33 lines
775 B
ReStructuredText
33 lines
775 B
ReStructuredText
========
|
|
ao_basis
|
|
========
|
|
|
|
This module describes the atomic orbitals basis set.
|
|
|
|
An |AO| :math:`\chi` centered on nucleus A is represented as:
|
|
|
|
.. math::
|
|
|
|
\chi_i({\bf r}) = (x-X_A)^a (y-Y_A)^b (z-Z_A)^c \sum_k c_{ki} e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2}
|
|
|
|
|
|
The |AO| coefficients are normalized as:
|
|
|
|
.. math::
|
|
|
|
{\tilde c}_{ki} = \frac{c_{ki}}{ \int \left( (x-X_A)^a (y-Y_A)^b (z-Z_A)^c e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2} \right)^2 dr}
|
|
|
|
|
|
.. warning::
|
|
|
|
`ao_coef` contains the |AO| coefficients given in input. These do not
|
|
include the normalization constant of the |AO|. The `ao_coef_normalized`
|
|
provider includes this normalization factor.
|
|
|
|
|
|
The |AOs| are also sorted by increasing exponent to accelerate the calculation of
|
|
the two electron integrals.
|
|
|
|
|
|
|