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81 lines
2.8 KiB
OCaml
81 lines
2.8 KiB
OCaml
(** Set of contracted Gaussians differing only by the powers of x, y and z, with a
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constant {!AngularMomentum.t}, all centered on the same center.
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In other words, it is the set of all contracted shells sharing the same center.
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{%
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\begin{align*}
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\chi_{n_x,n_y,n_z}(r) & = f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, g_{ij\,n_x,n_y,n_z}(r) \\
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& = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, \exp \left( -\alpha_{ij} |r-R_A|^2 \right)
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\end{align*}
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%}
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where:
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- {% $g_{ij\,n_x,n_y,n_z}(r)$ %} is the i-th {!PrimitiveShell.t} of the j-th {!ContractedShell.t}
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- {% $n_x + n_y + n_z = l$ %}, the total angular momentum
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- {% $\alpha_{ij}$ %} are the exponents (tabulated) of the j-th {!ContractedShell.t}
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- {% $d_{ij}$ %} are the contraction coefficients of the j-th {!ContractedShell.t}
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- {% $\mathcal{N}_{ij}$ %} is the normalization coefficient of the i-th primitive shell
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({!PrimitiveShell.norm_coef}) of the j-th {!ContractedShell.t}
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- {% $f(n_x,n_y,n_z)$ %} is a scaling factor adjusting the normalization coefficient for the
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particular powers of {% $x,y,z$ %} ({!PrimitiveShell.norm_coef_scale})
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*)
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type t
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val make : ?index:int -> ContractedShell.t array -> t
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(** Creates a contracted shell from a list of coefficients and primitives. *)
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val with_index : t -> int -> t
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(** Returns a copy of the contracted shell with a modified index. *)
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val index : t -> int
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(** Index in the basis set, represented as an array of contracted shells. *)
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val center : t -> Coordinate.t
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(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)
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val ang_mom : t -> AngularMomentum.t
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(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)
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val size : t -> int
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(** Number of contracted functions, {% $n$ %} in the definition. *)
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val contracted_shells: t -> ContractedShell.t array
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(** Array of contracted gaussians *)
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val exponents : t -> float array array
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(** Array of exponents {% $\alpha_{ij}$ %}. The first index is the index of
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the contracted function, and the second index is the index of the primitive.
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*)
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val coefficients : t -> float array array
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(** Array of contraction coefficients {% $d_{ij}$ %}. The first index is the index of
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the contracted function, and the second index is the index of the primitive.
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*)
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val normalizations : t -> float array array
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(** Normalization coefficients {% $\mathcal{N}_{ij}$ %}. The first index is the index of
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the contracted function, and the second index is the index of the primitive.
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*)
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val norm_scales : t -> float array
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(** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as
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[AngularMomentum.zkey_array ang_mom]. *)
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val size_of_shell : t -> int
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(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)
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(** {2 Printers} *)
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val pp : Format.formatter -> t -> unit
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