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Fixed f12 integrals
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342
Basis/F12.ml
342
Basis/F12.ml
@ -1,4 +1,342 @@
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(** Two-electron integrals over Slater geminals via a fit using Gaussian geminals.
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(** Two electron integral functor for operators that are separable among %{ $(x,y,z)$ %}.
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It is parameterized by the [zero_m] function.
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*)
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include TwoElectronIntegralsSeparable
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open Constants
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let cutoff = integrals_cutoff
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module Bs = Basis
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module Cs = ContractedShell
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module Csp = ContractedShellPair
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module Cspc = ContractedShellPairCouple
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module Fis = FourIdxStorage
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include FourIdxStorage
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(** Exponent of the geminal *)
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let expo_s = 1.0
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(** Coefficients and exponents of the Gaussian fit of the Slater Geminal*)
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let coef_g =
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[| 0.3144 ; 0.3037 ; 0.1681 ; 0.09811 ; 0.06024 ; 0.03726 |]
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let expo_sg_inv =
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Array.map (fun x -> 1. /. (x *. expo_s *. expo_s))
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[| 0.2209 ; 1.004 ; 3.622 ; 12.16 ; 45.87 ; 254.4 |]
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(*
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Fit of 1/r:
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let coef_g = [|
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841.88478132 ; 70.590185207 ; 18.3616020768 ; 7.2608642093 ;
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3.57483416444 ; 2.01376031082 ; 1.24216542801 ; 0.81754348620 ;
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0.564546514023 ; 0.404228610699 ; 0.297458536575 ; 0.223321219537 ;
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0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ;
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0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ;
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|]
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let expo_sg_inv =
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Array.map (fun x -> 1. /. (x *. expo_s *. expo_s))
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[| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ;
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47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ;
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2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ;
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0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ;
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0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |]
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*)
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let class_of_contracted_shell_pair_couple shell_pair_couple =
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F12RR.contracted_class_shell_pair_couple
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expo_sg_inv coef_g shell_pair_couple
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module Zero_m = struct
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let name = "F12"
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end
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let filter_contracted_shell_pairs ?(cutoff=integrals_cutoff) shell_pairs =
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List.map (fun pair ->
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match Cspc.make ~cutoff pair pair with
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| Some cspc ->
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let cls = class_of_contracted_shell_pair_couple cspc in
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(pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
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(* TODO \sum_k |coef_k * integral_k| *)
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| None -> (pair, -1.)
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) shell_pairs
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|> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
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|> List.map fst
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(* TODO
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let filter_contracted_shell_pair_couples
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?(cutoff=integrals_cutoff) shell_pair_couples =
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List.map (fun pair ->
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let cls =
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class_of_contracted_shell_pairs pair pair
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in
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(pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
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) shell_pairs
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|> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
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|> List.map fst
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*)
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let store_class basis ?(cutoff=integrals_cutoff) data contracted_shell_pair_couple cls =
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let to_powers x =
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let open Zkey in
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match to_powers x with
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| Three x -> x
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| _ -> assert false
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in
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let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple
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and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple
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in
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let s =
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Overlap.of_basis basis
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|> Overlap.matrix
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in
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let lambda_inv = 1. /. expo_s in
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Array.iteri (fun i_c powers_i ->
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let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in
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let xi = to_powers powers_i in
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Array.iteri (fun j_c powers_j ->
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let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in
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let xj = to_powers powers_j in
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Array.iteri (fun k_c powers_k ->
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let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in
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let xk = to_powers powers_k in
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Array.iteri (fun l_c powers_l ->
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let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in
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let xl = to_powers powers_l in
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let key = Zkey.of_powers_twelve xi xj xk xl in
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let value = Zmap.find cls key in
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lambda_inv *. s.{i_c,j_c} *. s.{k_c,l_c} -. value
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|> set_chem data i_c j_c k_c l_c
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) (Cs.zkey_array (Csp.shell_b shell_q))
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) (Cs.zkey_array (Csp.shell_a shell_q))
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) (Cs.zkey_array (Csp.shell_b shell_p))
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) (Cs.zkey_array (Csp.shell_a shell_p))
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let of_basis_serial basis =
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let n = Bs.size basis
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and shell = Bs.contracted_shells basis
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in
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let eri_array =
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Fis.create ~size:n `Dense
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(*
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Fis.create ~size:n `Sparse
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*)
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in
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let t0 = Unix.gettimeofday () in
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let shell_pairs =
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Csp.of_contracted_shell_array shell
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|> filter_contracted_shell_pairs ~cutoff
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in
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Printf.printf "%d significant shell pairs computed in %f seconds\n"
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(List.length shell_pairs) (Unix.gettimeofday () -. t0);
