open Util module Am = AngularMomentum module Asp = AtomicShellPair module Aspc = AtomicShellPairCouple module Co = Coordinate module Cs = ContractedShell module Csp = ContractedShellPair module Cspc = ContractedShellPairCouple module Po = Powers module Psp = PrimitiveShellPair module Pspc = PrimitiveShellPairCouple module Ps = PrimitiveShell let cutoff = Constants.integrals_cutoff 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 center_pa center_qc map_1d map_2d = (* Swap electrons 1 and 2 so that the max angular momentum is on 1 *) if angMom_a.Po.tot + angMom_b.Po.tot < angMom_c.Po.tot + angMom_d.Po.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 (Co.neg center_pq) center_qc center_pa map_1d map_2d else let maxm = angMom_a.Po.tot + angMom_b.Po.tot + angMom_c.Po.tot + angMom_d.Po.tot in let maxsze = maxm+1 in let get_xyz angMom = match angMom with | { Po.y=0 ; z=0 ; _ } -> Co.X | { z=0 ; _ } -> Co.Y | _ -> Co.Z in (** Vertical recurrence relations *) let rec vrr0 angMom_a = match angMom_a.Po.tot with | 0 -> zero_m_array | _ -> let key = Zkey.of_powers_three angMom_a in try Zmap.find map_1d key with | Not_found -> let result = let xyz = get_xyz angMom_a in let am = Po.decr xyz angMom_a in let amxyz = Po.get xyz am in let f1 = expo_inv_p *. Co.get xyz center_pq and f2 = expo_b *. expo_inv_p *. Co.get xyz center_ab in let result = Array.create_float (maxsze - angMom_a.Po.tot) in if amxyz = 0 then begin let v1 = vrr0 am in Array.iteri (fun m _ -> result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)) result end else begin let amm = Po.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 Array.iteri (fun m _ -> result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m) +. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1)) ) result end; result in Zmap.add map_1d key result; result and vrr angMom_a angMom_c = match angMom_a.Po.tot, angMom_c.Po.tot with | (i,0) -> if (i>0) then vrr0 angMom_a else zero_m_array | (_,_) -> let key = Zkey.of_powers_six angMom_a angMom_c in try Zmap.find map_2d key with | Not_found -> let result = (* angMom_c.Po.tot > 0 so cm.Po.tot >= 0 *) let xyz = get_xyz angMom_c in let cm = Po.decr xyz angMom_c in let cmxyz = Po.get xyz cm in let axyz = Po.get xyz angMom_a in let f1 = -. expo_d *. expo_inv_q *. Co.get xyz center_cd and f2 = expo_inv_q *. Co.get xyz center_pq in let result = Array.make (maxsze - angMom_a.Po.tot - angMom_c.Po.tot) 0. in if axyz > 0 then begin let am = Po.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 Array.iteri (fun m _ -> result.(m) <- result.(m) -. f5 *. v5.(m+1)) result 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 = Po.decr xyz cm in vrr angMom_a cmm in Array.iteri (fun m _ -> result.(m) <- result.(m) +. f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1)) ) result end end; if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then begin let v1 = vrr angMom_a cm in Array.iteri (fun m _ -> result.(m) <- result.(m) +. f1 *. v1.(m) -. f2 *. v1.(m+1) ) result end; result in Zmap.add map_2d key result; result (* and trr angMom_a angMom_c = match (angMom_a.Po.tot, angMom_c.Po.tot) with | (i,0) -> if (i>0) then (vrr0 angMom_a).(0) else zero_m_array.(0) | (_,_) -> let key = Zkey.of_powers_six angMom_a angMom_c in try (Zmap.find map_2d key).(0) with | Not_found -> let result = let xyz = get_xyz angMom_c in let axyz = Po.get xyz angMom_a in let cm = Po.decr xyz angMom_c in let cmxyz = Po.get xyz cm in let expo_inv_q_over_p = expo_inv_q /. expo_inv_p in let f = Co.get xyz center_qc +. expo_inv_q_over_p *. Co.get xyz center_pa in let result = 0. in let result = if cmxyz < 1 then result else let f = 0.5 *. (float_of_int cmxyz) *. expo_inv_q in if abs_float f < cutoff then 0. else let cmm = Po.decr xyz cm in let v3 = trr angMom_a cmm in result +. f *. v3 in let result = if abs_float f < cutoff then result else let v1 = trr angMom_a cm in result +. f *. v1 in let result = if cmxyz < 0 then result else let f = -. expo_inv_q_over_p in let ap = Po.incr xyz angMom_a in let v4 = trr ap cm in result +. v4 *. f in let result = if axyz < 1 then result else let f = 0.5 *. (float_of_int axyz) *. expo_inv_q in if abs_float f < cutoff then result else let am = Po.decr xyz angMom_a in let v2 = trr am cm in result +. f *. v2 in result in Zmap.add map_2d key [|result|]; result *) in let vrr a c = (vrr a c).(0) (* if maxm < 10 then (vrr a c).(0) else trr a c *) in (** Horizontal recurrence relations *) let rec hrr0 angMom_a angMom_b angMom_c = match angMom_b.Po.tot with | 1 -> let xyz = get_xyz angMom_b in let ap = Po.incr xyz angMom_a in let v1 = vrr ap angMom_c in let f2 = Co.get xyz center_ab in if (abs_float f2 < cutoff) then v1 else let v2 = vrr angMom_a angMom_c in v1 +. f2 *. v2 | 0 -> vrr angMom_a angMom_c | _ -> let xyz = get_xyz angMom_b in let bxyz = Po.get xyz angMom_b in if bxyz > 0 then let ap = Po.incr xyz angMom_a in let bm = Po.decr xyz angMom_b in let h1 = hrr0 ap bm angMom_c in let f2 = Co.