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67 lines
2.0 KiB
OCaml
67 lines
2.0 KiB
OCaml
(** Set of Gaussians differing only by the powers of x, y and z, with a
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constant {!AngularMomentum.t}.
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{% \\[
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g_{n_x,n_y,n_z}(\mathbf{r}) = (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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\\] %}
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where:
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- {% $\mathbf{r} = (x,y,z)$ %} is the electron coordinate
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- {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %} is the coordinate of center A
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- {% $n_x + n_y + n_z = l$ %}, the total angular momentum
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- {% $\alpha$ %} is the exponent
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*)
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type t
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val to_string : t -> string
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(** Pretty-printing of the primitive shell in a string. *)
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val make : AngularMomentum.t -> Coordinate.t -> float -> t
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(** Creates a primitive shell from the total angular momentum, the coordinates of the
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center and the exponent. *)
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val exponent : t -> float
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(** Exponent {% $\alpha$ %}. *)
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val center : t -> Coordinate.t
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(** Coordinate {% $\mathbf{A}$ %}.of the center. *)
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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 norm : t -> float
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(** Norm of the shell, defined as
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{% \\[ || g_{l,0,0}(\mathbf{r}) || =
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\sqrt{ \iiint \left[ (x-X_A)^{l}
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\exp (-\alpha |\mathbf{r}-\mathbf{A}|^2) \right]^2 \, dx\, dy\, dz}
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\\] %}
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*)
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val normalization : t -> float
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(** Normalization coefficient by which the shell has to be multiplied
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to be normalized :
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{% \\[ \mathcal{N} = \frac{1}{|| g_{l,0,0}(\mathbf{r}) ||} \\] %}.
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*)
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val norm_scales : t -> float array
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(** Scaling factors {% $f(n_x,n_y,n_z)$ %} adjusting the normalization coefficient
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for the powers of {% $x,y,z$ %}. The normalization coefficients of the
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functions of the shell are given by {% $\mathcal{N}\times f$ %}. They are
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given in the same order as [AngularMomentum.zkey_array ang_mom]:
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{% \\[ f(n_x,n_y,n_z) = \frac{|| g_{l,0,0}(\mathbf{r}) ||}{|| g_{n_x,n_y,n_z}(\mathbf{r}) ||} \\] %}
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*)
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val size_of_shell : t -> int
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(** Number of functions in the shell. *)
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val zkey_array : t -> Zkey.t array
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(** Returns the array of Zkeys associated with the primitive shell. *)
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