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let t0 = Unix.gettimeofday () in
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let ishell = ref 0 in
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List.iter (fun shell_p ->
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let () =
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if (Cs.index (Csp.shell_a shell_p) > !ishell) then
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(ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ())
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in
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let sp =
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Csp.shell_pairs shell_p
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in
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try
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List.iter (fun shell_q ->
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let () =
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if Cs.index (Csp.shell_a shell_q) >
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Cs.index (Csp.shell_a shell_p) then
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raise Exit
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in
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let sq = Csp.shell_pairs shell_q in
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let cspc =
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if Array.length sp < Array.length sq then
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Cspc.make ~cutoff shell_p shell_q
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else
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Cspc.make ~cutoff shell_q shell_p
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in
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match cspc with
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| Some cspc ->
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let cls =
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class_of_contracted_shell_pair_couple cspc
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in
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store_class basis ~cutoff eri_array cspc cls
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| None -> ()
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) shell_pairs
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with Exit -> ()
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) shell_pairs ;
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Printf.printf "Computed ERIs in %f seconds\n%!" (Unix.gettimeofday () -. t0);
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eri_array
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(* Parallel functions *)
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let of_basis_parallel basis =
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let n = Bs.size basis
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and shell = Bs.contracted_shells basis
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in
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let store_class_parallel
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?(cutoff=integrals_cutoff) contracted_shell_pair_couple cls =
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let to_powers x =
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let open Zkey in
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match to_powers x with
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| Three x -> x
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| _ -> assert false
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in
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let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple
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and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple
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in
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let result = ref [] in
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Array.iteri (fun i_c powers_i ->
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let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in
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let xi = to_powers powers_i in
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Array.iteri (fun j_c powers_j ->
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let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in
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let xj = to_powers powers_j in
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Array.iteri (fun k_c powers_k ->
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let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in
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let xk = to_powers powers_k in
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Array.iteri (fun l_c powers_l ->
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let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in
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let xl = to_powers powers_l in
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let key = Zkey.of_powers_twelve xi xj xk xl in
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let value = Zmap.find cls key in
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result := (i_c, j_c, k_c, l_c, value) :: !result
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) (Cs.zkey_array (Csp.shell_b shell_q))
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) (Cs.zkey_array (Csp.shell_a shell_q))
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) (Cs.zkey_array (Csp.shell_b shell_p))
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) (Cs.zkey_array (Csp.shell_a shell_p));
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!result
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in
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let t0 = Unix.gettimeofday () in
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let shell_pairs =
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Csp.of_contracted_shell_array shell
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|> filter_contracted_shell_pairs ~cutoff
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in
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if Parallel.master then
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Printf.printf "%d significant shell pairs computed in %f seconds\n"
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(List.length shell_pairs) (Unix.gettimeofday () -. t0);
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let t0 = Unix.gettimeofday () in
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let ishell = ref max_int in
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let input_stream = Stream.of_list (List.rev shell_pairs) in
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let f shell_p =
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let () =
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if Parallel.rank < 2 && Cs.index (Csp.shell_a shell_p) < !ishell then
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(ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ())
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in
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let sp =
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Csp.shell_pairs shell_p
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in
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let result = ref [] in
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try
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List.iter (fun shell_q ->
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let () =
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if Cs.index (Csp.shell_a shell_q) >
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Cs.index (Csp.shell_a shell_p) then
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raise Exit
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in
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let sq = Csp.shell_pairs shell_q in
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let cspc =
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if Array.length sp < Array.length sq then
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Cspc.make ~cutoff shell_p shell_q
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else
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Cspc.make ~cutoff shell_q shell_p
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in
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match cspc with
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| Some cspc ->
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let cls =
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class_of_contracted_shell_pair_couple cspc
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in
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result := (store_class_parallel ~cutoff cspc cls) :: !result;
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| None -> ()
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) shell_pairs;
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raise Exit
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with Exit -> List.concat !result |> Array.of_list
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in
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let eri_array =
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if Parallel.master then
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Fis.create ~size:n `Dense
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else
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Fis.create ~size:0 `Dense
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in
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let s =
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Overlap.of_basis basis
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|> Overlap.matrix
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in
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let lambda_inv = 1. /. expo_s in
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Farm.run ~ordered:false ~f input_stream
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|> Stream.iter (fun l ->
