open Util open Constants exception NullPair (** In chop f g, evaluate g only if f is non zero, and return f *. (g ()) *) let chop f g = if (abs_float f) < cutoff then 0. else f *. (g ()) (** Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr_one_e (angMom_a, angMom_b) (totAngMom_a, totAngMom_b) (maxm, zero_m_array) (expo_inv_p) (center_ab, center_pa, center_pc) map = let totAngMom_a = Angular_momentum.to_int totAngMom_a and totAngMom_b = Angular_momentum.to_int totAngMom_b in let maxm = totAngMom_a+totAngMom_b in let maxsze = maxm+1 in let empty = Array.make maxsze 0. in (** Vertical recurrence relations *) let rec vrr angMom_a totAngMom_a = let ax,ay,az = angMom_a in if (ax < 0) || (ay < 0) || (az < 0) then empty else match totAngMom_a with | 0 -> zero_m_array | _ -> let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in try Zmap.find map 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 f1 = Coordinate.coord center_pa xyz and f2 = expo_inv_p *. (Coordinate.coord center_pc xyz) in if amxyz < 1 then let v1 = vrr am (totAngMom_a-1) in Array.init maxsze (fun m -> if m = maxm then 0. else (f1 *. v1.(m) ) -. f2 *. v1.(m+1) ) else let v3 = vrr amm (totAngMom_a-2) in let v1 = vrr am (totAngMom_a-1) in let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 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 key result; result (** Horizontal recurrence relations *) and hrr angMom_a angMom_b totAngMom_a totAngMom_b = let bx,by,bz = angMom_b in if (bx < 0) || (by < 0) || (bz < 0) then 0. else match totAngMom_b with | 0 -> (vrr angMom_a totAngMom_a).(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 | (_,0,0) -> angMom_bx, 0 | (_,_,0) -> angMom_by, 1 | (_,_,_) -> angMom_bz, 2 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 = hrr ap bm (totAngMom_a+1) (totAngMom_b-1) in let f2 = (Coordinate.coord center_ab xyz) in if (abs_float f2 < cutoff) then h1 else let h2 = hrr angMom_a bm totAngMom_a (totAngMom_b-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)) totAngMom_a totAngMom_b (** Computes all the one-electron integrals of the contracted shell pair *) let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t = let shell_a = shell_p.(0).Shell_pair.shell_a and shell_b = shell_p.(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) in (* Pre-computation of integral class indices *) let class_indices = Angular_momentum.zkey_array (Angular_momentum.Doublet Contracted_shell.(totAngMom shell_a, totAngMom shell_b)) 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 try begin let coef_prod = shell_p.(ab).Shell_pair.coef in let norm_coef_scale_p = shell_p.(ab).Shell_pair.norm_coef_scale in (** Screening on the product of coefficients *) if (abs_float coef_prod) < 1.e-4*.cutoff then raise NullPair; let expo_pq_inv = shell_p.(ab).Shell_pair.expo_inv in let center_ab = shell_p.(ab).Shell_pair.center_ab in let center_pa = Coordinate.(center_ab |- shell_a.Contracted_shell.center) in for c=0 to Array.length geometry - 1 do let element, nucl_coord = geometry.(c) in let charge = Element.to_charge element |> Charge.to_float in let center_pc = Coordinate.(shell_p.(ab).Shell_pair.center |- nucl_coord ) in let norm_pq_sq = Coordinate.dot center_pc center_pc in let zero_m_array = zero_m ~maxm ~expo_pq_inv ~norm_pq_sq in match Contracted_shell.(totAngMom shell_a, totAngMom shell_b) with | Angular_momentum.(S,S) -> let integral = zero_m_array.(0) in contracted_class.(0) <- contracted_class.(0) -. coef_prod *. integral *. charge | _ -> let map = Zmap.create (2*maxm) in let norm_coef_scale = norm_coef_scale_p in (* Compute the integral class from the primitive shell quartet *) class_indices |> Array.iteri (fun i key -> let (angMomA,angMomB) = let a = Zkey.to_int_array Zkey.Kind_6 key in ( [| a.(0) ; a.(1) ; a.(2) |], [| a.(3) ; a.(4) ; a.(5) |]) in let norm = norm_coef_scale.(i) in let coef_prod = coef_prod *. norm in let integral = hvrr_one_e (angMomA, angMomB) (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b) (maxm, zero_m_array) shell_p.(ab).Shell_pair.expo_inv (center_ab, center_pa, center_pc) map in contracted_class.(i) <- contracted_class.(i) -. coef_prod *. integral *. charge ) done end with NullPair -> () 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