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849 lines
16 KiB
ReStructuredText
849 lines
16 KiB
ReStructuredText
.. _module_mo_basis:
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.. program:: mo_basis
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.. default-role:: option
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========
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mo_basis
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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 functions.
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The current set of |MOs| 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 :file:`mo_basis` directory of the |EZFIO| database
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is copied in the :file:`save` directory, named by the current `mo_label`. All
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this is done with the script named :file:`save_current_mos.sh` in the
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:file:`$QP_ROOT/scripts` directory.
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EZFIO parameters
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----------------
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.. option:: mo_num
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Total number of |MOs|
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.. option:: mo_coef
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Coefficient of the i-th |AO| on the j-th |MO|
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.. option:: mo_label
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Label characterizing the MOS (Local, Canonical, Natural, *etc*)
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.. option:: mo_occ
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|MO| occupation numbers
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.. option:: mo_class
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[ Core | Inactive | Active | Virtual | Deleted ], as defined by :ref:`qp_set_mo_class`
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.. option:: ao_md5
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MD5 checksum characterizing the |AO| basis set.
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Providers
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---------
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.. c:var:: mo_class
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File : :file:`mo_basis/mo_class.irp.f`
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.. code:: fortran
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character*(32), allocatable :: mo_class (mo_num)
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[ Core | Inactive | Active | Virtual | Deleted ], as defined by :ref:`qp_set_mo_class`
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ezfio_filename`
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* :c:data:`mo_num`
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* :c:data:`mpi_master`
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* :c:data:`output_wall_time_0`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`full_ijkl_bitmask`
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* :c:data:`list_act`
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* :c:data:`list_all_but_del_orb`
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* :c:data:`list_core`
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* :c:data:`list_del`
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* :c:data:`list_inact`
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* :c:data:`list_virt`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`n_act_orb`
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* :c:data:`n_all_but_del_orb`
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* :c:data:`n_core_orb`
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* :c:data:`n_del_orb`
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* :c:data:`n_inact_orb`
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* :c:data:`n_virt_orb`
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.. c:var:: mo_coef
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_coef (ao_num,mo_num)
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Molecular orbital coefficients on |AO| basis set
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mo_coef(i,j) = coefficient of the i-th |AO| on the jth |MO|
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mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`ao_ortho_canonical_coef`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_num`
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* :c:data:`mpi_master`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`mo_coef_in_ao_ortho_basis`
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* :c:data:`mo_coef_novirt`
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* :c:data:`mo_coef_transp`
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_integrals_n_e_per_atom`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_overlap`
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* :c:data:`mo_pseudo_integrals`
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* :c:data:`mo_spread_x`
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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* :c:data:`one_e_dm_alpha_ao_for_dft`
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* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
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* :c:data:`one_e_dm_ao_alpha`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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* :c:data:`one_e_spin_density_ao`
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* :c:data:`psi_det`
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* :c:data:`s_mo_coef`
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.. c:var:: mo_coef_imag
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_coef_imag (ao_num,mo_num)
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Molecular orbital coefficients on |AO| basis set
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mo_coef_imag(i,j) = coefficient of the i-th |AO| on the jth |MO|
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mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_num`
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* :c:data:`mpi_master`
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.. c:var:: mo_coef_in_ao_ortho_basis
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_coef_in_ao_ortho_basis (ao_num,mo_num)
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|MO| coefficients in orthogonalized |AO| basis
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:math:`C^{-1}.C_{mo}`
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`ao_ortho_canonical_coef_inv`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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.. c:var:: mo_coef_transp
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_coef_transp (mo_num,ao_num)
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|MO| coefficients on |AO| basis set
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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.. c:var:: mo_label
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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character*(64) :: mo_label
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|MO| coefficients on |AO| basis set
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mo_coef(i,j) = coefficient of the i-th |AO| on the j-th |MO|
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mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ezfio_filename`
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* :c:data:`mpi_master`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`n_det`
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* :c:data:`psi_coef`
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* :c:data:`psi_det`
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.. c:var:: mo_num