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Array.iter (fun (i_c,j_c,k_c,l_c,value) ->
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lambda_inv *. s.{i_c,j_c} *. s.{k_c,l_c} -. value
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|> set_chem eri_array i_c j_c k_c l_c) l);
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if Parallel.master then
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Printf.printf
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"Computed %s Integrals in parallel in %f seconds\n%!" Zero_m.name (Unix.gettimeofday () -. t0);
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Parallel.broadcast (lazy eri_array)
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let of_basis =
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match Parallel.size with
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| 1 -> of_basis_serial
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| _ -> of_basis_parallel
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117
CI/CI.ml
117
CI/CI.ml
@ -410,14 +410,11 @@ let make ?(n_states=1) det_space =
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let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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list_holes1 list_particles1 ?(unique=true)
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list_holes2 list_particles2 is_internal
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list_holes list_particles ?(unique=true) is_internal
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i_o1_alfa alfa_o2_i w_alfa psi0 =
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let list_holes1 = Array.of_list list_holes1 in
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let list_particles1 = Array.of_list list_particles1 in
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let list_holes2 = Array.of_list list_holes2 in
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let list_particles2 = Array.of_list list_particles2 in
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let list_holes = Array.of_list list_holes in
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let list_particles = Array.of_list list_particles in
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let psi0 =
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let stream =
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@ -473,12 +470,8 @@ let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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accu +. coef.{1} *. (i_o1_alfa det alfa)) 0. psi_filtered
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in
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let alfa_h_psi =
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if symmetric then
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psi_h_alfa
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else
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fun alfa ->
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List.fold_left (fun accu (det, coef) ->
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let alfa_h_psi alfa =
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List.fold_left (fun accu (det, coef) ->
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(* Single state here *)
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accu +. coef.{1} *. (alfa_o2_i alfa det)) 0. psi_filtered
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in
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@ -529,12 +522,12 @@ let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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accu
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else
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accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
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) 0. list_holes1
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) 0. list_particles1
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) 0. list_holes
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) 0. list_particles
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in
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accu +. single +. double
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) 0. list_holes2
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) 0. list_particles2
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) 0. list_holes
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) 0. list_particles
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) 0. [ Spin.Alfa ; Spin.Beta ]
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in
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@ -563,13 +556,13 @@ let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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accu
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else
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accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
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) 0. list_holes1
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) 0. list_particles1
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) 0. list_holes
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) 0. list_particles
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in
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accu +. double_ab
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) 0. list_holes2
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) 0. list_particles2
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) 0. list_holes
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) 0. list_particles
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in
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same_spin +. opposite_spin
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in
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@ -580,6 +573,68 @@ let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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let second_order_sum2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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list_holes list_particles i_o1_alfa e0 psi0 =
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let psi0 =
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let stream =
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Ds.determinant_stream det_space
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in
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Array.init (Ds.size det_space) (fun i ->
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(Stream.next stream), (Mat.copy_row psi0 (i+1)) )
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in
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let determinants =
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Ds.determinants_array det_space
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|> Array.to_list
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|> List.map (fun det_i ->
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[ Spin.Alfa ; Spin.Beta ]
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|> List.map (fun spin ->
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List.map (fun particle ->
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List.map (fun hole ->
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[ [ Determinant.single_excitation spin hole particle det_i ] ;
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List.map (fun particle' ->
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List.map (fun hole' ->
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Determinant.double_excitation
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spin hole particle
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spin hole' particle' det_i
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) list_holes
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) list_particles
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|> List.concat
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;
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List.map (fun particle' ->
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List.map (fun hole' ->
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Determinant.double_excitation
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spin hole particle
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(Spin.other spin) hole' particle' det_i
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) list_holes
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) list_particles
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|> List.concat
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]
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|> List.concat
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) list_holes
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) list_particles
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|> List.concat
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)
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|> List.concat
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)
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|> List.concat
|
||||
|> List.concat
|
||||
|> List.filter (fun alfa -> not (Determinant.is_none alfa))
|
||||
|> List.sort_uniq compare
|
||||
in
|
||||
|
||||
List.fold_left (fun accu alfa ->
|
||||
let alfa_o2 = i_o1_alfa alfa in
|
||||
let a_h_psi =
|
||||
Array.fold_left (fun accu (det,ci) -> ci.{1} *. (alfa_o2 det)) 0. psi0
|
||||
in
|
||||
accu +. (a_h_psi *. a_h_psi) /. (e0 -. (alfa_o2 alfa))
|
||||
) 0. determinants
|
||||
|
||||
|
||||
|
||||
|
||||
let is_internal det_space =
|
||||
let m l =
|
||||
@ -608,7 +663,7 @@ let is_internal det_space =
|
||||
Z.logand neg_active_mask beta = occ_mask
|
||||
|
||||
|
||||
let pt2_en ci =
|
||||
let _pt2_en ci =
|
||||
|
||||
let mo_basis = Ds.mo_basis ci.det_space in
|
||||
let psi0, e0 = Parallel.broadcast ci.eigensystem in
|
||||
@ -668,11 +723,25 @@ let pt2_en ci =
|
||||
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
||||
in
|
||||
|
||||
second_order_sum ci list_holes list_particles list_holes list_particles
|
||||
second_order_sum ci list_holes list_particles
|
||||
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
||||
|> List.fold_left (+.) 0.
