 +147,8 @@ let of_basis basis =
in
result.{i_c,j_c} <- value;
result.{j_c,i_c} <- value;
) (Contracted_shell.powers shell.(i));
) (Contracted_shell.powers shell.(j))
) shell.(i).powers
) shell.(j).powers
done;
done;
Mat.detri result;

16
Basis/NucInt.ml
View File

@ -6,6 +6,8 @@ open Lacaml.D
type t = Mat.t
module Bs = Basis
(** (0|0)^m : Fundamental electron-nucleus repulsion integral
$ \int \phi_p(r1) 1/r_{C} dr_1 $
@ -43,10 +45,8 @@ let of_basis_nuclei basis nuclei =
| _ -> assert false
in
let n =
Basis.size basis
and shell =
Basis.contracted_shells basis
let n = basis.Bs.size
and shell = basis.Bs.contracted_shells
in
let eni_array = Mat.create n n in
@ -71,10 +71,10 @@ let of_basis_nuclei basis nuclei =
(* Write the data in the output file *)
Array.iteri (fun i_c powers_i ->
let i_c = (Contracted_shell.index shell.(i)) + i_c + 1 in
let i_c = shell.(i).index + i_c + 1 in
let xi = to_powers powers_i in
Array.iteri (fun j_c powers_j ->
let j_c = (Contracted_shell.index shell.(j)) + j_c + 1 in
let j_c = shell.(j).index + j_c + 1 in
let xj = to_powers powers_j in
let key =
Zkey.of_powers (Zkey.Six (xi,xj))
@ -84,8 +84,8 @@ let of_basis_nuclei basis nuclei =
in
eni_array.{j_c,i_c} <- value;
eni_array.{i_c,j_c} <- value;
) (Contracted_shell.powers shell.(j))
) (Contracted_shell.powers shell.(i));
) shell.(j).powers
) shell.(i).powers
done;
done;
Mat.detri eni_array;

158
Basis/OneElectronRR.ml
View File

@ -1,10 +1,15 @@
open Util
open Constants
open Powers
open Coordinate
exception NullPair
module Am = Angular_momentum
module Co = Coordinate
module Cs = Contracted_shell
module Csp = ContractedShellPair
module Po = Powers
module Sp = ShellPair
(** 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.
@ -13,29 +18,28 @@ let chop f g =
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_one_e (angMom_a, angMom_b)
zero_m_array (expo_b) (expo_inv_p) (center_ab, center_pa, center_pc)
map
=
let hvrr_one_e angMom_a angMom_b
zero_m_array expo_b expo_inv_p
center_ab center_pa center_pc
map =
let maxm = angMom_a.tot + angMom_b.tot in
let maxm = angMom_a.Po.tot + angMom_b.Po.tot in
let maxsze = maxm+1 in
let empty = Array.make maxsze 0. in
let get_xyz angMom =
match angMom with
| { y=0 ; z=0 ; _ } -> X
| { z=0 ; _ } -> Y
| _ -> Z
| { Po.y=0 ; z=0 ; _ } -> Co.X
| { z=0 ; _ } -> Co.Y
| _ -> Co.Z
in
(** Vertical recurrence relations *)
let rec vrr angMom_a =
let { x=ax ; y=ay ; z=az } = angMom_a in
let { Po.x=ax ; y=ay ; z=az } = angMom_a in
if ax < 0 || ay < 0 || az < 0 then raise Exit
else
match angMom_a.tot with
match angMom_a.Po.tot with
| 0 -> zero_m_array
| _ ->
let key = Zkey.of_powers (Zkey.Three angMom_a) in
@ -43,35 +47,26 @@ let hvrr_one_e (angMom_a, angMom_b)
try Zmap.find map key with
| Not_found ->
let result =
let xyz = get_xyz angMom_a in
let am = Powers.decr xyz angMom_a in
let amxyz = Powers.get xyz am in
if amxyz < 0 then empty else
let f1 = Coordinate.get xyz center_pa
and f2 = expo_inv_p *. (Coordinate.get xyz center_pc)
in
if amxyz < 1 then
let v1 =
vrr am
in
Array.init maxsze (fun m ->
if m = maxm then (f1 *. v1.(m) ) else
(f1 *. v1.(m) ) -. f2 *. v1.(m+1) )
else
let xyz = get_xyz angMom_a in
let am = Po.decr xyz angMom_a in
let amxyz = Po.get xyz am in
let f1 = Co.get xyz center_pa in
let f2 = expo_inv_p *. Co.get xyz center_pc in
if amxyz < 1 then
let v1 = vrr am in
Array.init (maxsze - angMom_a.Po.tot)
(fun m -> f1 *. v1.(m) -. f2 *. v1.(m+1))
else
let v3 =
let amm = Powers.decr xyz am in
let amm = Po.decr xyz am in
vrr amm
in
let v1 =
vrr am
in
let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
Array.init maxsze (fun m -> f1 *. v1.(m) -.
