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107 lines
3.4 KiB
OCaml
107 lines
3.4 KiB
OCaml
(** Data structure describing a pair of primitive shells.
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A primitive shell pair is the cartesian product between two sets of functions, each
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set containing all the functions of a primitive shell.
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{% \\[
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\left\\{ p_{k_x,k_y,k_z}(\mathbf{r}) \right\\} =
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\left\\{ g_{n_x,n_y,n_z}(\mathbf{r}) \right\\} \times
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\left\\{ g_{m_x,m_y,m_z}'(\mathbf{r}) \right\\}
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\\] %}
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where
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{%
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\begin{align*}
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g_{n_x,n_y,n_z}(\mathbf{r}) & =
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(x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z}
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\exp \left( -\alpha |\mathbf{r}-\mathbf{A}|^2 \right) \\
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g_{m_x,m_y,m_z}'(\mathbf{r}) & =
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(x-X_B)^{m_x} (y-Y_B)^{m_y} (z-Z_B)^{m_z}
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\exp \left( -\beta |\mathbf{r}-\mathbf{B}|^2 \right)
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\end{align*}
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%}
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{!a_minus_b}, {!a_minus_b_sq} and {!norm_coef_scale} depend only on the
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centering of the two shells, and {!totAngMom} only depends on the angular
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momenta of the two shells. Hence, these quantities need to be computed only
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once when a {!ContractedShellPair.t} is built. Hence, there is the
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{!create_make_of} function which creates a [make] function which is suitable
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for a {!ContractedShellPair.t}.
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References:
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[1] {{:http://dx.doi.org/10.1002/qua.560400604} P.M. Gill, B.G. Johnson, and J.A. Pople, International Journal of Quantum Chemistry 40, 745 (1991)}.
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*)
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type t
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val make : PrimitiveShell.t -> PrimitiveShell.t -> t
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(** Creates a primitive shell pair using two primitive shells. *)
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val create_make_of : PrimitiveShell.t -> PrimitiveShell.t ->
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(PrimitiveShell.t -> PrimitiveShell.t -> float -> t option)
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(** Creates a make function [PrimitiveShell.t -> PrimitiveShell.t -> float -> t] in which
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all the quantities common to the shell and independent of the exponent
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are pre-computed.
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The result is None if the normalization coefficient of the resulting
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function is below the cutoff, given as a last argument.
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*)
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val totAngMom : t -> AngularMomentum.t
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(** Total angular momentum of the shell pair: sum of the angular momenta of
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the shells. *)
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val center : t -> Coordinate.t
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(** Coordinates of the center {% $\mathbf{P}$ %}. *)
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val monocentric : t -> bool
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(** True if both shells of the pair have the same center. *)
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val shell_a : t -> PrimitiveShell.t
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(** Returns the first primitive shell that was used to build the shell pair. *)
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val shell_b : t -> PrimitiveShell.t
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(** Returns the second primitive shell that was used to build the shell pair. *)
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val normalization : t -> float
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(** Normalization coefficient of the shell pair. *)
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val norm_scales : t -> float array
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(** Normalization factor, characteristic of the powers of x, y and z of
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both shells of the pair. It is the outer product of the 2
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{!PrimitiveShell.norm_coef_scale} arrays of the shells consituting the
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pair.
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*)
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val exponent : t -> float
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(** Exponent of the Gaussian output of the Gaussian product : {% \\[ \alpha + \beta \\] %}*)
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val exponent_inv : t -> float
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(** Inverse of the exponent : {% \\[ \sigma_P = \frac{1}{\alpha + \beta} \\] %}*)
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val a_minus_b : t -> Coordinate.t
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(** {% $\mathbf{A}-\mathbf{B}$ %} *)
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val a_minus_b_sq : t -> float
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(** {% $|\mathbf{A}-\mathbf{B}|^2$ %} *)
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val center_minus_a : t -> Coordinate.t
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(** {% $\mathbf{P}-\mathbf{A}$ %} *)
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val equivalent : t -> t -> bool
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(** True if two primitive shell pairs are equivalent. *)
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val hash : t -> int
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(** Returns an integer characteristic of the shell pair. *)
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val cmp : t -> t -> int
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(** Arbitray comparison function for sorting. *)
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