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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integer :: mo_num
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Number of MOs
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_ortho_canonical_coef`
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* :c:data:`ezfio_filename`
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* :c:data:`mpi_master`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`banned_excitation`
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* :c:data:`big_array_coulomb_integrals`
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* :c:data:`core_fock_operator`
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* :c:data:`data_one_e_dm_alpha_mo`
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* :c:data:`data_one_e_dm_beta_mo`
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* :c:data:`fock_operator_closed_shell_ref_bitmask`
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* :c:data:`fock_wee_closed_shell`
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* :c:data:`full_ijkl_bitmask`
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* :c:data:`list_act`
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* :c:data:`list_all_but_del_orb`
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* :c:data:`list_core`
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* :c:data:`list_core_inact`
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* :c:data:`list_core_inact_act`
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* :c:data:`list_del`
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* :c:data:`list_inact`
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* :c:data:`list_inact_act`
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* :c:data:`list_virt`
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* :c:data:`mo_class`
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* :c:data:`mo_coef`
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* :c:data:`mo_coef_begin_iteration`
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* :c:data:`mo_coef_imag`
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* :c:data:`mo_coef_in_ao_ortho_basis`
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* :c:data:`mo_coef_transp`
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_integrals_cache_min`
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* :c:data:`mo_integrals_map`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_integrals_n_e_per_atom`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_occ`
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* :c:data:`mo_one_e_integrals`
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* :c:data:`mo_overlap`
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* :c:data:`mo_pseudo_integrals`
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* :c:data:`mo_spread_x`
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`mo_two_e_integrals_jj`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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* :c:data:`n_act_orb`
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* :c:data:`n_all_but_del_orb`
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* :c:data:`n_core_orb`
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* :c:data:`n_del_orb`
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* :c:data:`n_inact_orb`
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* :c:data:`n_int`
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* :c:data:`n_virt_orb`
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* :c:data:`one_body_dm_mo_alpha_one_det`
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* :c:data:`one_e_dm_alpha_ao_for_dft`
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* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
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* :c:data:`one_e_dm_ao_alpha`
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* :c:data:`one_e_dm_average_alpha_mo_for_dft`
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* :c:data:`one_e_dm_average_beta_mo_for_dft`
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* :c:data:`one_e_dm_average_mo_for_dft`
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* :c:data:`one_e_dm_dagger_mo_spin_index`
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* :c:data:`one_e_dm_mo`
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* :c:data:`one_e_dm_mo_alpha`
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* :c:data:`one_e_dm_mo_alpha_average`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_alpha_for_dft_no_core`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft_no_core`
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* :c:data:`one_e_dm_mo_diff`
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* :c:data:`one_e_dm_mo_for_dft`
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* :c:data:`one_e_dm_mo_spin_index`
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* :c:data:`one_e_spin_density_ao`
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* :c:data:`one_e_spin_density_mo`
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* :c:data:`psi_energy_h_core`
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* :c:data:`s_mo_coef`
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* :c:data:`singles_alpha_csc_idx`
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* :c:data:`singles_beta_csc_idx`
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.. c:var:: mo_occ
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_occ (mo_num)
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|MO| occupation numbers
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`elec_alpha_num`
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* :c:data:`elec_beta_num`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_num`
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* :c:data:`mpi_master`
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Subroutines / functions
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-----------------------
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.. c:function:: ao_ortho_cano_to_ao:
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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subroutine ao_ortho_cano_to_ao(A_ao,LDA_ao,A,LDA)
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Transform A from the |AO| basis to the orthogonal |AO| basis
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$C^{-1}.A_{ao}.C^{\dagger-1}$
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`ao_ortho_canonical_coef_inv`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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.. c:function:: ao_to_mo:
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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subroutine ao_to_mo(A_ao,LDA_ao,A_mo,LDA_mo)
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Transform A from the |AO| basis to the |MO| basis
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$C^\dagger.A_{ao}.C$
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`four_idx_novvvv`
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_integrals_n_e_per_atom`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_pseudo_integrals`
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* :c:data:`mo_spread_x`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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* :c:func:`restore_symmetry`
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.. c:function:: give_all_mos_and_grad_and_lapl_at_r:
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File : :file:`mo_basis/mos_in_r.irp.f`
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.. code:: fortran
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subroutine give_all_mos_and_grad_and_lapl_at_r(r,mos_array,mos_grad_array,mos_lapl_array)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_all_aos_and_grad_and_lapl_at_r`
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.. c:function:: give_all_mos_and_grad_at_r:
