open Util let cutoff2 = cutoff *. cutoff exception NullQuartet exception Found let at_least_one_valid arr = try Array.fold_left (fun _ x -> if (abs_float x > cutoff) then raise Found else false ) false arr with Found -> true (** Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) (totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d) (maxm, zero_m_array) (expo_b, expo_d) (expo_inv_p, expo_inv_q) (center_ab, center_cd, center_pq) coef_prod map = let ncoef = (Array.length coef_prod) in let empty = Array.make ncoef 0. in let totAngMom_a = Angular_momentum.to_int totAngMom_a and totAngMom_b = Angular_momentum.to_int totAngMom_b and totAngMom_c = Angular_momentum.to_int totAngMom_c and totAngMom_d = Angular_momentum.to_int totAngMom_d in (** Vertical recurrence relations *) let rec vrr0_v m angMom_a = function | 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2 in let f = expo_b *. (Coordinate.coord center_ab i) in Array.mapi (fun k c -> c *. expo_inv_p *. ( (Coordinate.coord center_pq.(k) i) *. zero_m_array.(k).(m+1) -. f *. zero_m_array.(k).(m) ) ) coef_prod | 0 -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod | totAngMom_a -> let key = Zkey.of_int_tuple (Zkey.Three (angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) ) in let (found, result) = try (true, Zmap.find map.(m) key) with | Not_found -> (false, let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and xyz = match angMom_a with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in am.(xyz) <- am.(xyz) - 1; amm.(xyz) <- amm.(xyz) - 2; if am.(xyz) < 0 then empty else let v1 = let f = -. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz) in if (abs_float f < cutoff) then empty else Array.mapi (fun k v1k -> f *. v1k) (vrr0_v m am (totAngMom_a-1) ) in let p1 = Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p *. (Coordinate.coord center_pq.(k) xyz) *. v2k) (vrr0_v (m+1) am (totAngMom_a-1)) in if amm.(xyz) < 0 then p1 else let f = (float_of_int am.(xyz)) *. expo_inv_p *. 0.5 in if (abs_float f < cutoff) then empty else let v1 = vrr0_v m amm (totAngMom_a-2) in let v2 = if (abs_float (f *. expo_inv_p)) < cutoff then empty else vrr0_v (m+1) amm (totAngMom_a-2) in Array.mapi (fun k _ -> p1.(k) +. f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) coef_prod ) in if not found then Zmap.add map.(m) key result; result and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c = match (totAngMom_a, totAngMom_c) with | (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod | (_,0) -> vrr0_v m angMom_a totAngMom_a | (_,_) -> let key = Zkey.of_int_tuple (Zkey.Six ((angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1), (angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1)) ) in let (found, result) = try (true, Zmap.find map.(m) key) with | Not_found -> (false, let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and xyz = match angMom_c with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in am.(xyz) <- am.(xyz) - 1; cm.(xyz) <- cm.(xyz) - 1; cmm.(xyz) <- cmm.(xyz) - 2; if cm.(xyz) < 0 then empty else let f1 = Array.mapi (fun k _ -> expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz) ) expo_inv_q in let f2 = Array.mapi (fun k _ -> expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) ) expo_inv_q in let v1 = if (at_least_one_valid f1) then vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1) else empty and v2 = if (at_least_one_valid f2) then vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) else empty in let p1 = Array.mapi (fun k _ -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k)) coef_prod in let p2 = if cmm.(xyz) < 0 then p1 else let fcm = (float_of_int cm.(xyz)) *. 0.5 in let f1 = Array.mapi (fun k _ -> fcm *. expo_inv_q.(k) ) coef_prod in let f2 = Array.mapi (fun k _ -> f1.(k) *. expo_inv_q.(k) ) coef_prod in let v1 = if (at_least_one_valid f1) then vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2) else empty in let v2 = if (at_least_one_valid f2) then vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) else empty in Array.mapi (fun k _ -> p1.(k) +. f1.(k) *. v1.(k) +. f2.(k) *. v2.(k)) coef_prod in if (am.(xyz) < 0) || (cm.(xyz) < 0) then p2 else let fa = (float_of_int angMom_a.(xyz)) *. expo_inv_p *. 0.5 in let f1 = Array.mapi (fun k _ -> fa *. expo_inv_q.(k) ) coef_prod in if (at_least_one_valid f1) then let v = vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) in Array.mapi (fun k _ -> p2.(k) -. f1.(k) *. v.(k)) coef_prod else p2 ) in if not found then Zmap.add map.(m) key result; result (** Horizontal recurrence relations *) and hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c = match totAngMom_b with | 0 -> begin match (totAngMom_a, totAngMom_c) with | (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(0)) coef_prod | (_,0) -> vrr0_v 0 angMom_a totAngMom_a | (_,_) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c end | 1 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in ap.(xyz) <- ap.(xyz) + 1; let f = Coordinate.coord center_ab xyz in let v1 = vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c in if (abs_float f < cutoff) then v1 else let v2 = vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c in Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2 | _ -> let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |] and xyz = match angMom_b with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in ap.