open Util open Constants open Powers open Coordinate let debug=false let cutoff2 = cutoff *. cutoff exception NullQuartet (** Horizontal and Vertical Recurrence Relations (HVRR) *) let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d) zero_m_array (expo_b, expo_d) (expo_inv_p, expo_inv_q) (center_ab, center_cd, center_pq) map_1d map_2d map_1d' map_2d' = (* Swap electrons 1 and 2 so that the max angular momentum is on 1 *) if angMom_a.tot + angMom_b.tot < angMom_c.tot + angMom_d.tot then hvrr_two_e (angMom_c, angMom_d, angMom_a, angMom_b) zero_m_array (expo_d, expo_b) (expo_inv_q, expo_inv_p) (center_cd, center_ab, (Coordinate.neg center_pq) ) map_1d' map_2d' map_1d map_2d else let maxm = angMom_a.tot + angMom_b.tot + angMom_c.tot + angMom_d.tot in let maxsze = maxm+1 in let empty = Array.make (maxm+1) 0. in let get_xyz angMom = match angMom with | { y=0 ; z=0 ; _ } -> X | { z=0 ; _ } -> Y | _ -> Z in (** Vertical recurrence relations *) let rec vrr0 angMom_a = match angMom_a.tot with | 0 -> zero_m_array | _ -> let key = Zkey.of_powers (Zkey.Three angMom_a) in try Zmap.find map_1d key with | Not_found -> let result = let xyz = get_xyz angMom_a in let am = Powers.decr xyz angMom_a in let amxyz = Powers.get xyz am in if amxyz >= 0 then let f1 = expo_inv_p *. (Coordinate.get xyz center_pq) and f2 = expo_b *. expo_inv_p *. (Coordinate.get xyz center_ab) in let result = Array.create_float maxsze in if amxyz < 1 then begin let v1 = vrr0 am in for m=0 to maxm-1 do result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m) done; result.(maxm) <- -. f2 *. v1.(maxm) end else begin let amm = Powers.decr xyz am in let v3 = vrr0 amm in let v1 = vrr0 am in let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in for m=0 to maxm-1 do result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m) +. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1)) done; result.(maxm) <- f3 *. v3.(maxm) end; result else empty in Zmap.add map_1d key result; result and vrr angMom_a angMom_c = match (angMom_a.tot, angMom_c.tot) with | (i,0) -> if (i>0) then vrr0 angMom_a else zero_m_array | (_,_) -> let key = Zkey.of_powers (Zkey.Six (angMom_a, angMom_c)) in try Zmap.find map_2d key with | Not_found -> let result = let xyz = get_xyz angMom_c in let cm = Powers.decr xyz angMom_c in let cmxyz = Powers.get xyz cm in let axyz = Powers.get xyz angMom_a in if cmxyz >= 0 then let f1 = -. expo_d *. expo_inv_q *. (Coordinate.get xyz center_cd) and f2 = expo_inv_q *. (Coordinate.get xyz center_pq) in let result = Array.make maxsze 0. in if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then begin let v1 = vrr angMom_a cm in for m=0 to maxm-1 do result.(m) <- f1 *. v1.(m) -. f2 *. v1.(m+1) ; done; result.(maxm) <- f1 *. v1.(maxm) ; end; if cmxyz > 0 then begin let f3 = (float_of_int cmxyz) *. expo_inv_q *. 0.5 in if (abs_float f3 > cutoff) || (abs_float (f3 *. expo_inv_q) > cutoff) then begin let v3 = let cmm = Powers.decr xyz cm in vrr angMom_a cmm in for m=0 to maxm-1 do result.(m) <- result.(m) +. f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1)) done; result.(maxm) <- result.(maxm) +. f3 *. v3.(maxm) end end; if axyz > 0 && cmxyz >= 0 then begin let am = Powers.decr xyz angMom_a in let f5 = (float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5 in if (abs_float f5 > cutoff) then let v5 = vrr am cm in for m=0 to maxm-1 do result.(m) <- result.(m) -. f5 *. v5.(m+1) done end; result else empty in Zmap.add map_2d key result; result (** Horizontal recurrence relations *) and hrr0 angMom_a angMom_b angMom_c = match angMom_b.tot with | 0 -> (vrr angMom_a angMom_c).(0) | 1 -> let xyz = get_xyz angMom_b in let ap = Powers.incr xyz angMom_a in let v1 = vrr ap angMom_c in let f2 = Coordinate.get xyz center_ab in if (abs_float f2 < cutoff) then v1.(0) else let v2 = vrr angMom_a angMom_c in v1.(0) +. f2 *. v2.