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File : :file:`mo_basis/mos_in_r.irp.f`
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.. code:: fortran
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subroutine give_all_mos_and_grad_at_r(r,mos_array,mos_grad_array)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_all_aos_and_grad_at_r`
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.. c:function:: give_all_mos_at_r:
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File : :file:`mo_basis/mos_in_r.irp.f`
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.. code:: fortran
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subroutine give_all_mos_at_r(r,mos_array)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef_transp`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemv`
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* :c:func:`give_all_aos_at_r`
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.. c:function:: mix_mo_jk:
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File : :file:`mo_basis/mos.irp.f`
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.. code:: fortran
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subroutine mix_mo_jk(j,k)
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Rotates the j-th |MO| with the k-th |MO| to give two new |MOs| that are
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* $+ = \frac{1}{\sqrt{2}} ( | j\rangle + | k\rangle)$
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* $- = \frac{1}{\sqrt{2}} ( | j\rangle - | k\rangle)$
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by convention, the '+' |MO| is in the lowest index (min(j,k))
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by convention, the '-' |MO| is in the highest index (max(j,k))
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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.. c:function:: mo_as_eigvectors_of_mo_matrix:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine mo_as_eigvectors_of_mo_matrix(matrix,n,m,label,sign,output)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_label`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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* :c:func:`lapack_diag`
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* :c:func:`write_time`
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.. c:function:: mo_as_svd_vectors_of_mo_matrix:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine mo_as_svd_vectors_of_mo_matrix(matrix,lda,m,n,label)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_label`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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* :c:func:`svd`
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* :c:func:`write_time`
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.. c:function:: mo_as_svd_vectors_of_mo_matrix_eig:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine mo_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,eig,label)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_coef`
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* :c:data:`mo_label`
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* :c:data:`mo_num`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`set_natural_mos`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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* :c:func:`svd`
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* :c:func:`write_time`
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.. c:function:: mo_coef_new_as_svd_vectors_of_mo_matrix_eig:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine mo_coef_new_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,mo_coef_before,eig,mo_coef_new)
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You enter with matrix in the MO basis defined with the mo_coef_before.
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You SVD the matrix and set the eigenvectors as mo_coef_new ordered by increasing singular values
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`mo_num`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`dgemm`
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* :c:func:`svd`
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* :c:func:`write_time`
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.. c:function:: save_mos:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine save_mos
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_md5`
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* :c:data:`ao_num`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_class`
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* :c:data:`mo_coef`
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* :c:data:`mo_label`
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* :c:data:`mo_num`
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* :c:data:`mo_occ`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`save_natural_mos`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`ezfio_set_mo_basis_ao_md5`
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* :c:func:`ezfio_set_mo_basis_mo_class`
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* :c:func:`ezfio_set_mo_basis_mo_coef`
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* :c:func:`ezfio_set_mo_basis_mo_label`
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* :c:func:`ezfio_set_mo_basis_mo_num`
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* :c:func:`ezfio_set_mo_basis_mo_occ`
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* :c:func:`system`
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.. c:function:: save_mos_no_occ:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine save_mos_no_occ
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Needs:
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|
.. hlist::
|
|
:columns: 3
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* :c:data:`ao_num`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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Calls:
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|
.. hlist::
|
|
:columns: 3
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* :c:func:`ezfio_set_mo_basis_mo_coef`
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* :c:func:`system`
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.. c:function:: save_mos_truncated:
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File : :file:`mo_basis/utils.irp.f`
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.. code:: fortran
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subroutine save_mos_truncated(n)
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|
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Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
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* :c:data:`ao_md5`
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* :c:data:`ao_num`
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* :c:data:`ezfio_filename`
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* :c:data:`mo_class`
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* :c:data:`mo_coef`
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* :c:data:`mo_label`
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* :c:data:`mo_occ`
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|
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Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
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|
|
|
* :c:func:`ezfio_set_mo_basis_ao_md5`
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* :c:func:`ezfio_set_mo_basis_mo_class`
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* :c:func:`ezfio_set_mo_basis_mo_coef`
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* :c:func:`ezfio_set_mo_basis_mo_label`
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* :c:func:`ezfio_set_mo_basis_mo_num`
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* :c:func:`ezfio_set_mo_basis_mo_occ`
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* :c:func:`system`
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