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57 lines
2.0 KiB
OCaml
57 lines
2.0 KiB
OCaml
(** A contracted shell is the set of functions is given by
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{% \\[
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(x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} \sum_{i=1}^{m} \mathcal{N}_i f_i d_i \exp \left( -\alpha_i |r-R_A|^2 \right)
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\\] %}
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where:
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- {% $n_x + n_y + n_z = l$ %}, the total angular momentum
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- {% $\alpha_i$ %} are the exponents (tabulated)
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- {% $d_i$ %} are the contraction coefficients
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- {% $\mathcal{N}_i$ %} is the normalization coefficient of the i-th primitive:
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{% \\[
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\mathcal{N}_i = \sqrt{\iiint \left[ (x-X_A)^{l} \exp (-\alpha_i |r-R_A|^2) \right]^2 \, dx dy dz}
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\\] %}
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- {% $f_i$ %} is a scaling factor adjusting the normalization coefficient for the
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particular powers of {% $x,y,z$ %}:
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{% \\[
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f_i = \frac{1}{\mathcal{N}_i}
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\sqrt{\iiint \left[ (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} \exp (-\alpha_i |r-R_A|^2) \right]^2 \, dx dy dz}
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\\] %}
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*)
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type t = private {
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expo : float array; (** Array of exponents {% $\alpha_i$ %} *)
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coef : float array; (** Array of contraction coefficients {% $d_i$ %} *)
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center : Coordinate.t; (** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %} *)
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totAngMom : AngularMomentum.t; (** Total angular momentum : {% $l = n_x + n_y + n_z$ %} *)
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size : int; (** Number of contracted functions, {% $m$ %} in the formula *)
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norm_coef : float array; (** Normalization coefficients of primitive functions {% $\mathcal{N}_i$ %} *)
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norm_coef_scale : float array; (** Scaling factors {% $f_i$ %}, given in the same order as [powers]. *)
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powers : Zkey.t array; (** Triplets {% $(n_x,n_y,n_z)$ %} encoded in a {!Zkey.t}. *)
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index : int; (** Index in the basis set, represented as an array of contracted shells. *)
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}
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(** Pretty-printing of the contracted shell in a string *)
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val to_string : t -> string
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(** Creates a contracted shell *)
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val make :
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index:int ->
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expo:float array ->
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coef:float array ->
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center:Coordinate.t -> totAngMom:AngularMomentum.t -> t
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(** Returns a copy of the contracted shell with a modified index *)
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val with_index : t -> int -> t
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