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Generalized F12

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This commit is contained in:
Anthony Scemama 2019-03-26 10:38:50 +01:00
parent 97eacaba23
commit 0e34cde735
8 changed files with 133 additions and 110 deletions
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14
Basis/AOBasis.ml
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@ -24,7 +24,7 @@ let cartesian t = t.cartesian
let make ~cartesian ~basis nuclei = let make ~cartesian ~basis ?f12 nuclei =
let overlap = lazy ( let overlap = lazy (
Overlap.of_basis basis Overlap.of_basis basis
@ -46,9 +46,15 @@ let make ~cartesian ~basis nuclei =
ERI.of_basis basis ERI.of_basis basis
) in ) in
let f12_ints = lazy ( let f12_ints = lazy (
F12.of_basis basis let f12 =
) in match f12 with
| Some f12 -> f12
| None -> failwith "Missing f12 factor"
in
F12.of_basis f12 basis
)
in
{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ; { basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ;
cartesian ; cartesian ;

2
Basis/AOBasis.mli
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@ -31,7 +31,7 @@ val cartesian : t -> bool
(** {1 Creators} *) (** {1 Creators} *)
val make : cartesian:bool -> basis:Basis.t -> Nuclei.t -> t val make : cartesian:bool -> basis:Basis.t -> ?f12:F12.f12_factor -> Nuclei.t -> t
(** Creates the data structure for atomic orbitals from a {Basis.t} and the (** Creates the data structure for atomic orbitals from a {Basis.t} and the
molecular geometry {Nuclei.t} *) molecular geometry {Nuclei.t} *)

