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quantum_package/src/AOs
2015-01-08 16:22:19 +01:00
..
tests Corrected tests in AOs 2014-07-14 18:45:10 +02:00
ao_overlap.irp.f add ao_overlap.irp.f and NEEDED_MODULES for Molden 2015-01-08 16:22:19 +01:00
aos.ezfio_config Added MD5 key in AOs for check in MOs 2014-12-26 00:17:34 +01:00
aos.irp.f Merge branch 'master' of github.com:LCPQ/quantum_package 2015-01-07 18:05:09 +01:00
ASSUMPTIONS.rst Hartree-Fock works well 2014-06-25 14:58:58 +02:00
Makefile Simplified Makefiles 2014-04-03 11:28:54 +02:00
NEEDED_MODULES Updated documentation 2014-05-14 00:01:31 +02:00
README.rst Corrected tests in AOs 2014-07-14 18:45:10 +02:00

==========
AOs Module
==========

This module describes the atomic orbitals basis set.

An atomic orbital :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

Assumptions
===========

.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES file.

* The atomic orbitals are normalized:

  .. math::

   \int \left(\chi_i({\bf r}) \right)^2 dr = 1

* The AO coefficients in the EZFIO files are not necessarily normalized and are normalized after reading
* The AO coefficients and exponents are ordered in increasing order of exponents


Needed Modules
==============

.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES file.

* `Ezfio_files <http://github.com/LCPQ/quantum_package/tree/master/src/Ezfio_files>`_
* `Nuclei <http://github.com/LCPQ/quantum_package/tree/master/src/Nuclei>`_
* `Output <http://github.com/LCPQ/quantum_package/tree/master/src/Output>`_
* `Utils <http://github.com/LCPQ/quantum_package/tree/master/src/Utils>`_

Documentation
=============

.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES file.

`ao_coef <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L21>`_
  Coefficients, exponents and powers of x,y and z
  ao_coef(i,j) = coefficient of the jth primitive on the ith ao

`ao_coef_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L96>`_
  Transposed ao_coef and ao_expo

`ao_expo <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L20>`_
  Coefficients, exponents and powers of x,y and z
  ao_coef(i,j) = coefficient of the jth primitive on the ith ao

`ao_expo_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L97>`_
  Transposed ao_coef and ao_expo

`ao_nucl <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L146>`_
  Index of the nuclei on which the ao is centered

`ao_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L1>`_
  Number of atomic orbitals

`ao_num_align <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L2>`_
  Number of atomic orbitals

`ao_power <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L19>`_
  Coefficients, exponents and powers of x,y and z
  ao_coef(i,j) = coefficient of the jth primitive on the ith ao

`ao_prim_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L114>`_
  Number of primitives per atomic orbital

`ao_prim_num_max <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L136>`_
  Undocumented

`ao_prim_num_max_align <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L137>`_
  Undocumented