(0) | _ -> let xyz = get_xyz angMom_b in let bxyz = Powers.get xyz angMom_b in if bxyz > 0 then let ap = Powers.incr xyz angMom_a in let bm = Powers.decr xyz angMom_b in let h1 = hrr0 ap bm angMom_c in let f2 = Coordinate.get xyz center_ab in if abs_float f2 < cutoff then h1 else let h2 = hrr0 angMom_a bm angMom_c in h1 +. f2 *. h2 else 0. and hrr angMom_a angMom_b angMom_c angMom_d = match (angMom_b.tot, angMom_d.tot) with | (_,0) -> if (angMom_b.tot = 0) then (vrr angMom_a angMom_c).(0) else hrr0 angMom_a angMom_b angMom_c | (_,_) -> let xyz = get_xyz angMom_d in let cp = Powers.incr xyz angMom_c in let dm = Powers.decr xyz angMom_d in let h1 = hrr angMom_a angMom_b cp dm in let f2 = Coordinate.get xyz center_cd in if abs_float f2 < cutoff then h1 else let h2 = hrr angMom_a angMom_b angMom_c dm in h1 +. f2 *. h2 in hrr angMom_a angMom_b angMom_c angMom_d let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = let shell_a = shell_p.ContractedShellPair.shell_a and shell_b = shell_p.ContractedShellPair.shell_b and shell_c = shell_q.ContractedShellPair.shell_a and shell_d = shell_q.ContractedShellPair.shell_b and sp = shell_p.ContractedShellPair.shell_pairs and sq = shell_q.ContractedShellPair.shell_pairs in let maxm = shell_p.ContractedShellPair.totAngMomInt + shell_q.ContractedShellPair.totAngMomInt 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 let monocentric = shell_p.ContractedShellPair.monocentric && shell_q.ContractedShellPair.monocentric && Contracted_shell.center shell_p.ContractedShellPair.shell_a = Contracted_shell.center shell_q.ContractedShellPair.shell_a in (* Compute all integrals in the shell for each pair of significant shell pairs *) let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in for ab=0 to (Array.length sp - 1) do let cab = shell_p.ContractedShellPair.coef.(ab) in let b = sp.(ab).ShellPair.j in for cd=0 to (Array.length shell_q.ContractedShellPair.shell_pairs - 1) do let coef_prod = cab *. shell_q.ContractedShellPair.coef.(cd) in (** Screening on the product of coefficients *) try if (abs_float coef_prod) < 1.e-3*.cutoff then raise NullQuartet; let center_pq = sp.(ab).ShellPair.center |- sq.(cd).ShellPair.center in let norm_pq_sq = Coordinate.dot center_pq center_pq in let expo_pq_inv = shell_p.ContractedShellPair.expo_inv.(ab) +. shell_q.ContractedShellPair.expo_inv.(cd) 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.ContractedShellPair.shell_pairs.(cd).ShellPair.j in let map_1d = Zmap.create (4*maxm) in let map_2d = Zmap.create (Array.length class_indices) in let map_1d' = Zmap.create (4*maxm) in let map_2d' = Zmap.create (Array.length class_indices) in let norm_coef_scale = Array.to_list norm_coef_scale_p |> List.map (fun v1 -> Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q) |> Array.concat in (* Compute the integral class from the primitive shell quartet *) class_indices |> Array.iteri (fun i key -> let (angMom_a,angMom_b,angMom_c,angMom_d) = match Zkey.to_powers ~kind:Zkey.Kind_12 key with | Zkey.Twelve x -> x | _ -> assert false in try if monocentric then begin if ( ((1 land angMom_a.x+angMom_b.x+angMom_c.x+angMom_d.x)=1) || ((1 land angMom_a.y+angMom_b.y+angMom_c.y+angMom_d.y)=1) || ((1 land angMom_a.z+angMom_b.z+angMom_c.z+angMom_d.z)=1) ) then raise NullQuartet end; (* (* Schwartz screening *) if (maxm > 2) then ( let schwartz_p = let key = Zkey.of_int_tuple (Zkey.Twelve (angMomA, angMomB, angMomA, angMomB) ) 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_tuple (Zkey.Twelve (angMomC, angMomD, angMomC, angMomD) ) 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 (angMom_a, angMom_b, angMom_c, angMom_d) zero_m_array (Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d) (shell_p.ContractedShellPair.expo_inv.(ab), shell_q.ContractedShellPair.expo_inv.(cd) ) (sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq) map_1d map_2d 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 = ContractedShellPair.create ~cutoff shell_a shell_b and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d in contracted_class_shell_pairs ~zero_m shell_p shell_q