QCaml/gaussian/atomic_shell.org

• Atomic shell
  • Type
  • Access
  • Creation
  • Printers

Atomic shell

Set of contracted Gaussians differing only by the powers of $x$, $y$ and $z$, with a constant Angular_momentum.t, all centered on the same point.

In other words, it is the set of all contracted shells sharing the same center.

\begin{align*} \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) \\ & = (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) \end{align*}

where:

• $g_{ij\,n_x,n_y,n_z}(r)$ is the $i$-th PrimitiveShell.t of the $j$-th Contracted_shell.t
• $n_x + n_y + n_z = l$, the total angular momentum
• $\alpha_{ij}$ are the exponents (tabulated) of the $j$-th Contracted_shell.t
• $d_{ij}$ are the contraction coefficients of the $j$-th Contracted_shell.t
• $\mathcal{N}_{ij}$ is the normalization coefficient of the $i$-th primitive shell (PrimitiveShell.norm_coef) of the $j$-th Contracted_shell.t
• $f(n_x,n_y,n_z)$ is a scaling factor adjusting the normalization coefficient for the particular powers of $x,y,z$ (PrimitiveShell.norm_coef_scale)

Type

type t

open Common

Access

val ang_mom           : t -> Angular_momentum.t
val center            : t -> Coordinate.t
val coefficients      : t -> float array array
val contracted_shells : t -> Contracted_shell.t array
val exponents         : t -> float array array
val index             : t -> int
val normalizations    : t -> float array array
val norm_scales       : t -> float array
val size_of_shell     : t -> int
val size              : t -> int

ang_mom	Total angular momentum : $l = n_x + n_y + n_z$.
center	Coordinate of the center $\mathbf{A} = (X_A,Y_A,Z_A)$.
coefficients	Array of contraction coefficients $d_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive.
contracted_shells:	Array of contracted gaussians
exponents	Array of exponents $\alpha_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive.
index	Index in the basis set, represented as an array of contracted shells.
normalizations	Normalization coefficients $\mathcal{N}_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive.
norm_scales	Scaling factors $f(n_x,n_y,n_z)$, given in the same order as Angular_momentum.zkey_array ang_mom.
size	Number of contracted functions, $n$ in the definition.
size_of_shell	Number of contracted functions in the shell: length of norm_coef_scale.

Creation

val make : ?index:int -> Contracted_shell.t array -> t 

val with_index  : t -> int -> t

make	Creates a contracted shell from a list of coefficients and primitives.
with_index	Returns a copy of the contracted shell with a modified index.

Printers

val pp : Format.formatter -> t -> unit