|
||||
|
||||
|
||||
let pt2_en ci =
|
||||
|
||||
let mo_basis = Ds.mo_basis ci.det_space in
|
||||
let psi0, e0 = Parallel.broadcast ci.eigensystem in
|
||||
|
||||
let i_o1_alfa = h_ij mo_basis in
|
||||
|
||||
let mo_class = mo_class ci in
|
||||
let list_holes = List.concat
|
||||
[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
|
||||
and list_particles = List.concat
|
||||
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
||||
in
|
||||
second_order_sum2 ci list_holes list_particles i_o1_alfa e0.{1} psi0
|
||||
|
||||
|
||||
|
||||
@ -701,7 +770,7 @@ let pt2_mp ci =
|
||||
in
|
||||
|
||||
let psi0, _ = Parallel.broadcast ci.eigensystem in
|
||||
second_order_sum ci list_holes list_particles list_holes list_particles
|
||||
second_order_sum ci list_holes list_particles
|
||||
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
||||
|> List.fold_left (+.) 0.
|
||||
|
||||
@ -722,7 +791,7 @@ let variance ci =
|
||||
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
||||
in
|
||||
|
||||
second_order_sum ci list_holes list_particles list_holes list_particles
|
||||
second_order_sum ci list_holes list_particles
|
||||
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
||||
|> List.fold_left (+.) 0.
|
||||
|
||||
|
||||
49
CI/F12CI.ml
49
CI/F12CI.ml
@ -1,6 +1,3 @@
|
||||
let debug s =
|
||||
Printf.printf "%s\n%!" s;
|
||||
|
||||
open Lacaml.D
|
||||
|
||||
type t =
|
||||
@ -43,13 +40,22 @@ let h_ij mo_basis ki kj =
|
||||
|> List.hd
|
||||
|
||||
|
||||
let f_ij mo_basis ki kj =
|
||||
let f_ij gamma mo_basis ki kj =
|
||||
let integrals =
|
||||
List.map (fun f -> f mo_basis)
|
||||
[ f12_integrals ]
|
||||
in
|
||||
CIMatrixElement.make integrals ki kj
|
||||
|> List.hd
|
||||
let integral =
|
||||
CIMatrixElement.make integrals ki kj
|
||||
|> List.hd
|
||||
in
|
||||
gamma *. integral
|
||||
(*
|
||||
match Determinant.degrees ki kj with
|
||||
| (2,0)
|
||||
| (0,2) -> 0.5 *. gamma *. integral
|
||||
| _ -> gamma *. integral
|
||||
*)
|
||||
|
||||
|
||||
let is_internal det_space =
|
||||
@ -75,9 +81,7 @@ let is_internal det_space =
|
||||
Z.logand aux_mask beta = Z.zero
|
||||
|
||||
|
||||
let dressing_vector aux_basis f12_amplitudes ci =
|
||||
|
||||
debug "Computing dressing vector";
|
||||
let dressing_vector gamma aux_basis f12_amplitudes ci =
|
||||
|
||||
(*
|
||||
let i_o1_alfa = h_ij aux_basis in
|
||||
@ -93,9 +97,6 @@ debug "Computing dressing vector";
|
||||
and list_particles1 = List.concat
|
||||
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ; MOClass.auxiliary_mos mo_class ]
|
||||
in
|
||||
(*
|
||||
Util.debug_matrix "f12 amplitudes" f12_amplitudes;
|
||||
*)
|
||||
(* Single state here *)
|
||||
let result =
|