164
Basis/F12.ml
View File

@ -14,89 +14,86 @@ module Fis = FourIdxStorage
include FourIdxStorage include FourIdxStorage
(* type f12_factor =
type gaussian_geminal =
{ {
expo_s : float ; expo_s : float ;
coef_g : coef_g : float array;
*) expo_sg : float array;
(** Exponent of the geminal *) expo_sg_inv : float array;
let expo_s = 1.0 }
let make_gaussian_corr_factor expo_s coef_g expo_sg =
let expo_sg_inv =
Array.map (fun x -> 1. /. (x *. expo_s *. expo_s)) expo_sg
in
{
expo_s ; coef_g ; expo_sg ; expo_sg_inv
}
(** Slater geminal *) (* exp (-expo_s r) *)
let gaussian_geminal expo_s =
(** Coefficients and exponents of the Gaussian fit of the Slater Geminal*) let coef_g =
let coef_g = [| 0.3144 ; 0.3037 ; 0.1681 ; 0.09811 ; 0.06024 ; 0.03726 |];
[| 0.3144 ; 0.3037 ; 0.1681 ; 0.09811 ; 0.06024 ; 0.03726 |] and expo_sg =
[| 0.2209 ; 1.004 ; 3.622 ; 12.16 ; 45.87 ; 254.4 |];
let expo_sg_inv = in
Array.map (fun x -> 1. /. (x *. expo_s *. expo_s)) make_gaussian_corr_factor expo_s coef_g expo_sg
[| 0.2209 ; 1.004 ; 3.622 ; 12.16 ; 45.87 ; 254.4 |]
(*
(** r12 * Slater *)
(** Coefficients and exponents of the Gaussian fit of the Slater Geminal*) (** r12 * exp ( -expo_s * r) *)
let coef_g = let gaussian_geminal_times_r12 expo_s =
let coef_g =
[| 0.2454 ; 0.2938 ; 0.1815 ; 0.11281 ; 0.07502 ; 0.05280 |] [| 0.2454 ; 0.2938 ; 0.1815 ; 0.11281 ; 0.07502 ; 0.05280 |]
and expo_sg =
let expo_sg_inv =
Array.map (fun x -> 1. /. (x *. expo_s *. expo_s))
[| 0.1824 ; 0.7118; 2.252 ; 6.474 ; 19.66 ; 77.92 |] [| 0.1824 ; 0.7118; 2.252 ; 6.474 ; 19.66 ; 77.92 |]
*) in make_gaussian_corr_factor expo_s coef_g expo_sg
(*
(** Coefficients and exponents of the Gaussian fit of the Slater Geminal*)
let coef_g =
[|
-3.4793465193721626604883567779324948787689208984375 ;
-0.00571703486454788484955047422886309504974633455276489257812 ;
4.14878218728681513738365538301877677440643310546875 ;
0.202874298181392742623785352407139725983142852783203125 ;
0.0819187742387294803858566183407674543559551239013671875 ;
0.04225945671351955673644695821167260874062776565551757812 ;
|]
let expo_sg_inv =
Array.map (fun x -> 1. /. (x *. expo_s *. expo_s))
[|
0.63172472556807146570889699432882480323314666748046875;
26.3759196683467962429858744144439697265625;
0.63172102793029016876147352377302013337612152099609375;
7.08429025944207335641067402320913970470428466796875;
42.4442841447001910637482069432735443115234375;
391.44036073596890901171718724071979522705078125 ;
|]
*)
(* (* exp (-expo_s r) *)
let gaussian_geminal' expo_s =
Fit of 1/r: let coef_g =
[|
let coef_g = [| -3.4793465193721626604883567779324948787689208984375 ;
841.88478132 ; 70.590185207 ; 18.3616020768 ; 7.2608642093 ; -0.00571703486454788484955047422886309504974633455276489257812 ;
3.57483416444 ; 2.01376031082 ; 1.24216542801 ; 0.81754348620 ; 4.14878218728681513738365538301877677440643310546875 ;
0.564546514023 ; 0.404228610699 ; 0.297458536575 ; 0.223321219537 ; 0.202874298181392742623785352407139725983142852783203125 ;
0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ; 0.0819187742387294803858566183407674543559551239013671875 ;
0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ; 0.04225945671351955673644695821167260874062776565551757812 ;
|] |]
and expo_sg =
let expo_sg_inv = [|
Array.map (fun x -> 1. /. (x *. expo_s *. expo_s)) 0.63172472556807146570889699432882480323314666748046875;
[| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ; 26.3759196683467962429858744144439697265625;
47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ; 0.63172102793029016876147352377302013337612152099609375;
2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ; 7.08429025944207335641067402320913970470428466796875;
0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ; 42.4442841447001910637482069432735443115234375;
0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |] 391.44036073596890901171718724071979522705078125 ;
*) |]
in make_gaussian_corr_factor expo_s coef_g expo_sg
let one_over_r =
let coef_g = [|
841.88478132 ; 70.590185207 ; 18.3616020768 ; 7.2608642093 ;
3.57483416444 ; 2.01376031082 ; 1.24216542801 ; 0.81754348620 ;
0.564546514023 ; 0.404228610699 ; 0.297458536575 ; 0.223321219537 ;
0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ;
0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ;
|]
and expo_sg_inv =
[| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ;
47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ;
2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ;
0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ;
0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |]
in make_gaussian_corr_factor 1.0 coef_g expo_sg_inv
let class_of_contracted_shell_pair_couple shell_pair_couple =
F12RR.contracted_class_shell_pair_couple
expo_sg_inv coef_g shell_pair_couple
@ -105,13 +102,16 @@ module Zero_m = struct
let name = "F12" let name = "F12"
end end
let class_of_contracted_shell_pair_couple f12 shell_pair_couple =
F12RR.contracted_class_shell_pair_couple
f12.expo_sg_inv f12.coef_g shell_pair_couple
let filter_contracted_shell_pairs ?(cutoff=integrals_cutoff) shell_pairs = let filter_contracted_shell_pairs f12 ?(cutoff=integrals_cutoff) shell_pairs =
List.map (fun pair -> List.map (fun pair ->
match Cspc.make ~cutoff pair pair with match Cspc.make ~cutoff pair pair with
| Some cspc -> | Some cspc ->
let cls = class_of_contracted_shell_pair_couple cspc in let cls = class_of_contracted_shell_pair_couple f12 cspc in
(pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. ) (pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
(* TODO \sum_k |coef_k * integral_k| *) (* TODO \sum_k |coef_k * integral_k| *)
| None -> (pair, -1.) | None -> (pair, -1.)
@ -152,7 +152,7 @@ let store_class basis ?(cutoff=integrals_cutoff) data contracted_shell_pair_coup
Overlap.of_basis basis Overlap.of_basis basis
|> Overlap.matrix |> Overlap.matrix
in in
let lambda_inv = 1. /. expo_s in let lambda_inv = 1. /. f12.expo_s in
*) *)
Array.iteri (fun i_c powers_i -> Array.iteri (fun i_c powers_i ->
let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in
@ -183,7 +183,7 @@ let store_class basis ?(cutoff=integrals_cutoff) data contracted_shell_pair_coup
let of_basis_serial basis = let of_basis_serial f12 basis =
let n = Bs.size basis let n = Bs.size basis
and shell = Bs.contracted_shells basis and shell = Bs.contracted_shells basis
@ -200,7 +200,7 @@ let of_basis_serial basis =
let shell_pairs = let shell_pairs =
Csp.of_contracted_shell_array shell Csp.of_contracted_shell_array shell
|> filter_contracted_shell_pairs ~cutoff |> filter_contracted_shell_pairs f12 ~cutoff
in in
Printf.printf "%d significant shell pairs computed in %f seconds\n" Printf.printf "%d significant shell pairs computed in %f seconds\n"
@ -238,7 +238,7 @@ let of_basis_serial basis =
match cspc with match cspc with
| Some cspc -> | Some cspc ->
let cls = let cls =
class_of_contracted_shell_pair_couple cspc class_of_contracted_shell_pair_couple f12 cspc
in in
store_class basis ~cutoff eri_array cspc cls store_class basis ~cutoff eri_array cspc cls
| None -> () | None -> ()
@ -258,7 +258,7 @@ let of_basis_serial basis =
let of_basis_parallel basis = let of_basis_parallel f12 basis =
let n = Bs.size basis let n = Bs.size basis
and shell = Bs.contracted_shells basis and shell = Bs.contracted_shells basis
@ -306,7 +306,7 @@ let of_basis_parallel basis =
let shell_pairs = let shell_pairs =
Csp.of_contracted_shell_array shell Csp.of_contracted_shell_array shell
|> filter_contracted_shell_pairs ~cutoff |> filter_contracted_shell_pairs f12 ~cutoff
in in
if Parallel.master then if Parallel.master then
@ -348,7 +348,7 @@ let of_basis_parallel basis =
match cspc with match cspc with
| Some cspc -> | Some cspc ->
let cls = let cls =
class_of_contracted_shell_pair_couple cspc class_of_contracted_shell_pair_couple f12 cspc
in in
result := (store_class_parallel ~cutoff cspc cls) :: !result; result := (store_class_parallel ~cutoff cspc cls) :: !result;
| None -> () | None -> ()
@ -369,7 +369,7 @@ let of_basis_parallel basis =
Overlap.of_basis basis Overlap.of_basis basis
|> Overlap.matrix |> Overlap.matrix
in in
let lambda_inv = 1. /. expo_s in let lambda_inv = 1. /. f12.expo_s in
*) *)
Farm.run ~ordered:false ~f input_stream Farm.run ~ordered:false ~f input_stream
|> Stream.iter (fun l -> |> Stream.iter (fun l ->
@ -377,7 +377,7 @@ let of_basis_parallel basis =
(* (*
lambda_inv *. (s.{i_c,j_c} *. s.{k_c,l_c} -. value) lambda_inv *. (s.{i_c,j_c} *. s.{k_c,l_c} -. value)
*) *)
value value
|> set_chem eri_array i_c j_c k_c l_c) l); |> set_chem eri_array i_c j_c k_c l_c) l);
if Parallel.master then if Parallel.master then