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.Po.tot, angMom_d.Po.tot) with | (_,0) -> if (angMom_b.Po.tot = 0) then vrr angMom_a angMom_c else hrr0 angMom_a angMom_b angMom_c | (_,_) -> let xyz = get_xyz angMom_d in let cp = Po.incr xyz angMom_c in let dm = Po.decr xyz angMom_d in let h1 = hrr angMom_a angMom_b cp dm in let f2 = Co.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_pair_couple ~zero_m shell_pair_couple : float Zmap.t = let maxm = Am.to_int (Cspc.ang_mom shell_pair_couple) in (* Pre-computation of integral class indices *) let class_indices = Cspc.zkey_array shell_pair_couple in let contracted_class = Array.make (Array.length class_indices) 0.; in let monocentric = Cspc.monocentric shell_pair_couple in (* Compute all integrals in the shell for each pair of significant shell pairs *) let shell_p = Cspc.shell_pair_p shell_pair_couple and shell_q = Cspc.shell_pair_q shell_pair_couple in let center_ab = Csp.a_minus_b shell_p and center_cd = Csp.a_minus_b shell_q in let norm_scales = Cspc.norm_scales shell_pair_couple in List.iter (fun (coef_prod, spc) -> let sp_ab = Pspc.shell_pair_p spc and sp_cd = Pspc.shell_pair_q spc in let expo_inv_p = Psp.exponent_inv sp_ab in let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in let norm_pq_sq = Co.dot center_pq center_pq in let expo_inv_q = Psp.exponent_inv sp_cd in let expo_pq_inv = expo_inv_p +. expo_inv_q in let zero_m_array = zero_m ~maxm ~expo_pq_inv ~norm_pq_sq in begin match Cspc.ang_mom shell_pair_couple with | Am.S -> let integral = zero_m_array.(0) in contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral | _ -> let expo_b = Ps.exponent (Psp.shell_b sp_ab) and expo_d = Ps.exponent (Psp.shell_b sp_cd) and center_pa = Psp.center_minus_a sp_ab in let map_1d = Zmap.create (4*maxm) and map_2d = Zmap.create (Array.length class_indices) in let center_qc = Psp.center_minus_a sp_cd 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 key with | Zkey.Twelve x -> x | _ -> assert false in try if monocentric then begin if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) || ((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) || ((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1) ) then raise NullQuartet end; let norm = norm_scales.(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 expo_b expo_d expo_inv_p expo_inv_q center_ab center_cd center_pq center_pa center_qc map_1d map_2d in contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral with NullQuartet -> () ) end ) (Cspc.coefs_and_shell_pair_couples shell_pair_couple); let result = Zmap.create (Array.length contracted_class) in Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; result let contracted_class_atomic_shell_pair_couple ~zero_m atomic_shell_pair_couple : float Zmap.t = let maxm = Am.to_int (Aspc.ang_mom atomic_shell_pair_couple) in (* Pre-computation of integral class indices *) let class_indices = Aspc.zkey_array atomic_shell_pair_couple in let contracted_class = Array.make (Array.length class_indices) 0.; in let monocentric = Aspc.monocentric atomic_shell_pair_couple in let shell_p = Aspc.atomic_shell_pair_p atomic_shell_pair_couple and shell_q = Aspc.atomic_shell_pair_q atomic_shell_pair_couple in (* Compute all integrals in the shell for each pair of significant shell pairs *) let center_ab = Asp.a_minus_b shell_p and center_cd = Asp.a_minus_b shell_q in let norm_scales = Aspc.norm_scales atomic_shell_pair_couple in List.iter (fun cspc -> List.iter (fun (coef_prod, spc) -> let sp_ab = Pspc.shell_pair_p spc and sp_cd = Pspc.shell_pair_q spc in let expo_inv_p = Psp.exponent_inv sp_ab in let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in let norm_pq_sq = Co.dot center_pq center_pq in let expo_inv_q = Psp.exponent_inv sp_cd in let expo_pq_inv = expo_inv_p +. expo_inv_q in let zero_m_array = zero_m ~maxm ~expo_pq_inv ~norm_pq_sq in begin match Aspc.ang_mom atomic_shell_pair_couple with | Am.S -> let integral = zero_m_array.(0) in contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral | _ -> let expo_b = Ps.exponent (Psp.shell_b sp_ab) and expo_d = Ps.exponent (Psp.shell_b sp_cd) and center_pa = Psp.center_minus_a sp_ab in let map_1d = Zmap.create (4*maxm) and map_2d = Zmap.create (Array.length class_indices) in let center_qc = Psp.center_minus_a sp_cd 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 key with | Zkey.Twelve x -> x | _ -> assert false in try if monocentric then begin if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) || ((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) || ((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1) ) then raise NullQuartet end; let norm = norm_scales.(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 expo_b expo_d expo_inv_p expo_inv_q center_ab center_cd center_pq center_pa center_qc map_1d map_2d in contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral with NullQuartet -> () ) end ) (Cspc.coefs_and_shell_pair_couples cspc) ) (Aspc.contracted_shell_pair_couples atomic_shell_pair_couple); let result = Zmap.create (Array.length contracted_class) in Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; result