(if m = maxm then 0. else
f2 *. v1.(m+1) )
+. f3 *. (v3.(m) -. if m = maxm then 0. else
expo_inv_p *. v3.(m+1))
)
let v1 = vrr am in
let f3 = float_of_int amxyz *. expo_inv_p *. 0.5 in
Array.init (maxsze - angMom_a.Po.tot)
(fun m -> f1 *. v1.(m) -. f2 *. v1.(m+1) +.
f3 *. (v3.(m) -. expo_inv_p *. v3.(m+1))
)
in Zmap.add map key result;
result
@ -79,28 +74,19 @@ let hvrr_one_e (angMom_a, angMom_b)
(** Horizontal recurrence relations *)
and hrr angMom_a angMom_b =
let { x=bx ; y=by ; z=bz } = angMom_b in
if bx < 0 || by < 0 || bz < 0 then raise Exit
else
match angMom_b.tot with
| 0 -> (vrr angMom_a).(0)
| _ ->
let xyz = get_xyz angMom_b in
let bxyz = Powers.get xyz angMom_b in
if (bxyz < 1) then 0. else
let ap = Powers.incr xyz angMom_a in
let bm = Powers.decr xyz angMom_b in
let h1 =
hrr ap bm
in
let f2 =
Coordinate.get xyz center_ab
in
match angMom_b.Po.tot with
| 0 -> (vrr angMom_a).(0)
| _ ->
let xyz = get_xyz angMom_b in
let bxyz = Po.get xyz angMom_b in
if (bxyz < 1) then 0. else
let ap = Po.incr xyz angMom_a in
let bm = Po.decr xyz angMom_b in
let h1 = hrr ap bm in
let f2 = Co.get xyz center_ab in
if abs_float f2 < cutoff then h1 else
let h2 =
hrr angMom_a bm
in
h1 +. f2 *. h2
let h2 = hrr angMom_a bm in
h1 +. f2 *. h2
in
hrr angMom_a angMom_b
@ -116,19 +102,16 @@ let hvrr_one_e (angMom_a, angMom_b)
(** Computes all the one-electron integrals of the contracted shell pair *)
let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.ContractedShellPair.shell_b
let shell_a = shell_p.Csp.shell_a
and shell_b = shell_p.Csp.shell_b
in
let maxm =
let open Angular_momentum in
(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
(Am.to_int @@ shell_a.totAngMom) + (Am.to_int @@ shell_b.totAngMom)
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Doublet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b))
Am.zkey_array (Am.Doublet (shell_a.totAngMom, shell_b.totAngMom))
in
let contracted_class =
@ -137,52 +120,50 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
(* Compute all integrals in the shell for each pair of significant shell pairs *)
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale
let norm_coef_scale_p = shell_p.Csp.norm_coef_scale
in
for ab=0 to (Array.length shell_p.ContractedShellPair.shell_pairs - 1)
for ab=0 to (Array.length shell_p.Csp.shell_pairs - 1)
do
let b = shell_p.ContractedShellPair.shell_pairs.(ab).ShellPair.j in
let b = shell_p.Csp.shell_pairs.(ab).Sp.j in
try
begin
let coef_prod = shell_p.ContractedShellPair.coef.(ab) in
let coef_prod = shell_p.Csp.coef.(ab) in
(** Screening on the product of coefficients *)
if (abs_float coef_prod) < 1.e-4*.cutoff then
if abs_float coef_prod < 1.e-3 *. cutoff then
raise NullPair;
let expo_pq_inv =
shell_p.ContractedShellPair.expo_inv.(ab)
shell_p.Csp.expo_inv.(ab)
in
let center_ab =
shell_p.ContractedShellPair.center_ab
shell_p.Csp.center_ab
in
let center_p =
shell_p.ContractedShellPair.shell_pairs.(ab).ShellPair.center
shell_p.Csp.shell_pairs.(ab).Sp.center
