open Util let cutoff = 1.e-20 let log_cutoff = -. (log cutoff) (** (00|00)^m : Fundamental integral $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $ maxm : Maximum total angular momentum expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of $\phi_p$ and $\phi_q$ norm_pq_sq : square of the distance between the centers of $\phi_p$ and $\phi_q$ *) let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq = let exp_pq = 1. /. expo_pq_inv in let t = norm_pq_sq *. exp_pq in boys_function ~maxm t |> Array.mapi (fun m fm -> two_over_sq_pi *. (if m mod 2 = 0 then fm else -.fm) *. (pow exp_pq m) *. (sqrt exp_pq) ) (** 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 ghvrr m (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 = 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 (** Vertical recurrence relations *) let rec gvrr m angMom_a angMom_c totAngMom_a totAngMom_c = if angMom_a.(0) < 0 || angMom_a.(1) < 0 || angMom_a.(2) < 0 || angMom_c.(0) < 0 || angMom_c.(1) < 0 || angMom_c.(2) < 0 then 0. else match (totAngMom_a, totAngMom_c) with | (0,0) -> zero_m_array.(m) | (_,0) -> let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; |] |> Zkey.(of_int_array ~kind:Kind_3) in let (found, result) = try (true, Zmap.find map.(m) key) with | Not_found -> (false, let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and xyz = match angMom_a with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in am.(xyz) <- am.(xyz) - 1; amm.(xyz) <- amm.(xyz) - 2; chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)) (fun () -> gvrr m am angMom_c (totAngMom_a-1) totAngMom_c ) +. chop (expo_inv_p *. (Coordinate.coord center_pq xyz)) (fun () -> gvrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c ) +. chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5) (fun () -> gvrr m amm angMom_c (totAngMom_a-2) totAngMom_c +. chop expo_inv_p (fun () -> gvrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) in if not found then Zmap.add map.(m) key result; result | (_,_) -> let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1; |] |> Zkey.(of_int_array ~kind:Kind_6) in let (found, result) = try (true, Zmap.find map.(m) key) with | Not_found -> (false, let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and cm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and cmm = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |] and xyz = match angMom_c with | [|0;0;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in am.(xyz) <- am.(xyz) - 1; cm.(xyz) <- cm.(xyz) - 1; cmm.(xyz) <- cmm.(xyz) - 2; chop (-. expo_d *. expo_inv_q *. (Coordinate.coord center_cd xyz) ) (fun () -> gvrr m angMom_a cm totAngMom_a (totAngMom_c-1) ) -. chop (expo_inv_q *. (Coordinate.coord center_pq xyz)) (fun () -> gvrr (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) ) +. chop ((float_of_int cm.(xyz)) *. expo_inv_q *. 0.5 ) (fun () -> gvrr m angMom_a cmm totAngMom_a (totAngMom_c-2) +. chop expo_inv_q (fun () -> gvrr (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) ) ) -. chop ((float_of_int angMom_a.(xyz)) *. expo_inv_p *. expo_inv_q *. 0.5 ) (fun () -> gvrr (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) ) ) in if not found then Zmap.add map.(m) key result; result (** Horizontal recurrence relations *) and ghrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d = if angMom_b.(0) < 0 || angMom_b.(1) < 0 || angMom_b.(2) < 0 || angMom_d.(0) < 0 || angMom_d.(1) < 0 || angMom_d.(2) < 0 then 0. else match (totAngMom_b, totAngMom_d) with | (0,0) -> gvrr m angMom_a angMom_c totAngMom_a totAngMom_c | (_,_) -> let key = [| angMom_a.(0)+1; angMom_a.(1)+1; angMom_a.(2)+1; angMom_b.(0)+1; angMom_b.(1)+1; angMom_b.(2)+1; angMom_c.(0)+1; angMom_c.(1)+1; angMom_c.(2)+1; angMom_d.(0)+1; angMom_d.(1)+1; angMom_d.(2)+1; |] |> Zkey.(of_int_array ~kind:Kind_12) in let (found, result) = try (true, Zmap.find map.(m) key) with | Not_found -> (false, begin match totAngMom_d with | 0 -> 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;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in ap.(xyz) <- ap.(xyz) + 1; bm.(xyz) <- bm.(xyz) - 1; ghrr m ap bm angMom_c angMom_d (totAngMom_a+1) (totAngMom_b-1) totAngMom_c totAngMom_d +. chop (Coordinate.coord center_ab xyz) (fun () -> ghrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1) totAngMom_c totAngMom_d ) | _ -> 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;_|] -> 2 | [|0;_;_|] -> 1 | _ -> 0 in cp.(xyz) <- cp.(xyz) + 1; dm.(xyz) <- dm.(xyz) - 1; ghrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) +. chop (Coordinate.coord center_cd xyz) (fun () -> ghrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) ) end) in if not found then Zmap.add map.(m) key result; result in ghrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d (** Electron-electron repulsion integral *) let erint_contracted_class shell_a shell_b shell_c shell_d : float Zmap.t = let shell_p = Shell_pair.create_array shell_a shell_b and shell_q = Shell_pair.create_array shell_c shell_d and 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.Kind_4 (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b, Contracted_shell.totAngMom shell_c, Contracted_shell.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 b = shell_p.(ab).Shell_pair.j in for cd=0 to (Array.length shell_q - 1) do let d = shell_q.(cd).Shell_pair.j in 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 let map = Array.init maxm (fun _ -> Zmap.create 129) in (* Compute the integral class from the primitive shell quartet *) Array.iteri (fun i key -> let (angMomA,angMomB,angMomC,angMomD) = let a = Zkey.to_int_array Zkey.Kind_12 key in ( [| 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 let integral = ghvrr 0 (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 in let norm = shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD in let coef_prod = shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef *. norm in contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral ) class_indices 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