22
CI/F12CI.ml
View File

@ -2,7 +2,6 @@ open Lacaml.D
type t = type t =
{ {
gamma : float;
mo_basis : MOBasis.t ; mo_basis : MOBasis.t ;
aux_basis : MOBasis.t ; aux_basis : MOBasis.t ;
det_space : DeterminantSpace.t ; det_space : DeterminantSpace.t ;
@ -55,12 +54,6 @@ let f_ij mo_basis ki kj =
in in
CIMatrixElement.make integrals ki kj CIMatrixElement.make integrals ki kj
|> List.hd |> List.hd
(*
match Determinant.degrees ki kj with
| (2,0)
| (0,2) -> 0.5 *. gamma *. integral
| _ -> gamma *. integral
*)
let is_internal det_space = let is_internal det_space =
@ -97,7 +90,7 @@ let is_internal det_space =
Bitstring.logand aux_mask beta |> Bitstring.is_zero Bitstring.logand aux_mask beta |> Bitstring.is_zero
let dressing_vector gamma ~frozen_core aux_basis f12_amplitudes ci = let dressing_vector ~frozen_core aux_basis f12_amplitudes ci =
(* (*
let i_o1_alfa = h_ij aux_basis in let i_o1_alfa = h_ij aux_basis in
@ -215,8 +208,7 @@ let dressing_vector gamma ~frozen_core aux_basis f12_amplitudes ci =
let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename () = let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename () =
let gamma = -0.5 /. F12.expo_s in let f12 = Util.of_some @@ Simulation.f12 simulation in
let mo_num = MOBasis.size mo_basis in let mo_num = MOBasis.size mo_basis in
(* Add auxiliary basis set *) (* Add auxiliary basis set *)
@ -232,7 +224,7 @@ let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filen
general_basis ; GeneralBasis.read aux_basis_filename general_basis ; GeneralBasis.read aux_basis_filename
] ]
|> Basis.of_nuclei_and_general_basis nuclei |> Basis.of_nuclei_and_general_basis nuclei
|> Simulation.make ~charge ~multiplicity ~nuclei |> Simulation.make ~f12 ~charge ~multiplicity ~nuclei
in in
let aux_basis = let aux_basis =
@ -257,11 +249,13 @@ let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filen
*) *)
ignore @@ MOBasis.f12_ints aux_basis; ignore @@ MOBasis.f12_ints aux_basis;
let two_gamma_inv = -2. *. f12.F12.expo_s in
let f = fun ki kj -> let f = fun ki kj ->
if ki <> kj then if ki <> kj then
(f_ij aux_basis ki kj) (f_ij aux_basis ki kj)
else else
1./. gamma +. (f_ij aux_basis ki kj) two_gamma_inv +. (f_ij aux_basis ki kj)
in in
let m_F = let m_F =
CI.create_matrix_spin f det_space CI.create_matrix_spin f det_space
@ -287,7 +281,7 @@ let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filen
let rec iteration ?(state=1) psi = let rec iteration ?(state=1) psi =
let delta = let delta =
dressing_vector gamma ~frozen_core aux_basis (f12_amplitudes psi) ci dressing_vector ~frozen_core aux_basis (f12_amplitudes psi) ci
in in
let f = 1.0 /. psi.{1,1} in let f = 1.0 /. psi.{1,1} in
@ -357,6 +351,6 @@ TODO SINGLE STATE HERE
) )
in in
{ mo_basis ; aux_basis ; det_space ; ci ; eigensystem ; gamma } { mo_basis ; aux_basis ; det_space ; ci ; eigensystem }

11
Simulation.ml
View File

@ -4,6 +4,7 @@ type t = {
nuclei : Nuclei.t; nuclei : Nuclei.t;
basis : Basis.t; basis : Basis.t;
ao_basis : AOBasis.t; ao_basis : AOBasis.t;
f12 : F12.f12_factor option;
nuclear_repulsion : float; nuclear_repulsion : float;
} }
@ -13,10 +14,12 @@ let electrons t = t.electrons
let basis t = t.basis let basis t = t.basis
let ao_basis t = t.ao_basis let ao_basis t = t.ao_basis
let nuclear_repulsion t = t.nuclear_repulsion let nuclear_repulsion t = t.nuclear_repulsion
let f12 t = t.f12
let make ?cartesian:(cartesian=false) let make ?cartesian:(cartesian=false)
?multiplicity:(multiplicity=1) ?multiplicity:(multiplicity=1)
?charge:(charge=0) ?charge:(charge=0)
?f12
~nuclei ~nuclei
basis basis
= =
@ -34,7 +37,7 @@ let make ?cartesian:(cartesian=false)
in in
let ao_basis = let ao_basis =
AOBasis.make ~basis ~cartesian nuclei AOBasis.make ?f12 ~basis ~cartesian nuclei
in in
let nuclear_repulsion = let nuclear_repulsion =
@ -42,18 +45,18 @@ let make ?cartesian:(cartesian=false)
in in
{ {
charge ; basis ; nuclei ; electrons ; ao_basis ; charge ; basis ; nuclei ; electrons ; ao_basis ; f12 ;
nuclear_repulsion ; nuclear_repulsion ;
} }
let of_filenames ?(cartesian=false) ?(multiplicity=1) ?(charge=0) ~nuclei ?(aux_basis_filenames=[]) basis_filename = let of_filenames ?(cartesian=false) ?(multiplicity=1) ?(charge=0) ?f12 ~nuclei ?(aux_basis_filenames=[]) basis_filename =
let nuclei = let nuclei =
Nuclei.of_filename nuclei Nuclei.of_filename nuclei
in in
let basis = let basis =
Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filenames) Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filenames)
in in
lazy (make ~cartesian ~charge ~multiplicity ~nuclei basis) lazy (make ?f12 ~cartesian ~charge ~multiplicity ~nuclei basis)
|> Parallel.broadcast |> Parallel.broadcast