in
let center_pa =
Coordinate.(center_p |- Contracted_shell.center shell_a)
Co.(center_p |- shell_a.center)
in
for c=0 to Array.length geometry - 1 do
let element, nucl_coord = geometry.(c) in
let charge = Element.to_charge element |> Charge.to_float in
let center_pc =
Coordinate.(center_p |- nucl_coord )
Co.(center_p |- nucl_coord )
in
let norm_pq_sq =
Coordinate.dot center_pc center_pc
Co.dot center_pc center_pc
in
let zero_m_array =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b) with
| Angular_momentum.(S,S) ->
let integral =
zero_m_array.(0)
in
match (shell_a.totAngMom, shell_b.totAngMom) with
| Am.(S,S) ->
let integral = zero_m_array.(0) in
contracted_class.(0) <- contracted_class.(0) -. coef_prod *. integral *. charge
| _ ->
let map = Zmap.create (2*maxm) in
@ -198,11 +179,12 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
let norm = norm_coef_scale.(i) in
let coef_prod = coef_prod *. norm in
let integral =
hvrr_one_e (angMomA, angMomB)
zero_m_array
(Contracted_shell.expo shell_b b)
(shell_p.ContractedShellPair.expo_inv.(ab))
(center_ab, center_pa, center_pc)
hvrr_one_e
angMomA angMomB
zero_m_array
shell_b.expo.(b)
shell_p.Csp.expo_inv.(ab)
center_ab center_pa center_pc
map
in
contracted_class.(i) <- contracted_class.(i) -. coef_prod *. integral *. charge

48
Basis/Overlap.ml
View File

@ -1,22 +1,26 @@
open Util
open Constants
open Lacaml.D
open Coordinate
type t = Mat.t
module Am = Angular_momentum
module Bs = Basis
module Co = Coordinate
module Cs = Contracted_shell
module Csp = ContractedShellPair
module Sp = ShellPair
(** Computes all the overlap integrals of the contracted shell pair *)
let contracted_class shell_a shell_b : float Zmap.t =
let shell_p =
ContractedShellPair.create shell_a shell_b
Csp.create shell_a shell_b
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array (Angular_momentum.Doublet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b))
Am.zkey_array (Am.Doublet (shell_a.totAngMom, shell_b.totAngMom))
in
let contracted_class =
@ -24,13 +28,13 @@ let contracted_class shell_a shell_b : float Zmap.t =
in
let sp =
shell_p.ContractedShellPair.shell_pairs
shell_p.Csp.shell_pairs
in
let center_ab =
shell_p.ContractedShellPair.center_ab
shell_p.Csp.center_ab
in
let norm_coef_scale =
shell_p.ContractedShellPair.norm_coef_scale
shell_p.Csp.norm_coef_scale
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
@ -38,16 +42,16 @@ let contracted_class shell_a shell_b : float Zmap.t =
for ab=0 to (Array.length sp - 1)
do
let coef_prod =
shell_p.ContractedShellPair.coef.(ab)
shell_p.Csp.coef.(ab)
in
(** Screening on thr product of coefficients *)
if (abs_float coef_prod) > 1.e-4*.cutoff then
begin
let expo_inv =
shell_p.ContractedShellPair.expo_inv.(ab)
shell_p.Csp.expo_inv.(ab)
in
let center_pa =
sp.(ab).ShellPair.center_a
sp.(ab).Sp.center_a
in
Array.iteri (fun i key ->
@ -58,14 +62,14 @@ let contracted_class shell_a shell_b : float Zmap.t =
in
let f k =
let xyz = match k with
| 0 -> X
| 1 -> Y
