251 lines
8.1 KiB
ReStructuredText
251 lines
8.1 KiB
ReStructuredText
==========
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MOs Module
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==========
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Molecular orbitals are expressed as
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.. math::
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\phi_k({\bf r}) = \sum_i C_{ik} \chi_k({\bf r})
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where :math:`\chi_k` are *normalized* atomic basis set.
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The current set of molecular orbitals has a label ``mo_label``.
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When the orbitals are modified, the label should also be updated to keep
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everything consistent.
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When saving the MOs, the ``mo_basis`` directory of the EZFIO file is copied
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in the ``save`` directory, named by the current ``mo_label``. All this is
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done with the script named ``save_current_mos.sh`` in the ``scripts`` directory.
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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_CHILDREN file by the `update_README.py` script.
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ASSUMPTONS
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==========
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* The AO basis functions are normalized.
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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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* `AO_Basis <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis>`_
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* `Electrons <http://github.com/LCPQ/quantum_package/tree/master/src/Electrons>`_
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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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* `AO_Basis <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis>`_
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* `Electrons <http://github.com/LCPQ/quantum_package/tree/master/src/Electrons>`_
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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_cart_to_sphe_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L1>`_
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matrix of the coefficients of the mos generated by the
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orthonormalization by the S^{-1/2} canonical transformation of the aos
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ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital
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`ao_cart_to_sphe_inv <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L73>`_
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AO_cart_to_sphe_coef^(-1)
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`ao_cart_to_sphe_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L2>`_
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matrix of the coefficients of the mos generated by the
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orthonormalization by the S^{-1/2} canonical transformation of the aos
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ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital
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`ao_cart_to_sphe_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L51>`_
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AO overlap matrix in the spherical basis set
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`ao_ortho_cano_to_ao <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L329>`_
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Transform A from the AO basis to the orthogonal AO basis
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.br
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C^(-1).A_ao.Ct^(-1)
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`ao_ortho_canonical_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L95>`_
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matrix of the coefficients of the mos generated by the
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orthonormalization by the S^{-1/2} canonical transformation of the aos
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ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital
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`ao_ortho_canonical_coef_inv <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L86>`_
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ao_ortho_canonical_coef^(-1)
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`ao_ortho_canonical_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L96>`_
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matrix of the coefficients of the mos generated by the
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orthonormalization by the S^{-1/2} canonical transformation of the aos
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ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital
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`ao_ortho_canonical_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L144>`_
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overlap matrix of the ao_ortho_canonical.
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Expected to be the Identity
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`ao_to_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L213>`_
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Transform A from the AO basis to the MO basis
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.br
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Ct.A_ao.C
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`cholesky_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/cholesky_mo.irp.f#L1>`_
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Cholesky decomposition of AO Density matrix
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.br
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n : Number of AOs
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m : Number of MOs
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.br
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P(LDP,n) : Density matrix in AO basis
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.br
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C(LDC,m) : MOs
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.br
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tol_in : tolerance
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.br
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rank : Nomber of local MOs (output)
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.br
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`give_all_mos_at_r <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L276>`_
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Undocumented
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`give_specific_mos_at_r <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L283>`_
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Undocumented
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`mix_mo_jk <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L295>`_
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subroutine that rotates the jth MO with the kth MO
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to give two new MO's that are
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'+' = 1/sqrt(2) (|j> + |k>)
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'-' = 1/sqrt(2) (|j> - |k>)
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by convention, the '+' MO is in the lower index (min(j,k))
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by convention, the '-' MO is in the greater index (max(j,k))
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`mo_as_eigvectors_of_mo_matrix <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L47>`_
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Undocumented
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`mo_as_eigvectors_of_mo_matrix_sort_by_observable <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L155>`_
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Undocumented
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`mo_as_svd_vectors_of_mo_matrix <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L108>`_
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Undocumented
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`mo_class <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ezfio_interface.irp.f#L6>`_
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Core|Inactive|Active|Virtual|Deleted
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`mo_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L57>`_
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Molecular orbital coefficients on AO basis set
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mo_coef(i,j) = coefficient of the ith ao on the jth mo
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mo_label : Label characterizing the MOS (local, canonical, natural, etc)
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`mo_coef_in_ao_ortho_basis <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L105>`_
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MO coefficients in orthogonalized AO basis
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.br
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C^(-1).C_mo
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`mo_coef_transp <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L150>`_
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Molecular orbital coefficients on AO basis set
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`mo_label <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L119>`_
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Molecular orbital coefficients on AO basis set
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mo_coef(i,j) = coefficient of the ith ao on the jth mo
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mo_label : Label characterizing the MOS (local, canonical, natural, etc)
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`mo_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L38>`_
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mo_tot_num without the highest deleted MOs
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`mo_occ <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L178>`_
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MO occupation numbers
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`mo_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mo_overlap.irp.f#L2>`_
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Undocumented
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`mo_sort_by_observable <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L237>`_
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Undocumented
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`mo_to_ao <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L241>`_
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Transform A from the MO basis to the AO basis
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.br
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(S.C).A_mo.(S.C)t
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`mo_to_ao_no_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L268>`_
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Transform A from the MO basis to the S^-1 AO basis
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Useful for density matrix
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`mo_tot_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L1>`_
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Number of MOs
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`permut_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mo_permutation.irp.f#L1>`_
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Undocumented
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`s_mo_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L165>`_
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Product S.C where S is the overlap matrix in the AO basis and C the mo_coef matrix.
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`save_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L1>`_
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Undocumented
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`save_mos_truncated <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L24>`_
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Undocumented
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`svd_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/cholesky_mo.irp.f#L53>`_
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Singular value decomposition of the AO Density matrix
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.br
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n : Number of AOs
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m : Number of MOs
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.br
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P(LDP,n) : Density matrix in AO basis
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.br
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C(LDC,m) : MOs
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.br
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tol_in : tolerance
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.br
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rank : Nomber of local MOs (output)
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.br
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`swap_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/swap_mos.irp.f#L1>`_
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Undocumented
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