open Util let cutoff = Constants.cutoff 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_1d map_2d = 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 xyz = match angMom_a with | (1,_,_) -> 0 | (_,1,_) -> 1 | _ -> 2 in let f = expo_b *. (Coordinate.coord center_ab xyz) in Array.init ncoef (fun k -> coef_prod.(k) *. expo_inv_p *. ( (Coordinate.coord center_pq.(k) xyz) *. zero_m_array.(m+1).(k) -. f *. zero_m_array.(m).(k) ) ) | 0 -> Array.map2 ( *. ) zero_m_array.(m) coef_prod | totAngMom_a -> let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in try Zmap.find map_1d.(m) key with | Not_found -> let result = let am, amm, amxyz, xyz = match angMom_a with | (x,0,0) -> (* 28_336 *) (x-1,0,0),(x-2,0,0), x-1, 0 | (x,y,0) -> (* 52_221 *) (x,y-1,0),(x,y-2,0), y-1, 1 | (x,y,z) -> (* 87_215 *) (x,y,z-1),(x,y,z-2), z-1, 2 in if amxyz < 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.map (fun 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 amxyz < 1 then p1 else let f = (float_of_int amxyz) *. 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.init ncoef (fun k -> p1.(k) +. f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) in Zmap.add map_1d.(m) key result; result and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c = match (totAngMom_a, totAngMom_c) with | (i,0) -> if (i>0) then vrr0_v m angMom_a totAngMom_a else Array.map2 ( *. ) zero_m_array.(m) coef_prod | (_,_) -> let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c)) in try Zmap.find map_2d.(m) key with | Not_found -> let result = begin let am, cm, cmm, axyz, cxyz, xyz = let angMom_ax, angMom_ay, angMom_az = angMom_a and angMom_cx, angMom_cy, angMom_cz = angMom_c in match angMom_c with | (_,0,0) -> (* 321_984 *) (angMom_ax-1, angMom_ay, angMom_az), (angMom_cx-1, angMom_cy, angMom_cz), (angMom_cx-2, angMom_cy, angMom_cz), angMom_ax,angMom_cx, 0 | (_,_,0) -> (* 612_002 *) (angMom_ax, angMom_ay-1, angMom_az), (angMom_cx, angMom_cy-1, angMom_cz), (angMom_cx, angMom_cy-2, angMom_cz), angMom_ay,angMom_cy, 1 | _ -> (* 1_067_324 *) (angMom_ax, angMom_ay, angMom_az-1), (angMom_cx, angMom_cy, angMom_cz-1), (angMom_cx, angMom_cy, angMom_cz-2), angMom_az,angMom_cz, 2 in if cxyz < 1 then empty else let f1 = Array.init ncoef (fun k -> expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz) ) in let f2 = Array.init ncoef (fun k -> expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) ) 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.init ncoef (fun k -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k)) in let p2 = if cxyz < 2 then p1 else let fcm = (float_of_int (cxyz-1)) *. 0.5 in let f1 = Array.map (fun e -> fcm *. e) expo_inv_q in let f2 = Array.map2 ( *. ) f1 expo_inv_q 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.init ncoef (fun k -> p1.(k) +. f1.(k) *. v1.(k) +. f2.(k) *. v2.(k)) in if (axyz < 1) || (cxyz < 1) then p2 else let fa = (float_of_int axyz) *. expo_inv_p *. 0.5 in let f1 = Array.map (fun e -> fa *. e ) expo_inv_q in if (at_least_one_valid f1) then let v = vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) in Array.init ncoef (fun k -> p2.(k) -. f1.(k) *. v.(k)) else p2 end in Zmap.add map_2d.(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.map2 ( *. ) zero_m_array.(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 angMom_ax, angMom_ay, angMom_az = angMom_a in (* 5_045_008 *) let ap, xyz = match angMom_b with | (1,_,_) -> (angMom_ax+1,angMom_ay,angMom_az), 0 | (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), 1 | (_,_,_) -> (angMom_ax,angMom_ay,angMom_az+1), 2 in 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 angMom_ax, angMom_ay, angMom_az = angMom_a and angMom_bx, angMom_by, angMom_bz = angMom_b in (* 3_403_478 *) let bxyz, xyz = match angMom_b with | (1,_,_) -> angMom_bx, 0 | (_,1,_) -> angMom_by, 1 | (_,_,_) -> angMom_bz, 2 in if (bxyz < 1) then empty else let ap, bm = match xyz with | 0 -> (angMom_ax+1,angMom_ay,angMom_az),(angMom_bx-1,angMom_by,angMom_bz) | 1 -> (angMom_ax,angMom_ay+1,angMom_az),(angMom_bx,angMom_by-1,angMom_bz) | _ -> (angMom_ax,angMom_ay,angMom_az+1),(angMom_bx,angMom_by,angMom_bz-1) in 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) -> if (totAngMom_b = 0) then vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c else hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c | (_,_) -> let (angMom_cx, angMom_cy, angMom_cz) = angMom_c and (angMom_dx, angMom_dy, angMom_dz) = angMom_d in let cp, dm, xyz = match angMom_d with | (_,0,0) -> (* 1_524_451 *) (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), 0 | (_,_,0) -> (* 1_302_937 *) (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), 1 | _ -> (* 1_302_937 *) (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), 2 in 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.(0),angMom_a.(1),angMom_a.(2)) (angMom_b.(0),angMom_b.(1),angMom_b.(2)) (angMom_c.(0),angMom_c.(1),angMom_c.(2)) (angMom_d.(0),angMom_d.(1),angMom_d.(2)) 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:0 ~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 norm_coef_scale_p = shell_ab.Shell_pair.norm_coef_scale in let b = shell_ab.Shell_pair.j in let common = Array.map (fun 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) ) shell_q |> Array.to_list |> List.filter (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> 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) -> zero_m_array) common and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> expo_inv ) common and d = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> d) common and center_cd = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> center_cd) common and center_pq = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> center_pq) common and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, center_cd, center_pq,coef_prod) -> coef_prod) common in (* Transpose zero_m_array *) let zero_m_array = let result = Array.init (maxm+1) (fun _ -> Array.make (Array.length coef_prod) 0.) in for m=0 to maxm do for k=0 to (Array.length coef_prod-1) do result.(m).(k) <- zero_m_array.(k).(m) done; done; result in (* Compute the integral class from the primitive shell quartet *) let map_1d = Array.init maxm (fun _ -> Zmap.create (4*maxm)) in let map_2d = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in let norm = let norm_coef_scale_q = shell_q.(0).Shell_pair.norm_coef_scale in Array.map (fun v1 -> Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q ) norm_coef_scale_p |> Array.to_list |> Array.concat 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 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_1d map_2d in let x = Array.fold_left (+.) 0. integral in contracted_class.(i) <- contracted_class.(i) +. x *. norm.(i) ) 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