| _ -> Z
| 0 -> Co.X
| 1 -> Co.Y
| _ -> Co.Z
in
Overlap_primitives.hvrr (angMomA.(k), angMomB.(k))
expo_inv
(Coordinate.get xyz center_ab,
Coordinate.get xyz center_pa)
(Co.get xyz center_ab,
Co.get xyz center_pa)
in
let norm = norm_coef_scale.(i) in
let integral = chop norm (fun () -> (f 0)*.(f 1)*.(f 2)) in
@ -89,10 +93,8 @@ let of_basis basis =
| _ -> assert false
in
let n =
Basis.size basis
and shell =
Basis.contracted_shells basis
let n = basis.Bs.size
and shell = basis.Bs.contracted_shells
in
let result = Mat.create n n in
@ -104,10 +106,10 @@ let of_basis basis =
in
Array.iteri (fun j_c powers_j ->
let j_c = Contracted_shell.index shell.(j) + j_c + 1 in
let j_c = shell.(j).index + j_c + 1 in
let xj = to_powers powers_j in
Array.iteri (fun i_c powers_i ->
let i_c = Contracted_shell.index shell.(i) + i_c + 1 in
let i_c = shell.(i).index + i_c + 1 in
let xi = to_powers powers_i in
let key =
Zkey.of_powers (Zkey.Six (xi,xj))
@ -118,8 +120,8 @@ let of_basis basis =
in
result.{i_c,j_c} <- value;
result.{j_c,i_c} <- value;
) (Contracted_shell.powers shell.(i));
) (Contracted_shell.powers shell.(j))
) shell.(i).powers
) shell.(j).powers
done;
done;
Mat.detri result;

219
Basis/TwoElectronRR.ml
View File

@ -1,7 +1,12 @@
open Util
open Constants
open Powers
open Coordinate
module Am = Angular_momentum
module Co = Coordinate
module Cs = Contracted_shell
module Csp = ContractedShellPair
module Sp = ShellPair
module Po = Powers
let debug=false
@ -10,43 +15,44 @@ let cutoff2 = cutoff *. cutoff
exception NullQuartet
(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
let rec hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
zero_m_array
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq)
(center_pa, center_qc)
map_1d map_2d
=
expo_b expo_d
expo_inv_p expo_inv_q
center_ab center_cd center_pq
center_pa center_qc
map_1d map_2d =
(* Swap electrons 1 and 2 so that the max angular momentum is on 1 *)
if angMom_a.tot + angMom_b.tot < angMom_c.tot + angMom_d.tot then
hvrr_two_e (angMom_c, angMom_d, angMom_a, angMom_b)
if angMom_a.Po.tot + angMom_b.Po.tot < angMom_c.Po.tot + angMom_d.Po.tot then
hvrr_two_e
angMom_c angMom_d angMom_a angMom_b
zero_m_array
(expo_d, expo_b)
(expo_inv_q, expo_inv_p)
(center_cd, center_ab, (Coordinate.neg center_pq) )
(center_qc, center_pa)
expo_d expo_b
expo_inv_q expo_inv_p
center_cd center_ab (Co.neg center_pq)
center_qc center_pa
map_1d map_2d
else
let maxm = angMom_a.tot + angMom_b.tot + angMom_c.tot + angMom_d.tot in
let maxm = angMom_a.Po.tot + angMom_b.Po.tot + angMom_c.Po.tot + angMom_d.Po.tot in
let maxsze = maxm+1 in
let get_xyz angMom =
match angMom with
| { y=0 ; z=0 ; _ } -> X
| { z=0 ; _ } -> Y
| _ -> Z
| { Po.y=0 ; z=0 ; _ } -> Co.X
| { z=0 ; _ } -> Co.Y
| _ -> Co.Z
in
(** Vertical recurrence relations *)
let rec vrr0 angMom_a =
match angMom_a.tot with
match angMom_a.Po.tot with
| 0 -> zero_m_array
| _ ->
let key = Zkey.of_powers_three angMom_a in
@ -55,13 +61,13 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
