mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-12-26 22:33:36 +01:00
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
|
|
constant {!AngularMomentum.t}.
|
|
|
|
{% \\[
|
|
g_{n_x,n_y,n_z}(\mathbf{r}) = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z}
|
|
\exp \left( -\alpha |\mathbf{r}-\mathbf{A}|^2 \right)
|
|
\\] %}
|
|
|
|
where:
|
|
|
|
- {% $\mathbf{r} = (x,y,z)$ %} is the electron coordinate
|
|
|
|
- {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %} is the coordinate of center A
|
|
|
|
- {% $n_x + n_y + n_z = l$ %}, the total angular momentum
|
|
|
|
- {% $\alpha$ %} is the exponent
|
|
|
|
*)
|
|
|
|
type t
|
|
|
|
val to_string : t -> string
|
|
(** Pretty-printing of the primitive shell in a string. *)
|
|
|
|
val make : AngularMomentum.t -> Coordinate.t -> float -> t
|
|
(** Creates a primitive shell from the total angular momentum, the coordinates of the
|
|
center and the exponent. *)
|
|
|
|
val exponent : t -> float
|
|
(** Exponent {% $\alpha$ %}. *)
|
|
|
|
val center : t -> Coordinate.t
|
|
(** Coordinate {% $\mathbf{A}$ %}.of the center. *)
|
|
|
|
val ang_mom : t -> AngularMomentum.t
|
|
(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)
|
|
|
|
val norm : t -> float
|
|
(** Norm of the shell, defined as
|
|
{% \\[ || g_{l,0,0}(\mathbf{r}) || =
|
|
\sqrt{ \iiint \left[ (x-X_A)^{l}
|
|
\exp (-\alpha |\mathbf{r}-\mathbf{A}|^2) \right]^2 \, dx\, dy\, dz}
|
|
\\] %}
|
|
*)
|
|
|
|
val normalization : t -> float
|
|
(** Normalization coefficient by which the shell has to be multiplied
|
|
to be normalized :
|
|
{% \\[ \mathcal{N} = \frac{1}{|| g_{l,0,0}(\mathbf{r}) ||} \\] %}.
|
|
*)
|
|
|
|
val norm_scales : t -> float array
|
|
(** Scaling factors {% $f(n_x,n_y,n_z)$ %} adjusting the normalization coefficient
|
|
for the powers of {% $x,y,z$ %}. The normalization coefficients of the
|
|
functions of the shell are given by {% $\mathcal{N}\times f$ %}. They are
|
|
given in the same order as [AngularMomentum.zkey_array ang_mom]:
|
|
{% \\[ f(n_x,n_y,n_z) = \frac{|| g_{l,0,0}(\mathbf{r}) ||}{|| g_{n_x,n_y,n_z}(\mathbf{r}) ||} \\] %}
|
|
*)
|
|
|
|
val size_of_shell : t -> int
|
|
(** Number of functions in the shell. *)
|
|
|
|
val zkey_array : t -> Zkey.t array
|
|
(** Returns the array of Zkeys associated with the primitive shell. *)
|
|
|