mirror of https://gitlab.com/scemama/QCaml.git
98 lines
3.1 KiB
OCaml
98 lines
3.1 KiB
OCaml
(** Atomic Shell *)
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(**
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* Set of contracted Gaussians differing only by the powers of $x$, $y$
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* and $z$, with a constant ~Angular_momentum.t~, all centered on the same
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* point.
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*
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* In other words, it is the set of all contracted shells sharing the same
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* 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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*
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* - $g_{ij\,n_x,n_y,n_z}(r)$ is the $i$-th ~PrimitiveShell.t~ of the
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* $j$-th ~Contracted_shell.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
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* ~Contracted_shell.t~
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* - $d_{ij}$ are the contraction coefficients of the $j$-th
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* ~Contracted_shell.t~
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* - $\mathcal{N}_{ij}$ is the normalization coefficient of the $i$-th
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* primitive shell
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* (~PrimitiveShell.norm_coef~) of the $j$-th ~Contracted_shell.t~
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* - $f(n_x,n_y,n_z)$ is a scaling factor adjusting the normalization
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* coefficient for the particular powers of $x,y,z$
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* (~PrimitiveShell.norm_coef_scale~)
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*)
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(** Types and modules *)
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type t
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open Common
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(** Access *)
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val ang_mom : t -> Angular_momentum.t
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(** Total angular momentum : $l = n_x + n_y + n_z$. *)
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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 coefficients : t -> float array array
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(** Array of contraction coefficients $d_{ij}$. The first index is the index
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* of the contracted function, and the second index is the index of the
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* primitive.
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*)
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val contracted_shells : t -> Contracted_shell.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 the
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* contracted function, and the second index is the index of the primitive.
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*)
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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 normalizations : t -> float array array
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(** Normalization coefficients $\mathcal{N}_{ij}$. The first index is the
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* index of the contracted function, and the second index is the index of
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* 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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* ~Angular_momentum.zkey_array ang_mom~.
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*)
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val size_of_shell : t -> int
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(** Number of contracted functions in the shell: length of
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* ~norm_coef_scale~.
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*)
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val size : t -> int
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(** Number of contracted functions, $n$ in the definition. *)
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(** Creation *)
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val make : ?index:int -> Contracted_shell.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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(** Printers *)
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val pp : Format.formatter -> t -> unit
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