| Not_found ->
let result =
let xyz = get_xyz angMom_a in
let am = Powers.decr xyz angMom_a in
let amxyz = Powers.get xyz am in
let am = Po.decr xyz angMom_a in
let amxyz = Po.get xyz am in
let f1 = expo_inv_p *. (Coordinate.get xyz center_pq)
and f2 = expo_b *. expo_inv_p *. (Coordinate.get xyz center_ab)
let f1 = expo_inv_p *. Co.get xyz center_pq
and f2 = expo_b *. expo_inv_p *. Co.get xyz center_ab
in
let result = Array.create_float (maxsze-angMom_a.tot) in
let result = Array.create_float (maxsze - angMom_a.Po.tot) in
if amxyz = 0 then
begin
let v1 = vrr0 am in
@ -70,7 +76,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
end
else
begin
let amm = Powers.decr xyz am in
let amm = Po.decr xyz am in
let v3 = vrr0 amm in
let v1 = vrr0 am in
let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
@ -85,7 +91,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
and vrr angMom_a angMom_c =
match angMom_a.tot, angMom_c.tot with
match angMom_a.Po.tot, angMom_c.Po.tot with
| (i,0) -> if (i>0) then vrr0 angMom_a
else zero_m_array
| (_,_) ->
@ -94,21 +100,21 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
try Zmap.find map_2d key with
| Not_found ->
let result =
(* angMom_c.tot > 0 so cm.tot >= 0 *)
(* angMom_c.Po.tot > 0 so cm.Po.tot >= 0 *)
let xyz = get_xyz angMom_c in
let cm = Powers.decr xyz angMom_c in
let cmxyz = Powers.get xyz cm in
let axyz = Powers.get xyz angMom_a in
let cm = Po.decr xyz angMom_c in
let cmxyz = Po.get xyz cm in
let axyz = Po.get xyz angMom_a in
let f1 =
-. expo_d *. expo_inv_q *. (Coordinate.get xyz center_cd)
-. expo_d *. expo_inv_q *. Co.get xyz center_cd
and f2 =
expo_inv_q *. (Coordinate.get xyz center_pq)
expo_inv_q *. Co.get xyz center_pq
in
let result = Array.make (maxsze - angMom_a.tot - angMom_c.tot) 0. in
let result = Array.make (maxsze - angMom_a.Po.tot - angMom_c.Po.tot) 0. in
if axyz > 0 then
begin
let am = Powers.decr xyz angMom_a in
let am = Po.decr xyz angMom_a in
let f5 =
(float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5
in
@ -128,7 +134,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
(abs_float (f3 *. expo_inv_q) > cutoff) then
begin
let v3 =
let cmm = Powers.decr xyz cm in
let cmm = Po.decr xyz cm in
vrr angMom_a cmm
in
Array.iteri (fun m _ ->
@ -151,7 +157,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
(*
and trr angMom_a angMom_c =
match (angMom_a.tot, angMom_c.tot) with
match (angMom_a.Po.tot, angMom_c.Po.tot) with
| (i,0) -> if (i>0) then (vrr0 angMom_a).(0)
else zero_m_array.(0)
| (_,_) ->
@ -161,14 +167,14 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
| Not_found ->
let result =
let xyz = get_xyz angMom_c in
let axyz = Powers.get xyz angMom_a in
let cm = Powers.decr xyz angMom_c in
let cmxyz = Powers.get xyz cm in
let axyz = Po.get xyz angMom_a in
let cm = Po.decr xyz angMom_c in
let cmxyz = Po.get xyz cm in
let expo_inv_q_over_p = expo_inv_q /. expo_inv_p in
let f =
Coordinate.get xyz center_qc +. expo_inv_q_over_p *.
