open Util open Constants let cutoff2 = cutoff *. cutoff exception NullQuartet (** Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr_two_e (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) map_1d map_2d = (* 2_011_273 *) 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 let maxm = totAngMom_a + totAngMom_b + totAngMom_c + totAngMom_d in let empty = Array.make (maxm+1) 0. in (** Vertical recurrence relations *) let rec vrr0 angMom_a totAngMom_a = (* 1_137_164 *) match totAngMom_a with | 0 -> (* 66_288 *) zero_m_array | _ -> (* 1_070_876 *) let maxsze = maxm+1 in let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in try Zmap.find map_1d 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 = vrr0 am (totAngMom_a-1) in let f1 = expo_inv_p *. (Coordinate.coord center_pq xyz) and f2 = expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz) in if amxyz < 1 then Array.init maxsze (fun m -> (* 544_860 *) if m = maxm then 0. else (f1 *. v1.(m+1) ) -. f2 *. v1.(m) ) else let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in let v3 = vrr0 amm (totAngMom_a-2) in Array.init maxsze (fun m -> (* 484_257 *) (if m = maxm then 0. else (f1 *. v1.(m+1) ) -. f2 *. v1.(m) ) +. f3 *. (v3.(m) +. if m = maxm then 0. else expo_inv_p *. v3.(m+1)) ) in Zmap.add map_1d key result; result and vrr angMom_a angMom_c totAngMom_a totAngMom_c = (* 11_580_843 *) match (totAngMom_a, totAngMom_c) with | (i,0) -> (* 959_629 *) if (i>0) then vrr0 angMom_a totAngMom_a else zero_m_array | (_,_) -> (* 10_621_214 *) let maxsze = maxm+1 in let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c) ) in try Zmap.find map_2d key with | Not_found -> let result = 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 = -. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) in let f2 = expo_inv_q *. (Coordinate.coord center_pq xyz) in let result = if ( (abs_float f1 < cutoff) && (abs_float f2 < cutoff) ) then empty else let v1 = vrr angMom_a cm totAngMom_a (totAngMom_c-1) in Array.init maxsze (fun m -> (* 9_232_029 *) f1 *. v1.(m) -. (if m = maxm then 0. else f2 *. v1.(m+1)) ) in let result = if cxyz < 2 then result else let f3 = (float_of_int (cxyz-1)) *. expo_inv_q *. 0.5 in if (abs_float f3 < cutoff) && (abs_float (f3 *. expo_inv_q) < cutoff) then result else ( let v3 = vrr angMom_a cmm totAngMom_a (totAngMom_c-2) in Array.init maxsze (fun m -> (* 7_322_025 *) result.(m) +. f3 *. (v3.(m) +. (if m=maxm then 0. else expo_inv_q *. v3.(m+1)) )) ) in let result = if axyz < 1 || cxyz < 1 then result else let f5 = (float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5 in if (abs_float f5 < cutoff) then result else let v5 = vrr am cm (totAngMom_a-1) (totAngMom_c-1) in Array.init (maxsze) (fun m -> (* 7_963_213 *) result.(m) -. (if m = maxm then 0. else f5 *. v5.(m+1))) in result in Zmap.add map_2d key result; result (** Horizontal recurrence relations *) and hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c = (* 8_448_486 *) match totAngMom_b with | 0 -> (* 0 *) (vrr (angMom_a.(0) ,angMom_a.(1) ,angMom_a.(2)) (angMom_c.(0) ,angMom_c.(1) ,angMom_c.(2)) totAngMom_a totAngMom_c).(0) | 1 -> (* 5_045_008 *) 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 v1 = vrr (ap.(0),ap.(1),ap.(2)) (angMom_c.(0) ,angMom_c.(1) ,angMom_c.(2)) (totAngMom_a+1) totAngMom_c in let f2 = (Coordinate.coord center_ab xyz) in if (abs_float f2 < cutoff) then v1.(0) else let v2 = vrr (angMom_a.(0) ,angMom_a.(1) ,angMom_a.(2)) (angMom_c.(0) ,angMom_c.(1) ,angMom_c.(2)) totAngMom_a totAngMom_c in v1.(0) +. f2 *. v2.(0) | _ -> (* 3_403_478 *) 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|] -> (* 677_315 *) 0 | [|_;_;0|] -> (* 1_136_646 *) 1 | _ -> (* 1_589_517 *) 2 in ap.(xyz) <- ap.(xyz) + 1; bm.(xyz) <- bm.(xyz) - 1; if (bm.