(xyz) <- ap.(xyz) + 1; bm.(xyz) <- bm.(xyz) - 1; if (bm.(xyz) < 0) then empty else let h1 = hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c in let f = (Coordinate.coord center_ab xyz) in if (abs_float f < cutoff) then h1 else let h2 = hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2 and hrr_v angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d = match (totAngMom_b, totAngMom_d) with | (0,0) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c | (_,0) -> hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c | (_,_) -> let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |] and xyz = match angMom_d with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in cp.(xyz) <- cp.(xyz) + 1; dm.(xyz) <- dm.(xyz) - 1; let h1 = hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) and h2 = hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) in Array.mapi (fun k center_cd -> h1.(k) +. h2.(k) *. (Coordinate.coord center_cd xyz)) center_cd in hrr_v angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = let shell_a = shell_p.(0).Shell_pair.shell_a and shell_b = shell_p.(0).Shell_pair.shell_b and shell_c = shell_q.(0).Shell_pair.shell_a and shell_d = shell_q.(0).Shell_pair.shell_b in let maxm = let open Angular_momentum in (to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b) + (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d) in (* Pre-computation of integral class indices *) let class_indices = Angular_momentum.zkey_array (Angular_momentum.Quartet Contracted_shell.(totAngMom shell_a, totAngMom shell_b, totAngMom shell_c, totAngMom shell_d)) in let contracted_class = Array.make (Array.length class_indices) 0.; in (* Compute all integrals in the shell for each pair of significant shell pairs *) begin match Contracted_shell.(totAngMom shell_a, totAngMom shell_b, totAngMom shell_c, totAngMom shell_d) with | Angular_momentum.(S,S,S,S) -> contracted_class.(0) <- Array.fold_left (fun accu shell_ab -> accu +. Array.fold_left (fun accu shell_cd -> let coef_prod = shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef in (** Screening on the product of coefficients *) try if (abs_float coef_prod) < 1.e-3*.cutoff then raise NullQuartet; let expo_pq_inv = shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv in let center_pq = Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.center) in let norm_pq_sq = Coordinate.dot center_pq center_pq in let zero_m_array = zero_m ~maxm ~expo_pq_inv ~norm_pq_sq in accu +. coef_prod *. zero_m_array.(0) with NullQuartet -> accu ) 0. shell_q ) 0. shell_p | _ -> Array.iter (fun shell_ab -> let b = shell_ab.Shell_pair.j in let common = Array.mapi (fun idx shell_cd -> let coef_prod = shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef in let expo_pq_inv = shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv in let center_pq = Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.center) in let norm_pq_sq = Coordinate.dot center_pq center_pq in let zero_m_array = zero_m ~maxm ~expo_pq_inv ~norm_pq_sq in let d = shell_cd.Shell_pair.j in (zero_m_array, shell_cd.Shell_pair.expo_inv, Contracted_shell.expo shell_d d, shell_cd.Shell_pair.center_ab, center_pq,coef_prod,idx) ) shell_q |> Array.to_list |> List.filter (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> abs_float coef_prod >= 1.e-4 *. cutoff) |> Array.of_list in let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> zero_m_array) common and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> expo_inv ) common and d = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> d) common and center_cd = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> center_cd) common and center_pq = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> center_pq) common and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> coef_prod) common and idx = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod,idx) -> idx) common in (* Compute the integral class from the primitive shell quartet *) let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in Array.iteri (fun i key -> let a = Zkey.to_int_array Zkey.Kind_12 key in let (angMomA,angMomB,angMomC,angMomD) = ( [| a.(0) ; a.(1) ; a.(2) |], [| a.(3) ; a.(4) ; a.(5) |], [| a.(6) ; a.(7) ; a.(8) |], [| a.(9) ; a.(10) ; a.(11) |] ) in let norm = Array.map (fun shell_cd -> shell_ab.Shell_pair.norm_fun angMomA angMomB *. shell_cd.Shell_pair.norm_fun angMomC angMomD ) shell_q in let integral = hvrr_two_e_vector (angMomA, angMomB, angMomC, angMomD) (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b, Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d) (maxm, zero_m_array) (Contracted_shell.expo shell_b b, d) (shell_ab.Shell_pair.expo_inv, expo_inv) (shell_ab.Shell_pair.center_ab, center_cd, center_pq) coef_prod map |> Array.mapi (fun i x -> x *. norm.(idx.(i)) ) in let x = Array.fold_left (+.) 0. integral in contracted_class.(i) <- contracted_class.(i) +. x ) class_indices ) shell_p end; let result = Zmap.create (Array.length contracted_class) in Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; result (** 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 = Shell_pair.create_array ~cutoff shell_a shell_b and shell_q = Shell_pair.create_array ~cutoff shell_c shell_d in contracted_class_shell_pairs ~zero_m shell_p shell_q