(Coordinate.get xyz center_pa)
Co.get xyz center_qc +. expo_inv_q_over_p *.
Co.get xyz center_pa
in
let result = 0. in
@ -176,7 +182,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
if cmxyz < 1 then result else
let f = 0.5 *. (float_of_int cmxyz) *. expo_inv_q in
if abs_float f < cutoff then 0. else
let cmm = Powers.decr xyz cm in
let cmm = Po.decr xyz cm in
let v3 = trr angMom_a cmm in
result +. f *. v3
in
@ -188,7 +194,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
let result =
if cmxyz < 0 then result else
let f = -. expo_inv_q_over_p in
let ap = Powers.incr xyz angMom_a in
let ap = Po.incr xyz angMom_a in
let v4 = trr ap cm in
result +. v4 *. f
in
@ -196,7 +202,7 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
if axyz < 1 then result else
let f = 0.5 *. (float_of_int axyz) *. expo_inv_q in
if abs_float f < cutoff then result else
let am = Powers.decr xyz angMom_a in
let am = Po.decr xyz angMom_a in
let v2 = trr am cm in
result +. f *. v2
in
@ -220,24 +226,24 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
(** Horizontal recurrence relations *)
let rec hrr0 angMom_a angMom_b angMom_c =
match angMom_b.tot with
match angMom_b.Po.tot with
| 1 ->
let xyz = get_xyz angMom_b in
let ap = Powers.incr xyz angMom_a in
let ap = Po.incr xyz angMom_a in
let v1 = vrr ap angMom_c in
let f2 = Coordinate.get xyz center_ab in
let f2 = Co.get xyz center_ab in
if (abs_float f2 < cutoff) then v1 else
let v2 = vrr angMom_a angMom_c in
v1 +. f2 *. v2
| 0 -> vrr angMom_a angMom_c
| _ ->
let xyz = get_xyz angMom_b in
let bxyz = Powers.get xyz angMom_b in
let bxyz = Po.get xyz angMom_b in
if bxyz > 0 then
let ap = Powers.incr xyz angMom_a in
let bm = Powers.decr xyz angMom_b in
let ap = Po.incr xyz angMom_a in
let bm = Po.decr xyz angMom_b in
let h1 = hrr0 ap bm angMom_c in
let f2 = Coordinate.get xyz center_ab in
let f2 = Co.get xyz center_ab in
if abs_float f2 < cutoff then h1 else
let h2 = hrr0 angMom_a bm angMom_c in
h1 +. f2 *. h2
@ -246,18 +252,18 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
and hrr angMom_a angMom_b angMom_c angMom_d =
match (angMom_b.tot, angMom_d.tot) with
match (angMom_b.Po.tot, angMom_d.Po.tot) with
| (_,0) ->
if (angMom_b.tot = 0) then
if (angMom_b.Po.tot = 0) then
vrr angMom_a angMom_c
else
hrr0 angMom_a angMom_b angMom_c
| (_,_) ->
let xyz = get_xyz angMom_d in
let cp = Powers.incr xyz angMom_c in
let dm = Powers.decr xyz angMom_d in
let cp = Po.incr xyz angMom_c in
let dm = Po.decr xyz angMom_d in
let h1 = hrr angMom_a angMom_b cp dm in
let f2 = Coordinate.get xyz center_cd in
let f2 = Co.get xyz center_cd in
if abs_float f2 < cutoff then h1 else
let h2 = hrr angMom_a angMom_b angMom_c dm in
h1 +. f2 *. h2
@ -270,24 +276,20 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.ContractedShellPair.shell_b
and shell_c = shell_q.ContractedShellPair.shell_a
and shell_d = shell_q.ContractedShellPair.shell_b
and sp = shell_p.ContractedShellPair.shell_pairs
and sq = shell_q.ContractedShellPair.shell_pairs
in
let maxm =
shell_p.ContractedShellPair.totAngMomInt +
shell_q.ContractedShellPair.totAngMomInt
let shell_a = shell_p.Csp.shell_a
and shell_b = shell_p.Csp.shell_b
and shell_c = shell_q.Csp.shell_a
and shell_d = shell_q.Csp.shell_b
and sp = shell_p.Csp.shell_pairs