10
Simulation.mli
View File

@ -18,14 +18,18 @@ val ao_basis : t -> AOBasis.t
val nuclear_repulsion : t -> float val nuclear_repulsion : t -> float
(** Nuclear repulsion energy *) (** Nuclear repulsion energy *)
val f12 : t -> F12.f12_factor option
(** f12 correlation factor *)
(** {1 Creation} *) (** {1 Creation} *)
val make : val make :
?cartesian:bool -> ?cartesian:bool ->
?multiplicity:int -> ?charge:int -> nuclei:Nuclei.t -> Basis.t -> t ?multiplicity:int -> ?charge:int -> ?f12:F12.f12_factor ->
nuclei:Nuclei.t -> Basis.t -> t
val of_filenames : val of_filenames :
?cartesian:bool -> ?cartesian:bool ->
?multiplicity:int -> ?charge:int -> nuclei:string -> ?multiplicity:int -> ?charge:int -> ?f12:F12.f12_factor ->
?aux_basis_filenames:string list -> string -> t nuclei:string -> ?aux_basis_filenames:string list -> string -> t

2
Utils/FourIdxStorage.ml
View File

@ -358,7 +358,7 @@ let four_index_transform coef source =
Stream.of_list range_mo Stream.of_list range_mo
|> Farm.run ~f:task ~ordered:false |> Farm.run ~f:task ~ordered:false
|> Stream.iter (fun l -> |> Stream.iter (fun l ->
if Parallel.master then (Printf.eprintf "\r%d / %d%!" !n mo_num; incr n); if Parallel.master then (incr n ; Printf.eprintf "\r%d / %d%!" !n mo_num);
Array.iter (fun (alpha, beta, gamma, delta, x) -> Array.iter (fun (alpha, beta, gamma, delta, x) ->
set_chem destination alpha beta gamma delta x) l); set_chem destination alpha beta gamma delta x) l);

18
run_fci_f12.ml
View File

@ -23,6 +23,10 @@ let () =
{ short='c' ; long="charge" ; opt=Optional; { short='c' ; long="charge" ; opt=Optional;
arg=With_arg "<int>"; arg=With_arg "<int>";
doc="Total charge of the molecule. Default is 0"; } ; doc="Total charge of the molecule. Default is 0"; } ;
{ short='e' ; long="expo" ; opt=Optional;
arg=With_arg "<float>";
doc="Exponent of the Gaussian geminal"; } ;
] ]
end; end;
@ -39,6 +43,12 @@ let () =
| None -> 0 | None -> 0
in in
let expo =
match Command_line.get "expo" with
| Some x -> float_of_string x
| None -> 1.0
in
let multiplicity = let multiplicity =
match Command_line.get "multiplicity" with match Command_line.get "multiplicity" with
| Some x -> int_of_string x | Some x -> int_of_string x
@ -50,8 +60,12 @@ let () =
else Printing.ppf_dev_null else Printing.ppf_dev_null
in in
let f12 =
F12.gaussian_geminal expo
in
let simulation = let simulation =
Simulation.of_filenames ~charge ~multiplicity ~nuclei:nuclei_file basis_file Simulation.of_filenames ~f12 ~charge ~multiplicity ~nuclei:nuclei_file basis_file
in in
let hf = HartreeFock.make simulation in let hf = HartreeFock.make simulation in
@ -64,7 +78,9 @@ let () =
let fcif12 = let fcif12 =
F12CI.make ~simulation ~frozen_core:true ~mo_basis ~aux_basis_filename () F12CI.make ~simulation ~frozen_core:true ~mo_basis ~aux_basis_filename ()
in in
let ci = F12CI.ci fcif12 in let ci = F12CI.ci fcif12 in
Format.fprintf ppf "FCI energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion simulation); Format.fprintf ppf "FCI energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion simulation);
let _, e_cif12 = F12CI.eigensystem fcif12 in let _, e_cif12 = F12CI.eigensystem fcif12 in
Format.fprintf ppf "FCI-F12 energy : %20.16f@." (e_cif12.{1} +. Simulation.nuclear_repulsion simulation); Format.fprintf ppf "FCI-F12 energy : %20.16f@." (e_cif12.{1} +. Simulation.nuclear_repulsion simulation);