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QCaml/Basis/ERI.ml

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(** Electron-electron repulsion integrals *)
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open Util
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open Constants
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type t = FourIdxStorage.t
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module Am = AngularMomentum
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module As = AtomicShell
module Asp = AtomicShellPair
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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
let get_chem = Fis.get_chem
let get_phys = Fis.get_phys
let set_chem = Fis.set_chem
let set_phys = Fis.set_phys
let to_file = Fis.to_file
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let cutoff = integrals_cutoff
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(** (00|00)^m : Fundamental electron repulsion integral
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$ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
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maxm : Maximum total angular momentum
expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of
$\phi_p$ and $\phi_q$
norm_pq_sq : square of the distance between the centers of $\phi_p$
and $\phi_q$
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*)
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let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
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let exp_pq = 1. /. expo_pq_inv in
let t = norm_pq_sq *. exp_pq in
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let f = two_over_sq_pi *. (sqrt exp_pq) in
let result = boys_function ~maxm t in
let rec aux accu k = function
| 0 -> result.(k) <- result.(k) *. accu
| l ->
begin
result.(k) <- result.(k) *. accu;
let new_accu = -. accu *. exp_pq in
aux new_accu (k+1) (l-1)
end
in
aux f 0 maxm;
result
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let class_of_contracted_shell_pair_couple shell_pair_couple =
let shell_p = Cspc.shell_pair_p shell_pair_couple
and shell_q = Cspc.shell_pair_q shell_pair_couple
in
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if Array.length (Csp.shell_pairs shell_p) + (Array.length (Csp.shell_pairs shell_q)) < 4 then
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TwoElectronRR.contracted_class_shell_pair_couple ~zero_m shell_pair_couple
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else
TwoElectronRRVectorized.contracted_class_shell_pairs ~zero_m shell_p shell_q
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let filter_contracted_shell_pairs ?(cutoff=integrals_cutoff) shell_pairs =
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List.map (fun pair ->
match Cspc.make ~cutoff pair pair with
| Some cspc ->
let cls = class_of_contracted_shell_pair_couple cspc in
(pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
| None -> (pair, -1.)
) shell_pairs
|> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
|> List.map fst
(* TODO
let filter_contracted_shell_pair_couples ?(cutoff=integrals_cutoff) shell_pair_couples =
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List.map (fun pair ->
let cls =
class_of_contracted_shell_pairs pair pair
in
(pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
) shell_pairs
|> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
|> List.map fst
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*)
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let store_class ?(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
match to_powers x with
| Three x -> x
| _ -> assert false
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in
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let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple
and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple
in
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Array.iteri (fun i_c powers_i ->
let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in
let xi = to_powers powers_i in
Array.iteri (fun j_c powers_j ->
let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in
let xj = to_powers powers_j in
Array.iteri (fun k_c powers_k ->
let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in
let xk = to_powers powers_k in
Array.iteri (fun l_c powers_l ->
let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in
let xl = to_powers powers_l in
let key = Zkey.of_powers_twelve xi xj xk xl in
let value = Zmap.find cls key in
set_chem data i_c j_c k_c l_c value;
) (Cs.zkey_array (Csp.shell_b shell_q))
) (Cs.zkey_array (Csp.shell_a shell_q))
) (Cs.zkey_array (Csp.shell_b shell_p))
) (Cs.zkey_array (Csp.shell_a shell_p))
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let of_basis basis =
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let n = Bs.size basis
and shell = Bs.contracted_shells basis
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in
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let eri_array =
Fis.create ~size:n `Dense
(*
Fis.create ~size:n `Sparse
*)
in
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"
(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 () =
if (Cs.index (Csp.shell_a shell_p) > !ishell) then
(ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ())
in
let sp =
Csp.shell_pairs shell_p
in
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try
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List.iter (fun shell_q ->
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let () =
if Cs.index (Csp.shell_a shell_q) >
Cs.index (Csp.shell_a shell_p) then
raise Exit
in
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let sq = Csp.shell_pairs shell_q in
let cspc =
if Array.length sp < Array.length sq then
Cspc.make ~cutoff shell_p shell_q
else
Cspc.make ~cutoff shell_q shell_p
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in
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match cspc with
| Some cspc -> let cls = class_of_contracted_shell_pair_couple cspc in
store_class ~cutoff eri_array cspc cls
| 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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