and sq = shell_q.Csp.shell_pairs
in
let maxm = shell_p.Csp.totAngMomInt + shell_q.Csp.totAngMomInt in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Quartet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d))
Am.zkey_array (Am.Quartet
(shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom ))
in
let contracted_class =
@ -295,53 +297,53 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
in
let monocentric =
shell_p.ContractedShellPair.monocentric &&
shell_q.ContractedShellPair.monocentric &&
Contracted_shell.center shell_p.ContractedShellPair.shell_a =
Contracted_shell.center shell_q.ContractedShellPair.shell_a
shell_p.Csp.monocentric &&
shell_q.Csp.monocentric &&
shell_p.Csp.shell_a.Cs.center =
shell_q.Csp.shell_a.Cs.center
in
(* Compute all integrals in the shell for each pair of significant shell pairs *)
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
let norm_coef_scale_p = shell_p.Csp.norm_coef_scale in
let norm_coef_scale_q = shell_q.Csp.norm_coef_scale in
for ab=0 to (Array.length sp - 1) do
let cab = shell_p.ContractedShellPair.coef.(ab) in
let b = sp.(ab).ShellPair.j in
for cd=0 to (Array.length shell_q.ContractedShellPair.shell_pairs - 1) do
let cab = shell_p.Csp.coef.(ab) in
let b = sp.(ab).Sp.j in
for cd=0 to (Array.length shell_q.Csp.shell_pairs - 1) do
let coef_prod =
cab *. shell_q.ContractedShellPair.coef.(cd)
cab *. shell_q.Csp.coef.(cd)
in
(** Screening on the product of coefficients *)
try
if (abs_float coef_prod) < 1.e-3*.cutoff then
if (abs_float coef_prod) < 1.e-3 *. cutoff then
raise NullQuartet;
let center_pq =
sp.(ab).ShellPair.center |- sq.(cd).ShellPair.center
Co.(sp.(ab).Sp.center |- sq.(cd).Sp.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
Co.dot center_pq center_pq
in
let expo_pq_inv =
shell_p.ContractedShellPair.expo_inv.(ab) +.
shell_q.ContractedShellPair.expo_inv.(cd)
shell_p.Csp.expo_inv.(ab) +.
shell_q.Csp.expo_inv.(cd)
in
let zero_m_array =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
begin
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d) with
| Angular_momentum.(S,S,S,S) ->
match (shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom) with
| Am.(S,S,S,S) ->
let integral =
zero_m_array.(0)
in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
| _ ->
let d = shell_q.ContractedShellPair.shell_pairs.(cd).ShellPair.j in
let d = shell_q.Csp.shell_pairs.(cd).Sp.j in
let map_1d = Zmap.create (4*maxm) in
let map_2d = Zmap.create (Array.length class_indices) in
let norm_coef_scale =
@ -362,20 +364,20 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
try
if monocentric then
begin
if ( ((1 land angMom_a.x+angMom_b.x+angMom_c.x+angMom_d.x)=1) ||
((1 land angMom_a.y+angMom_b.y+angMom_c.y+angMom_d.y)=1) ||
((1 land angMom_a.z+angMom_b.z+angMom_c.z+angMom_d.z)=1)
if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) ||
((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) ||
((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1)
) then
raise NullQuartet
end;
(*
(* Schwartz screening *)
if (maxm > 2) then
(*
if (maxm > 8) then
(
let schwartz_p =
let key = Zkey.of_int_tuple (Zkey.Twelve
(angMomA, angMomB, angMomA, angMomB) )
let key =
Zkey.of_powers_twelve angMom_a angMom_b angMom_a angMom_b
in
match schwartz_p with
| None -> 1.
