150 lines
5.7 KiB
ReStructuredText
150 lines
5.7 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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.. Do not edit this section. It was auto-generated from the
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.. NEEDED_MODULES file.
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Needed Modules
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==============
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.. Do not edit this section. It was auto-generated from the
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.. NEEDED_MODULES file.
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* `Ezfio_files <http://github.com/LCPQ/quantum_package/tree/master/src/Ezfio_files>`_
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* `Nuclei <http://github.com/LCPQ/quantum_package/tree/master/src/Nuclei>`_
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* `Output <http://github.com/LCPQ/quantum_package/tree/master/src/Output>`_
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* `Utils <http://github.com/LCPQ/quantum_package/tree/master/src/Utils>`_
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Documentation
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=============
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.. Do not edit this section. It was auto-generated from the
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.. NEEDED_MODULES file.
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`ao_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/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/AOs/ao_overlap.irp.f#L65>`_
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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/AOs/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/AOs/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/AOs/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_coef <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L62>`_
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AO Coefficients, read from input. Those should not be used directly, as
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the MOs are expressed on the basis of **normalized** AOs.
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`ao_coef_normalized <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L84>`_
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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/AOs/aos.irp.f#L107>`_
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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/AOs/aos.irp.f#L133>`_
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Transposed ao_coef_normalized_ordered
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`ao_expo <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L41>`_
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AO Exponents read from input
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`ao_expo_ordered <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L108>`_
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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/AOs/aos.irp.f#L147>`_
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Transposed ao_expo_ordered
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`ao_l <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L162>`_
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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/AOs/aos.irp.f#L163>`_
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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/AOs/aos.irp.f#L311>`_
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Undocumented
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`ao_md5 <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L403>`_
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MD5 key characteristic of the AO basis
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`ao_nucl <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L209>`_
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Index of the nuclei on which the ao is centered
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`ao_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L1>`_
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Number of atomic orbitals
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`ao_num_align <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L2>`_
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Number of atomic orbitals
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`ao_power <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L19>`_
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Powers of x,y and z read from input
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`ao_prim_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L177>`_
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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/AOs/aos.irp.f#L199>`_
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Undocumented
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`ao_prim_num_max_align <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L200>`_
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Undocumented
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`l_to_charater <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L218>`_
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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/AOs/aos.irp.f#L231>`_
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Number of AOs per atom
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`nucl_aos <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L244>`_
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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/AOs/aos.irp.f#L262>`_
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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/AOs/aos.irp.f#L230>`_
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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/AOs/aos.irp.f#L263>`_
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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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