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781 lines
16 KiB
ReStructuredText
781 lines
16 KiB
ReStructuredText
.. _module_mo_one_e_ints:
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.. program:: mo_one_e_ints
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.. default-role:: option
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==================
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mo_one_e_integrals
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==================
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All the one-electron integrals in |MO| basis are defined here.
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The most important providers for usual quantum-chemistry calculation are:
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* `mo_kinetic_integrals` which are the kinetic operator integrals on the |AO| basis (see :file:`kin_mo_ints.irp.f`)
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* `mo_integrals_n_e` which are the nuclear-elctron operator integrals on the |AO| basis (see :file:`pot_mo_ints.irp.f`)
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* `mo_one_e_integrals` which are the the h_core operator integrals on the |AO| basis (see :file:`mo_mono_ints.irp.f`)
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Note that you can find other interesting integrals related to the position operator in :file:`spread_dipole_mo.irp.f`.
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EZFIO parameters
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----------------
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.. option:: mo_integrals_n_e
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Nucleus-electron integrals in |MO| basis set
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.. option:: io_mo_integrals_n_e
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Read/Write |MO| electron-nucleus attraction integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: mo_integrals_kinetic
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Kinetic energy integrals in |MO| basis set
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.. option:: io_mo_integrals_kinetic
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Read/Write |MO| one-electron kinetic integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: mo_integrals_pseudo
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Pseudopotential integrals in |MO| basis set
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.. option:: io_mo_integrals_pseudo
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Read/Write |MO| pseudopotential integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: mo_one_e_integrals
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One-electron integrals in |MO| basis set
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.. option:: io_mo_one_e_integrals
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Read/Write |MO| one-electron integrals from/to disk [ Write | Read | None ]
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Default: None
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Providers
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---------
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.. c:var:: ao_one_e_integrals_from_mo
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File : :file:`mo_one_e_ints/ao_to_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_one_e_integrals_from_mo (ao_num,ao_num)
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Integrals of the one e hamiltonian obtained from the integrals on the MO basis
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WARNING : this is equal to ao_one_e_integrals only if the AO and MO basis have the same number of functions
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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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* :c:data:`mo_one_e_integrals`
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* :c:data:`s_mo_coef`
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.. c:var:: mo_dipole_x
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_dipole_x (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_y (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_z (mo_num,mo_num)
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array of the integrals of MO_i * x MO_j
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array of the integrals of MO_i * y MO_j
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array of the integrals of MO_i * z MO_j
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_dipole_x`
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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_spread_centered_x`
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* :c:data:`multi_s_dipole_moment`
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* :c:data:`z_dipole_moment`
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.. c:var:: mo_dipole_y
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_dipole_x (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_y (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_z (mo_num,mo_num)
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array of the integrals of MO_i * x MO_j
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array of the integrals of MO_i * y MO_j
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array of the integrals of MO_i * z MO_j
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_dipole_x`
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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_spread_centered_x`
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* :c:data:`multi_s_dipole_moment`
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* :c:data:`z_dipole_moment`
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.. c:var:: mo_dipole_z
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_dipole_x (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_y (mo_num,mo_num)
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double precision, allocatable :: mo_dipole_z (mo_num,mo_num)
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array of the integrals of MO_i * x MO_j
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array of the integrals of MO_i * y MO_j
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array of the integrals of MO_i * z MO_j
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_dipole_x`
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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_spread_centered_x`
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* :c:data:`multi_s_dipole_moment`
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* :c:data:`z_dipole_moment`
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.. c:var:: mo_integrals_n_e
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File : :file:`mo_one_e_ints/pot_mo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_integrals_n_e (mo_num,mo_num)
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Nucleus-electron interaction on the |MO| basis
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_n_e`
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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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* :c:data:`read_mo_integrals_n_e`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`mo_one_e_integrals`
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* :c:data:`ref_bitmask_energy`
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* :c:data:`v_ne_psi_energy`
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.. c:var:: mo_integrals_n_e_per_atom
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File : :file:`mo_one_e_ints/pot_mo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_integrals_n_e_per_atom (mo_num,mo_num,nucl_num)
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mo_integrals_n_e_per_atom(i,j,k) =
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:math:`\langle \phi_i| -\frac{1}{|r-R_k|} | \phi_j \rangle` .
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where R_k is the coordinate of the k-th nucleus.
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_n_e_per_atom`
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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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* :c:data:`nucl_num`
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.. c:var:: mo_kinetic_integrals
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File : :file:`mo_one_e_ints/kin_mo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_kinetic_integrals (mo_num,mo_num)
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Kinetic energy integrals in the MO basis
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_kinetic_integrals`
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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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* :c:data:`read_mo_integrals_kinetic`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`mo_one_e_integrals`
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* :c:data:`ref_bitmask_energy`
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.. c:var:: mo_one_e_integrals
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File : :file:`mo_one_e_ints/mo_one_e_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_one_e_integrals (mo_num,mo_num)
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array of the one-electron Hamiltonian on the |MO| basis :
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sum of the kinetic and nuclear electronic potentials (and pseudo potential if needed)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`read_mo_one_e_integrals`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_one_e_integrals_from_mo`
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* :c:data:`core_energy`
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* :c:data:`etwo`
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* :c:data:`fock_operator_closed_shell_ref_bitmask`
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* :c:data:`h_core_ri`
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* :c:data:`one_ints_no`
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* :c:data:`psi_energy_h_core`
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* :c:data:`ref_bitmask_energy`
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.. c:var:: mo_overlap
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File : :file:`mo_one_e_ints/mo_overlap.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_overlap (mo_num,mo_num)
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Provider to check that the MOs are indeed orthonormal.