||||
CI.second_order_sum ci list_holes list_particles1 list_holes list_particles2
|
||||
@ -130,7 +131,7 @@ Util.debug_matrix "f12 amplitudes" f12_amplitudes;
|
||||
let m_F_aux =
|
||||
Array.map (fun ki ->
|
||||
Array.map (fun kj ->
|
||||
f_ij aux_basis ki kj
|
||||
f_ij gamma aux_basis ki kj
|
||||
) out_dets
|
||||
) in_dets
|
||||
|> Mat.of_array
|
||||
@ -148,7 +149,7 @@ Util.debug_matrix "f12 amplitudes" f12_amplitudes;
|
||||
|
||||
let make ~simulation ?(threshold=1.e-12) ?(frozen_core=true) ~mo_basis ~aux_basis_filename () =
|
||||
|
||||
let gamma = 1.0 in
|
||||
let gamma = 0.5 in
|
||||
|
||||
let mo_num = MOBasis.size mo_basis in
|
||||
|
||||
@ -188,24 +189,19 @@ let make ~simulation ?(threshold=1.e-12) ?(frozen_core=true) ~mo_basis ~aux_basi
|
||||
(* While in a sequential region, initiate the parallel
|
||||
4-idx transformation to avoid nested parallel jobs
|
||||
*)
|
||||
debug "Four-idx transform of f12 intergals";
|
||||
ignore @@ MOBasis.f12_ints aux_basis;
|
||||
|
||||
let f = fun ki kj ->
|
||||
if ki <> kj then
|
||||
gamma *. (f_ij aux_basis ki kj)
|
||||
(f_ij gamma aux_basis ki kj)
|
||||
else
|
||||
1. +. gamma *. (f_ij aux_basis ki kj)
|
||||
1. +. (f_ij gamma aux_basis ki kj)
|
||||
in
|
||||
let m_F =
|
||||
CI.create_matrix_spin f det_space
|
||||
|> Lazy.force
|
||||
in
|
||||
fun ci_coef ->
|
||||
(*
|
||||
Util.debug_matrix "F" (Matrix.to_mat m_F);
|
||||
debug "Solving linear system";
|
||||
*)
|
||||
Matrix.ax_eq_b m_F (Matrix.dense_of_mat ci_coef)
|
||||
|> Matrix.to_mat
|
||||
in
|
||||
@ -222,14 +218,10 @@ debug "Solving linear system";
|
||||
let m_H =
|
||||
Lazy.force ci.CI.m_H
|
||||
in
|
||||
(*
|
||||
Util.debug_matrix "H" (Matrix.to_mat m_H);
|
||||
*)
|
||||
|
||||
let rec iteration ?(state=1) psi =
|
||||
debug "Iteration";
|
||||
let delta =
|
||||
dressing_vector aux_basis (f12_amplitudes psi) ci
|
||||
dressing_vector gamma aux_basis (f12_amplitudes psi) ci
|
||||
in
|
||||
|
||||
let f = 1.0 /. psi.{1,1} in
|
||||
@ -273,7 +265,9 @@ TODO SINGLE STATE HERE
|
||||
in
|
||||
|
||||
let eigenvectors, eigenvalues =
|
||||
Parallel.broadcast (lazy (
|
||||
Davidson.make ~threshold:1.e-6 ~guess:psi ~n_states diagonal matrix_prod
|
||||
))
|
||||
in
|
||||
|
||||
let conv =
|
||||
@ -281,7 +275,8 @@ TODO SINGLE STATE HERE
|
||||
(Mat.to_col_vecs psi).(0)
|
||||
(Mat.to_col_vecs eigenvectors).(0) )
|
||||
in
|
||||
Printf.printf "Convergence : %e %f\n" conv (eigenvalues.{1} +. e_shift);
|
||||
if Parallel.master then
|
||||
Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{1} +. e_shift);
|
||||
|
||||
if conv > threshold then
|
||||
iteration eigenvectors
|
||||
|
||||
Loading…
Reference in New Issue
Block a user