open Util open Constants let cutoff2 = cutoff *. cutoff let debug = false 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 = 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 if debug then begin Printf.printf "\n---- %d %d %d %d ----\n" totAngMom_a totAngMom_b totAngMom_c totAngMom_d; Printf.printf "%d %d %d\n" angMom_a.(0) angMom_a.(1) angMom_a.(2) ; Printf.printf "%d %d %d\n" angMom_b.(0) angMom_b.(1) angMom_b.(2) ; Printf.printf "%d %d %d\n" angMom_c.(0) angMom_c.(1) angMom_c.(2) ; Printf.printf "%d %d %d\n" angMom_d.(0) angMom_d.(1) angMom_d.(2) ; Printf.printf "%f %f %f %f\n%f %f %f\n%f %f %f\n%f %f %f\n" expo_b expo_d expo_inv_p expo_inv_q (Coordinate.coord center_ab 0) (Coordinate.coord center_ab 1) (Coordinate.coord center_ab 2) (Coordinate.coord center_cd 0) (Coordinate.coord center_cd 1) (Coordinate.coord center_cd 2) (Coordinate.coord center_pq 0) (Coordinate.coord center_pq 1) (Coordinate.coord center_pq 2) end; (** Vertical recurrence relations *) let rec vrr0 angMom_a totAngMom_a = if debug then begin let (x,y,z) = angMom_a in Printf.printf "vrr0: %d : %d %d %d\n" totAngMom_a x y z end; match totAngMom_a with | 0 -> zero_m_array | _ -> 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) -> (x-1,0,0),(x-2,0,0), x-1, 0 | (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1 | (x,y,z) -> (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 -> 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 -> (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 = if debug then begin let angMom_ax, angMom_ay, angMom_az = angMom_a in let angMom_cx, angMom_cy, angMom_cz = angMom_c in Printf.printf "vrr : %d %d : %d %d %d %d %d %d\n" totAngMom_a totAngMom_c angMom_ax angMom_ay angMom_az angMom_cx angMom_cy angMom_cz end; match (totAngMom_a, totAngMom_c) with | (i,0) -> if (i>0) then vrr0 angMom_a totAngMom_a else zero_m_array | (_,_) -> 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 if (angMom_cz > 0) then (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 else if (angMom_cy > 0) then (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 else (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 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 -> 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 -> 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 -> 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 = if debug then begin let angMom_ax, angMom_ay, angMom_az = angMom_a and angMom_bx, angMom_by, angMom_bz = angMom_b and angMom_cx, angMom_cy, angMom_cz = angMom_c in Printf.printf "hrr0: %d %d %d : %d %d %d %d %d %d %d %d %d\n" totAngMom_a totAngMom_b totAngMom_c angMom_ax angMom_ay angMom_az angMom_bx angMom_by angMom_bz angMom_cx angMom_cy angMom_cz end; match totAngMom_b with | 0 -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0) | 1 -> let angMom_ax, angMom_ay, angMom_az = angMom_a in let ap, xyz = match angMom_b with | (_,_,1) -> (angMom_ax,angMom_ay,angMom_az+1), 2 | (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), 1 | _ -> (angMom_ax+1,angMom_ay,angMom_az), 0 in let v1 = vrr ap angMom_c (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 angMom_c totAngMom_a totAngMom_c in v1.(0) +. f2 *. v2.(0) | _ -> let angMom_ax, angMom_ay, angMom_az = angMom_a and angMom_bx, angMom_by, angMom_bz = angMom_b in let bxyz, xyz = match angMom_b with | (_,_,1) -> angMom_bz, 2 | (_,1,_) -> angMom_by, 1 | _ -> angMom_bx, 0 in if (bxyz < 1) then 0. 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 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 = if debug then begin let angMom_ax, angMom_ay, angMom_az = angMom_a in let angMom_bx, angMom_by, angMom_bz = angMom_b in let angMom_cx, angMom_cy, angMom_cz = angMom_c in let angMom_dx, angMom_dy, angMom_dz = angMom_d in Printf.printf "hrr : %d %d %d %d : %d %d %d %d %d %d %d %d %d %d %d %d\n" totAngMom_a totAngMom_b totAngMom_c totAngMom_d angMom_ax angMom_ay angMom_az angMom_bx angMom_by angMom_bz angMom_cx angMom_cy angMom_cz angMom_dx angMom_dy angMom_dz end; match (totAngMom_b, totAngMom_d) with | (_,0) -> if (totAngMom_b = 0) then (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0) else hrr0 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) -> (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), 0 | (_,_,0) -> (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), 1 | _ -> (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), 2 in 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.(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 *) 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) -> let integral = zero_m_array.(0) in contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral | _ -> 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 -> Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q ) norm_coef_scale_p |> Array.to_list |> Array.concat in (* let monocentric = shell_p.(ab).Shell_pair.monocentric && shell_q.(cd).Shell_pair.monocentric in *) (* Compute the integral class from the primitive shell quartet *) class_indices |> 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 try (* if monocentric then begin if ( ((1 land (a.(0) + a.(3) + a.(6) + a.( 9)))=1) || ((1 land (a.(1) + a.(4) + a.(7) + a.(10)))=1) || ((1 land (a.(2) + a.(5) + a.(8) + a.(11)))=1) ) then raise NullQuartet end; *) (* 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 = 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 -> 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