open Common open Linear_algebra open Gaussian open Constants type t = (Basis.t, Basis.t) Matrix.t array (* [| "x"; "y"; "z"; "x2"; "y2"; "z2" |] *) module Am = Angular_momentum module Bs = Basis module Co = Coordinate module Cs = Contracted_shell module Csp = Contracted_shell_pair module Po = Powers module Psp = Primitive_shell_pair let matrix t = function | "x" -> t.(0) | "y" -> t.(1) | "z" -> t.(2) | "x2" -> t.(3) | "y2" -> t.(4) | "z2" -> t.(5) | "xy" -> t.(6) | "xz" -> t.(8) | "yz" -> t.(7) | "x3" -> t.(9) | "y3" -> t.(10) | "z3" -> t.(11) | "x4" -> t.(12) | "y4" -> t.(13) | "z4" -> t.(14) | _ -> Util.not_implemented "Multipole" let cutoff = integrals_cutoff let to_powers x = let open Zkey in match to_powers x with | Six x -> x | _ -> assert false (** Computes all the integrals of the contracted shell pair *) let contracted_class shell_a shell_b : float Zmap.t array = match Csp.make shell_a shell_b with | None -> Array.init 15 (fun _ -> Zmap.create 0) | Some shell_p -> begin (* Pre-computation of integral class indices *) let class_indices = Csp.zkey_array shell_p in let contracted_class = Array.init 15 (fun _ -> Array.make (Array.length class_indices) 0.) in let a_minus_b = Csp.a_minus_b shell_p in let norm_coef_scales = Csp.norm_scales shell_p in (* Compute all integrals in the shell for each pair of significant shell pairs *) let xyz_of_int k = match k with | 0 -> Co.X | 1 -> Co.Y | _ -> Co.Z in List.iter (fun (coef_prod, psp) -> (* Screening on the product of coefficients *) if (abs_float coef_prod) > 1.e-6*.cutoff then begin let expo_inv = Psp.exponent_inv psp and center_pa = Psp.center_minus_a psp and xa = Co.(get X) @@ Cs.center shell_a and ya = Co.(get Y) @@ Cs.center shell_a and za = Co.(get Z) @@ Cs.center shell_a in Array.iteri (fun i key -> let (angMomA, angMomB) = to_powers key in (* 1D Overlap *) let f k = let xyz = xyz_of_int k in Overlap_primitives.hvrr (Po.get xyz angMomA, Po.get xyz angMomB) expo_inv (Co.get xyz a_minus_b, Co.get xyz center_pa) in (* 1D *) let g k = let xyz = xyz_of_int k in Overlap_primitives.hvrr (Po.get xyz angMomA + 1, Po.get xyz angMomB) expo_inv (Co.get xyz a_minus_b, Co.get xyz center_pa) in (* 1D *) let h k = let xyz = xyz_of_int k in Overlap_primitives.hvrr (Po.get xyz angMomA + 2, Po.get xyz angMomB) expo_inv (Co.get xyz a_minus_b, Co.get xyz center_pa) in (* 1D *) let j k = let xyz = xyz_of_int k in Overlap_primitives.hvrr (Po.get xyz angMomA + 3, Po.get xyz angMomB) expo_inv (Co.get xyz a_minus_b, Co.get xyz center_pa) in (* 1D *) let l k = let xyz = xyz_of_int k in Overlap_primitives.hvrr (Po.get xyz angMomA + 4, Po.get xyz angMomB) expo_inv (Co.get xyz a_minus_b, Co.get xyz center_pa) in let norm = norm_coef_scales.(i) in let f0, f1, f2, g0, g1, g2, h0, h1, h2, j0, j1, j2 , l0, l1, l2 = f 0, f 1, f 2, g 0, g 1, g 2, h 0, h 1, h 2, j 0, j 1, j 2, l 0, l 1, l 2 in let x = g0 +. f0 *. xa in let y = g1 +. f1 *. ya in let z = g2 +. f2 *. za in let x2 = h0 +. xa *. (2. *. x -. xa *. f0) in let y2 = h1 +. ya *. (2. *. y -. ya *. f1) in let z2 = h2 +. za *. (2. *. z -. za *. f2) in let x3 = j0 +. xa *. f0 *. (3. *. x2 -. 