@ -383,15 +385,15 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
in
if schwartz_p < cutoff then raise NullQuartet;
let schwartz_q =
let key = Zkey.of_int_tuple (Zkey.Twelve
(angMomC, angMomD, angMomC, angMomD) )
let key =
Zkey.of_powers_twelve angMom_c angMom_d angMom_c angMom_d
in
match schwartz_q with
| None -> 1.
| Some schwartz_q -> Zmap.find schwartz_q key
in
if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
);
);
*)
@ -399,13 +401,14 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
let coef_prod = coef_prod *. norm in
let integral =
hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
hvrr_two_e
angMom_a angMom_b angMom_c angMom_d
zero_m_array
(Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d)
(shell_p.ContractedShellPair.expo_inv.(ab),
shell_q.ContractedShellPair.expo_inv.(cd) )
(sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq)
(sp.(ab).ShellPair.center_a , sq.(cd).ShellPair.center_a)
shell_b.expo.(b) shell_d.expo.(d)
shell_p.Csp.expo_inv.(ab)
shell_q.Csp.expo_inv.(cd)
sp.(ab).Sp.center_ab sq.(cd).Sp.center_ab center_pq
sp.(ab).Sp.center_a sq.(cd).Sp.center_a
map_1d map_2d
in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
@ -427,8 +430,8 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
(** 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 = ContractedShellPair.create ~cutoff shell_a shell_b
and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
let shell_p = Csp.create ~cutoff shell_a shell_b
and shell_q = Csp.create ~cutoff shell_c shell_d
in
contracted_class_shell_pairs ~zero_m shell_p shell_q

21
Basis/TwoElectronRRVectorized.ml
View File

@ -3,6 +3,7 @@ open Lacaml.D
open Bigarray
open Powers
open Coordinate
open Contracted_shell_type
let cutoff = Constants.cutoff
let cutoff2 = cutoff *. cutoff
@ -565,8 +566,8 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Quartet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d))
(shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom))
in
let contracted_class =
@ -576,8 +577,8 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
let monocentric =
shell_p.ContractedShellPair.monocentric &&
shell_q.ContractedShellPair.monocentric &&
Contracted_shell.center shell_p.ContractedShellPair.shell_a =
Contracted_shell.center shell_q.ContractedShellPair.shell_a
shell_p.ContractedShellPair.shell_a.center =
shell_q.ContractedShellPair.shell_a.center
in
(** Screening on the product of coefficients *)
@ -620,8 +621,8 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
(* Compute all integrals in the shell for each pair of significant shell pairs *)
begin
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d) with
match (shell_a.totAngMom, shell_b.totAngMom,
shell_c.totAngMom, shell_d.totAngMom) with
| Angular_momentum.(S,S,S,S) ->
contracted_class.(0) <-
begin
@ -681,9 +682,9 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
in
let expo_b =
Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
Array.map (fun shell_ab -> shell_b.expo.(shell_ab.ShellPair.j)) sp
and expo_d =
Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
Array.map (fun shell_cd -> shell_d.expo.(shell_cd.ShellPair.j)) sq
in
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
@ -716,7 +717,7 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
Array.init np (fun ab ->
let shell_ab = sp.(ab) in
let cpa =
shell_ab.ShellPair.center |- Contracted_shell.center shell_a
shell_ab.ShellPair.center |- shell_a.center
in
match xyz with
| 0 -> Coordinate.get X cpa;
@ -735,7 +736,7 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
Array.init nq (fun cd ->
let shell_cd = sq.(cd) in
let cqc =
shell_cd.ShellPair.center |- Contracted_shell.center shell_c
shell_cd.ShellPair.center |- shell_c.center
in
match xyz with
| 0 -> Coordinate.get X cqc;

2
Utils/Util.ml
View File

@ -3,8 +3,8 @@ external erf_float : float -> float = "erf_float_bytecode" "erf_float" [@@unboxe
external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float" [@@unboxed] [@@noalloc]
external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float" [@@unboxed] [@@noalloc]
open Lacaml.D
open Constants
open Lacaml.D
let factmax = 150