quantum_package/src/MO_Basis/README.rst

==========
MOs Module
==========

Molecular orbitals are expressed as 

.. math::

  \phi_k({\bf r}) = \sum_i C_{ik} \chi_k({\bf r})

where :math:`\chi_k` are *normalized* atomic basis set.

The current set of molecular orbitals has a label ``mo_label``.
When the orbitals are modified, the label should also be updated to keep
everything consistent.

When saving the MOs, the ``mo_basis`` directory of the EZFIO file is copied
in the ``save`` directory, named by the current ``mo_label``. All this is
done with the script named ``save_current_mos.sh`` in the ``scripts`` directory.

Assumptions
===========

.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES_CHILDREN file by the `update_README.py` script.

ASSUMPTONS
==========

* The AO basis functions are normalized.


Needed Modules
==============

.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.

.. image:: tree_dependency.png

* `AO_Basis <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis>`_
* `Electrons <http://github.com/LCPQ/quantum_package/tree/master/src/Electrons>`_

Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.


.. image:: tree_dependency.png

* `AO_Basis <http://github.com/LCPQ/quantum_package/tree/master/src/AO_Basis>`_
* `Electrons <http://github.com/LCPQ/quantum_package/tree/master/src/Electrons>`_

Documentation
=============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.


`ao_cart_to_sphe_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L1>`_
  matrix of the coefficients of the mos generated by the
  orthonormalization by the S^{-1/2} canonical transformation of the aos
  ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital


`ao_cart_to_sphe_inv <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L73>`_
  AO_cart_to_sphe_coef^(-1)


`ao_cart_to_sphe_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L2>`_
  matrix of the coefficients of the mos generated by the
  orthonormalization by the S^{-1/2} canonical transformation of the aos
  ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital


`ao_cart_to_sphe_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L51>`_
  AO overlap matrix in the spherical basis set


`ao_ortho_cano_to_ao <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L329>`_
  Transform A from the AO basis to the orthogonal AO basis
  .br
  C^(-1).A_ao.Ct^(-1)


`ao_ortho_canonical_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L95>`_
  matrix of the coefficients of the mos generated by the
  orthonormalization by the S^{-1/2} canonical transformation of the aos
  ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital


`ao_ortho_canonical_coef_inv <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L86>`_
  ao_ortho_canonical_coef^(-1)


`ao_ortho_canonical_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L96>`_
  matrix of the coefficients of the mos generated by the
  orthonormalization by the S^{-1/2} canonical transformation of the aos
  ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital


`ao_ortho_canonical_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ao_ortho_canonical.irp.f#L144>`_
  overlap matrix of the ao_ortho_canonical.
  Expected to be the Identity


`ao_to_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L213>`_
  Transform A from the AO basis to the MO basis
  .br
  Ct.A_ao.C


`cholesky_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/cholesky_mo.irp.f#L1>`_
  Cholesky decomposition of AO Density matrix
  .br
  n : Number of AOs
  m : Number of MOs
  .br
  P(LDP,n) : Density matrix in AO basis
  .br
  C(LDC,m) : MOs
  .br
  tol_in : tolerance
  .br
  rank : Nomber of local MOs (output)
  .br


`give_all_mos_at_r <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L276>`_
  Undocumented


`give_specific_mos_at_r <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L283>`_
  Undocumented


`mix_mo_jk <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L295>`_
  subroutine that rotates the jth MO with the kth MO
  to give two new MO's that are
  '+' = 1/sqrt(2) (|j> + |k>)
  '-' = 1/sqrt(2) (|j> - |k>)
  by convention, the '+' MO is in the lower index (min(j,k))
  by convention, the '-' MO is in the greater index (max(j,k))


`mo_as_eigvectors_of_mo_matrix <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L47>`_
  Undocumented


`mo_as_eigvectors_of_mo_matrix_sort_by_observable <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L155>`_
  Undocumented


`mo_as_svd_vectors_of_mo_matrix <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L108>`_
  Undocumented


`mo_class <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/ezfio_interface.irp.f#L6>`_
  Core|Inactive|Active|Virtual|Deleted


`mo_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L57>`_
  Molecular orbital coefficients on AO basis set
  mo_coef(i,j) = coefficient of the ith ao on the jth mo
  mo_label : Label characterizing the MOS (local, canonical, natural, etc)


`mo_coef_in_ao_ortho_basis <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L105>`_
  MO coefficients in orthogonalized AO basis
  .br
  C^(-1).C_mo


`mo_coef_transp <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L150>`_
  Molecular orbital coefficients on AO basis set


`mo_label <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L119>`_
  Molecular orbital coefficients on AO basis set
  mo_coef(i,j) = coefficient of the ith ao on the jth mo
  mo_label : Label characterizing the MOS (local, canonical, natural, etc)


`mo_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L38>`_
  mo_tot_num without the highest deleted MOs


`mo_occ <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L178>`_
  MO occupation numbers


`mo_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mo_overlap.irp.f#L2>`_
  Undocumented


`mo_sort_by_observable <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L237>`_
  Undocumented


`mo_to_ao <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L241>`_
  Transform A from the MO basis to the AO basis
  .br
  (S.C).A_mo.(S.C)t


`mo_to_ao_no_overlap <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L268>`_
  Transform A from the MO basis to the S^-1 AO basis
  Useful for density matrix


`mo_tot_num <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L1>`_
  Number of MOs


`permut_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mo_permutation.irp.f#L1>`_
  Undocumented


`s_mo_coef <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/mos.irp.f#L165>`_
  Product S.C where S is the overlap matrix in the AO basis and C the mo_coef matrix.


`save_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L1>`_
  Undocumented


`save_mos_truncated <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/utils.irp.f#L24>`_
  Undocumented


`svd_mo <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/cholesky_mo.irp.f#L53>`_
  Singular value decomposition of the AO Density matrix
  .br
  n : Number of AOs
  m : Number of MOs
  .br
  P(LDP,n) : Density matrix in AO basis
  .br
  C(LDC,m) : MOs
  .br
  tol_in : tolerance
  .br
  rank : Nomber of local MOs (output)
  .br


`swap_mos <http://github.com/LCPQ/quantum_package/tree/master/src/MO_Basis/swap_mos.irp.f#L1>`_
  Undocumented