3. *. x *. xa +. xa *. xa) in let y3 = j1 +. ya *. f1 *. (3. *. y2 -. 3. *. y *. ya +. ya *. ya) in let z3 = j2 +. za *. f2 *. (3. *. z2 -. 3. *. z *. za +. za *. za) in let x4 = l0 +. xa *. f0 *. ( 4. *. x3 -. 6. *. x2 *. xa +. 4. *. x *. xa *. xa -. xa *. xa *. xa) in let y4 = l1 +. ya *. f1 *. ( 4. *. y3 -. 6. *. y2 *. ya +. 4. *. y *. ya *. ya -. ya *. ya *. ya) in let z4 = l2 +. za *. f2 *. ( 4. *. z3 -. 6. *. z2 *. za +. 4. *. z *. za *. za -. za *. za *. za) in let c = contracted_class in let d = coef_prod *. norm in c.(0).(i) <- c.(0).(i) +. d *. x *. f1 *. f2; c.(1).(i) <- c.(1).(i) +. d *. f0 *. y *. f2; c.(2).(i) <- c.(2).(i) +. d *. f0 *. f1 *. z; c.(3).(i) <- c.(3).(i) +. d *. x2 *. f1 *. f2; c.(4).(i) <- c.(4).(i) +. d *. f0 *. y2 *. f2; c.(5).(i) <- c.(5).(i) +. d *. f0 *. f1 *. z2; c.(6).(i) <- c.(6).(i) +. d *. x *. y *. f2; c.(7).(i) <- c.(7).(i) +. d *. f0 *. y *. z; c.(8).(i) <- c.(8).(i) +. d *. x *. f1 *. z; c.(9).(i) <- c.(9).(i) +. d *. x3 *. f1 *. f2; c.(10).(i) <- c.(10).(i) +. d *. f0 *. y3 *. f2; c.(11).(i) <- c.(11).(i) +. d *. f0 *. f1 *. z3; c.(12).(i) <- c.(12).(i) +. d *. x4 *. f1 *. f2; c.(13).(i) <- c.(13).(i) +. d *. f0 *. y4 *. f2; c.(14).(i) <- c.(14).(i) +. d *. f0 *. f1 *. z4; ) class_indices end ) (Csp.coefs_and_shell_pairs shell_p); let result = Array.map (fun c -> Zmap.create (Array.length c) ) contracted_class in for j=0 to Array.length result -1 do let rj = result.(j) in let cj = contracted_class.(j) in Array.iteri (fun i key -> Zmap.add rj key cj.(i)) class_indices done; result end (** Create multipole matrices *) let of_basis basis = let to_powers x = let open Zkey in match to_powers x with | Three x -> x | _ -> assert false in let n = Bs.size basis and shell = Bs.contracted_shells basis in let result = Array.init 15 (fun _ -> Matrix.create n n |> Matrix.to_bigarray_inplace) in for j=0 to (Array.length shell) - 1 do for i=0 to j do (* Compute all the integrals of the class *) let cls = contracted_class shell.(i) shell.(j) in for k=0 to 14 do Array.iteri (fun j_c powers_j -> let j_c = Cs.index shell.(j) + j_c + 1 in let xj = to_powers powers_j in Array.iteri (fun i_c powers_i -> let i_c = Cs.index shell.(i) + i_c + 1 in let xi = to_powers powers_i in let key = Zkey.of_powers_six xi xj in let value = try Zmap.find cls.(k) key with Not_found -> 0. in result.(k).{i_c,j_c} <- value; result.(k).{j_c,i_c} <- value; ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i)))) ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j)))) done; done; done; let result = Array.map Matrix.of_bigarray_inplace result in Array.iter Matrix.detri_inplace result; result let to_file ~filename eni_array = let n = Matrix.dim1 eni_array in let eni_array = Matrix.to_bigarray_inplace eni_array in let oc = open_out filename in for j=1 to n do for i=1 to j do let value = eni_array.{i,j} in if (value <> 0.) then Printf.fprintf oc " %5d %5d %20.15f\n" i j value; done; done; close_out oc