(xyz) < 0) then 0. else let h1 = hrr0 ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c in let f2 = (Coordinate.coord center_ab xyz) in if (abs_float f2 < cutoff) then h1 else let h2 = hrr0 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c in h1 +. f2 *. h2 and hrr angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d = (* 7_738_602 *) match (totAngMom_b, totAngMom_d) with | (_,0) -> (* 3_608_781 *) if (totAngMom_b = 0) then (vrr (angMom_a.(0) ,angMom_a.(1) ,angMom_a.(2)) (angMom_c.(0) ,angMom_c.(1) ,angMom_c.(2)) totAngMom_a totAngMom_c).(0) else hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c | (_,_) -> (* 4_130_325 *) 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|] -> (* 1_524_451 *) 0 | [|_;_;0|] -> (* 1_302_937 *) 1 | _ -> (* 1_302_937 *) 2 in cp.(xyz) <- cp.(xyz) + 1; dm.(xyz) <- dm.(xyz) - 1; let h1 = hrr angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) in let f2 = Coordinate.coord center_cd xyz in if (abs_float f2 < cutoff) then h1 else let h2 = hrr angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) in h1 +. f2 *. h2 in hrr 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 = (* 12850 *) 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 *) for ab=0 to (Array.length shell_p - 1) do let cab = shell_p.(ab).Shell_pair.coef in let b = shell_p.(ab).Shell_pair.j in let norm_coef_scale_p = shell_p.(ab).Shell_pair.norm_coef_scale in for cd=0 to (Array.length shell_q - 1) do let coef_prod = cab *. shell_q.(cd).Shell_pair.coef in (** Screening on the product of coefficients *) try if (abs_float coef_prod) < 1.e-4*.cutoff then raise NullQuartet; let expo_pq_inv = shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv in let center_pq = Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(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 begin match Contracted_shell.(totAngMom shell_a, totAngMom shell_b, totAngMom shell_c, totAngMom shell_d) with | Angular_momentum.(S,S,S,S) -> (* 14_700 *) let integral = zero_m_array.(0) in contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral | _ -> (* 15_577 *) let d = shell_q.(cd).Shell_pair.j in let map_1d = Zmap.create (4*maxm) in let map_2d = Zmap.create (Array.length class_indices) in let norm_coef_scale_q = shell_q.(cd).Shell_pair.norm_coef_scale in let norm_coef_scale = Array.map (fun v1 -> (* 165_245 *) Array.map (fun v2 -> (* 2_011_273 *) v1 *. v2) norm_coef_scale_q ) norm_coef_scale_p |> Array.to_list |> Array.concat in (* Compute the integral class from the primitive shell quartet *) class_indices |> Array.iteri (fun i key -> (* 2_011_273 *) 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 try (* Schwartz screening *) (* let schwartz_p = let key = Zkey.of_int_array Zkey.Kind_12 [| a.(0) ; a.(1) ; a.(2) ; a.(3) ; a.(4) ; a.(5) ; a.(0) ; a.(1) ; a.(2) ; a.(3) ; a.(4) ; a.(5) |] in match schwartz_p with | None -> 1. | Some schwartz_p -> Zmap.find schwartz_p key in if schwartz_p < cutoff then raise NullQuartet; let schwartz_q = let key = Zkey.of_int_array Zkey.Kind_12 [| a.(6) ; a.(7) ; a.(8) ; a.(9) ; a.(10) ; a.(11) ; a.(6) ; a.(7) ; a.(8) ; a.(9) ; a.(10) ; a.(11) |] in match schwartz_q with | None -> 1. | Some schwartz_q -> Zmap.find schwartz_q key in if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet; *) let norm = norm_coef_scale.(i) in let coef_prod = coef_prod *. norm in let integral = (* 2_011_273 *) hvrr_two_e (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, Contracted_shell.expo shell_d d) (shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv) (shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq) map_1d map_2d in contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral with NullQuartet -> () ) end with NullQuartet -> () done done; let result = Zmap.create (Array.length contracted_class) in Array.iteri (fun i key -> (* 1_929_480 *) 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 = (* 0 *) 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