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mirror of https://github.com/QuantumPackage/qp2.git synced 2024-06-16 01:25:18 +02:00
qp2/src/ao_basis
2023-06-22 18:26:52 +02:00
..
aos_in_r.irp.f fixed bug in nucl_aos 2023-06-22 18:26:52 +02:00
aos_transp.irp.f fixed bug in nucl_aos 2023-06-22 18:26:52 +02:00
aos.irp.f Add ao_first_of_shell for trexio 2021-10-12 16:01:16 +02:00
cosgtos.irp.f Improve 5idx 2023-06-02 20:32:31 +02:00
dimensions_integrals.irp.f Initial commit 2019-01-25 11:39:31 +01:00
EZFIO.cfg Fix ao_basis/use_cosgtos not found in EZFIO file 2023-06-01 17:47:00 +02:00
NEED Added basis module for easy export 2021-05-21 18:26:50 +02:00
README.rst Warnings in documentation 2019-01-29 17:09:08 +01:00
spherical_to_cartesian.irp.f Remove debug 2022-03-16 10:26:18 +01:00

========
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.