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