2014-04-03 16:23:27 +02:00
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==========
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AOs Module
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==========
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2014-04-10 22:07:04 +02:00
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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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Assumptions
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===========
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.. Do not edit this section. It was auto-generated from the
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2014-05-13 13:57:58 +02:00
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.. NEEDED_MODULES file.
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2014-04-10 22:07:04 +02:00
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* The atomic orbitals are normalized:
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.. math::
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\int \left(\chi_i({\bf r}) \right)^2 dr = 1
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2014-07-14 18:45:10 +02:00
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* The AO coefficients in the EZFIO files are not necessarily normalized and are normalized after reading
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2014-04-10 22:07:04 +02:00
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* The AO coefficients and exponents are ordered in increasing order of exponents
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2014-04-03 16:23:27 +02:00
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Needed Modules
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2014-04-04 00:41:43 +02:00
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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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2014-04-03 16:23:27 +02:00
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2014-04-04 00:47:13 +02:00
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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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2014-05-14 00:01:31 +02:00
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* `Output <http://github.com/LCPQ/quantum_package/tree/master/src/Output>`_
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2014-04-04 00:47:13 +02:00
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* `Utils <http://github.com/LCPQ/quantum_package/tree/master/src/Utils>`_
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2014-04-03 16:23:27 +02:00
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2014-05-13 13:57:58 +02:00
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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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2015-04-13 10:44:49 +02:00
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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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2014-05-14 00:01:31 +02:00
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`ao_coef <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L21>`_
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Coefficients, exponents and powers of x,y and z
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2014-05-13 13:57:58 +02:00
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2015-04-13 10:44:49 +02:00
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`ao_coef_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L157>`_
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2014-05-13 13:57:58 +02:00
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Transposed ao_coef and ao_expo
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2015-04-13 10:44:49 +02:00
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`ao_coef_unnormalized <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L116>`_
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Coefficients, exponents and powers of x,y and z as in the EZFIO file
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ao_coef(i,j) = coefficient of the jth primitive on the ith ao
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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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2014-05-14 00:01:31 +02:00
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`ao_expo <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L20>`_
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Coefficients, exponents and powers of x,y and z
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2014-05-13 13:57:58 +02:00
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2015-04-13 10:44:49 +02:00
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`ao_expo_transp <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L158>`_
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2014-05-13 13:57:58 +02:00
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Transposed ao_coef and ao_expo
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2015-04-13 10:44:49 +02:00
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`ao_expo_unsorted <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L117>`_
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Coefficients, exponents and powers of x,y and z as in the EZFIO file
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ao_coef(i,j) = coefficient of the jth primitive on the ith ao
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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 <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L118>`_
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Coefficients, exponents and powers of x,y and z as in the EZFIO file
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ao_coef(i,j) = coefficient of the jth primitive on the ith ao
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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#L119>`_
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Coefficients, exponents and powers of x,y and z as in the EZFIO file
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ao_coef(i,j) = coefficient of the jth primitive on the ith ao
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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#L309>`_
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Undocumented
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`ao_md5 <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L400>`_
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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#L207>`_
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2014-05-13 13:57:58 +02:00
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Index of the nuclei on which the ao is centered
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2014-05-14 00:01:31 +02:00
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`ao_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L1>`_
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2014-05-13 13:57:58 +02:00
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Number of atomic orbitals
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2014-05-14 00:01:31 +02:00
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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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2014-05-13 13:57:58 +02:00
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Number of atomic orbitals
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2014-05-14 00:01:31 +02:00
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`ao_power <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L19>`_
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Coefficients, exponents and powers of x,y and z
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2014-05-13 13:57:58 +02:00
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2015-04-13 10:44:49 +02:00
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`ao_prim_num <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L175>`_
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2014-05-13 13:57:58 +02:00
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Number of primitives per atomic orbital
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2015-04-13 10:44:49 +02:00
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`ao_prim_num_max <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L197>`_
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2014-05-14 00:07:58 +02:00
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Undocumented
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2015-04-13 10:44:49 +02:00
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`ao_prim_num_max_align <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L198>`_
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2014-05-14 00:07:58 +02:00
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Undocumented
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2015-04-13 10:44:49 +02:00
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`l_to_charater <http://github.com/LCPQ/quantum_package/tree/master/src/AOs/aos.irp.f#L216>`_
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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#L229>`_
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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#L242>`_
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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#L260>`_
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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#L228>`_
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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#L261>`_
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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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2014-05-13 13:57:58 +02:00
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