==========
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
Warning: ``ao_coef`` contains the AO coefficients given in input. These do not
include the normalization constant of the AO. The ``ao_coef_normalized`` includes
this normalization factor.
The AOs are also sorted by increasing exponent to accelerate the calculation of
the two electron integrals.
Assumptions
===========
* The AO coefficients in the EZFIO files are not necessarily normalized and are normalized after reading
Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
.. image:: tree_dependency.png
* `Nuclei <http://github.com/LCPQ/quantum_package/tree/master/src/Nuclei>`_
Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
.. image:: tree_dependency.png
* `Nuclei <http://github.com/LCPQ/quantum_package/tree/master/src/Nuclei>`_
Documentation
=============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
`ao_cartesian <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L110>`_
If true, use AOs in Cartesian coordinates (6d,10f,...)
`ao_coef <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L40>`_
Primitive coefficients, read from input. Those should not be used directly, as the MOs are expressed on the basis of **normalized** AOs.
`ao_coef_normalization_factor <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L10>`_
Coefficients including the AO normalization
`ao_coef_normalization_libint_factor <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L46>`_
Coefficients including the AO normalization
`ao_coef_normalized <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L9>`_
Coefficients including the AO normalization
`ao_coef_normalized_ordered <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L79>`_
Sorted primitives to accelerate 4 index MO transformation
`ao_coef_normalized_ordered_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L105>`_
Transposed ao_coef_normalized_ordered
`ao_expo <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L248>`_
Exponents for each primitive of each AO
`ao_expo_ordered <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L80>`_
Sorted primitives to accelerate 4 index MO transformation
`ao_expo_ordered_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L119>`_
Transposed ao_expo_ordered
`ao_l <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L133>`_
ao_l = l value of the AO: a+b+c in x^a y^b z^c
`ao_l_char <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L135>`_
ao_l = l value of the AO: a+b+c in x^a y^b z^c
`ao_l_char_space <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L259>`_
Undocumented
`ao_l_max <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L134>`_
ao_l = l value of the AO: a+b+c in x^a y^b z^c
`ao_md5 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L6>`_
MD5 key, specific of the AO basis
`ao_nucl <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L213>`_
Index of the nucleus on which the AO is centered
`ao_num <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L144>`_
number of AOs
`ao_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L1>`_
Overlap between atomic basis functions:
:math:`\int \chi_i(r) \chi_j(r) dr)`
`ao_overlap_abs <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L72>`_
Overlap between absolute value of atomic basis functions:
:math:`\int |\chi_i(r)| |\chi_j(r)| dr)`
`ao_overlap_x <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L2>`_
Overlap between atomic basis functions:
:math:`\int \chi_i(r) \chi_j(r) dr)`
`ao_overlap_y <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L3>`_
Overlap between atomic basis functions:
:math:`\int \chi_i(r) \chi_j(r) dr)`
`ao_overlap_z <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L4>`_
Overlap between atomic basis functions:
:math:`\int \chi_i(r) \chi_j(r) dr)`
`ao_power <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L75>`_
Powers of x, y and z for each AO
`ao_power_index <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L148>`_
Unique index given to a triplet of powers:
.br
1/2 (l-n_x)*(l-n_x+1) + n_z + 1
`ao_prim_num <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ezfio_interface.irp.f#L178>`_
Number of primitives per atomic orbital
`ao_prim_num_max <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L1>`_
max number of primitives
`ao_value <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos_value.irp.f#L1>`_
return the value of the ith ao at point r
`cart_to_sphe_0 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L7>`_
Spherical -> Cartesian Transformation matrix for l=0
`cart_to_sphe_1 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L18>`_
Spherical -> Cartesian Transformation matrix for l=1
`cart_to_sphe_2 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L31>`_
Spherical -> Cartesian Transformation matrix for l=2
`cart_to_sphe_3 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L49>`_
Spherical -> Cartesian Transformation matrix for l=3
`cart_to_sphe_4 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L75>`_
Spherical -> Cartesian Transformation matrix for l=4
`cart_to_sphe_5 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L113>`_
Spherical -> Cartesian Transformation matrix for l=5
`cart_to_sphe_6 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L169>`_
Spherical -> Cartesian Transformation matrix for l=6
`cart_to_sphe_7 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L249>`_
Spherical -> Cartesian Transformation matrix for l=7
`cart_to_sphe_8 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L361>`_
Spherical -> Cartesian Transformation matrix for l=8
`cart_to_sphe_9 <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/spherical_to_cartesian.irp.f#L512>`_
Spherical -> Cartesian Transformation matrix for l=9
`give_all_aos_at_r <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos_value.irp.f#L34>`_
gives the values of aos at a given point r
`l_to_charater <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L162>`_
character corresponding to the "L" value of an AO orbital
`n_aos_max <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L179>`_
Number of AOs per atom
`n_pt_max_i_x <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/dimensions_integrals.irp.f#L2>`_
Undocumented
`n_pt_max_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/dimensions_integrals.irp.f#L1>`_
Undocumented
`nucl_aos <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L192>`_
List of AOs attached on each atom
`nucl_list_shell_aos <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L210>`_
Index of the shell type Aos and of the corresponding Aos
Per convention, for P,D,F and G AOs, we take the index
of the AO with the the corresponding power in the "X" axis
`nucl_n_aos <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L178>`_
Number of AOs per atom
`nucl_num_shell_aos <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/aos.irp.f#L211>`_
Index of the shell type Aos and of the corresponding Aos
Per convention, for P,D,F and G AOs, we take the index
of the AO with the the corresponding power in the "X" axis
`s_half <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L193>`_
S^{1/2}
`s_half_inv <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L134>`_
Matrix X = S^{-1/2} obtained by SVD
`s_inv <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis/ao_overlap.irp.f#L126>`_
S^-1
Anthony Scemama
87109fb96b