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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_overlap`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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.. c:var:: mo_pseudo_integrals
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File : :file:`mo_one_e_ints/pot_mo_pseudo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_pseudo_integrals (mo_num,mo_num)
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Pseudopotential integrals in |MO| basis
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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_pseudo_integrals`
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* :c:data:`do_pseudo`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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* :c:data:`read_mo_integrals_pseudo`
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.. c:var:: mo_pseudo_integrals_local
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File : :file:`mo_one_e_ints/pot_mo_pseudo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_pseudo_integrals_local (mo_num,mo_num)
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Pseudopotential integrals in |MO| basis
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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_pseudo_integrals_local`
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* :c:data:`do_pseudo`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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.. c:var:: mo_pseudo_integrals_non_local
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File : :file:`mo_one_e_ints/pot_mo_pseudo_ints.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_pseudo_integrals_non_local (mo_num,mo_num)
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Pseudopotential integrals in |MO| basis
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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_pseudo_integrals_non_local`
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* :c:data:`do_pseudo`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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.. c:var:: mo_spread_centered_x
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_centered_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_z (mo_num,mo_num)
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array of the integrals of MO_i * (x^2 - <MO_i|x|MO_j>^2) MO_j = MO_i x^2 MO_j - (MO_i x MO_j)^2
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array of the integrals of MO_i * (y^2 - <MO_i|y|MO_j>^2) MO_j = MO_i y^2 MO_j - (MO_i y MO_j)^2
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array of the integrals of MO_i * (z^2 - <MO_i|z|MO_j>^2) MO_j = MO_i z^2 MO_j - (MO_i z MO_j)^2
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_num`
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* :c:data:`mo_spread_x`
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.. c:var:: mo_spread_centered_y
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_centered_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_z (mo_num,mo_num)
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array of the integrals of MO_i * (x^2 - <MO_i|x|MO_j>^2) MO_j = MO_i x^2 MO_j - (MO_i x MO_j)^2
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array of the integrals of MO_i * (y^2 - <MO_i|y|MO_j>^2) MO_j = MO_i y^2 MO_j - (MO_i y MO_j)^2
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array of the integrals of MO_i * (z^2 - <MO_i|z|MO_j>^2) MO_j = MO_i z^2 MO_j - (MO_i z MO_j)^2
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_num`
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* :c:data:`mo_spread_x`
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.. c:var:: mo_spread_centered_z
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_centered_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_centered_z (mo_num,mo_num)
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array of the integrals of MO_i * (x^2 - <MO_i|x|MO_j>^2) MO_j = MO_i x^2 MO_j - (MO_i x MO_j)^2
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array of the integrals of MO_i * (y^2 - <MO_i|y|MO_j>^2) MO_j = MO_i y^2 MO_j - (MO_i y MO_j)^2
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array of the integrals of MO_i * (z^2 - <MO_i|z|MO_j>^2) MO_j = MO_i z^2 MO_j - (MO_i z MO_j)^2
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_dipole_x`
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* :c:data:`mo_num`
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* :c:data:`mo_spread_x`
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.. c:var:: mo_spread_x
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_z (mo_num,mo_num)
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array of the integrals of MO_i * x^2 MO_j
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array of the integrals of MO_i * y^2 MO_j
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array of the integrals of MO_i * z^2 MO_j
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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_spread_x`
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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_spread_centered_x`
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.. c:var:: mo_spread_y
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_z (mo_num,mo_num)
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array of the integrals of MO_i * x^2 MO_j
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array of the integrals of MO_i * y^2 MO_j
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array of the integrals of MO_i * z^2 MO_j
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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_spread_x`
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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_spread_centered_x`
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.. c:var:: mo_spread_z
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File : :file:`mo_one_e_ints/spread_dipole_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: mo_spread_x (mo_num,mo_num)
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double precision, allocatable :: mo_spread_y (mo_num,mo_num)
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double precision, allocatable :: mo_spread_z (mo_num,mo_num)
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array of the integrals of MO_i * x^2 MO_j
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array of the integrals of MO_i * y^2 MO_j
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array of the integrals of MO_i * z^2 MO_j
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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_spread_x`
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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_spread_centered_x`
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.. c:var:: s_mo_coef
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File : :file:`mo_one_e_ints/ao_to_mo.irp.f`
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.. code:: fortran
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double precision, allocatable :: s_mo_coef (ao_num,mo_num)
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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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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_overlap`
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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:`ao_one_e_integrals_from_mo`
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* :c:data:`fock_matrix_ao`
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Subroutines / functions
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-----------------------
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.. c:function:: mo_to_ao:
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File : :file:`mo_one_e_ints/ao_to_mo.irp.f`
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.. code:: fortran
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subroutine mo_to_ao(A_mo,LDA_mo,A_ao,LDA_ao)
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Transform A from the MO basis to the AO basis
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$(S.C).A_{mo}.(S.C)^\dagger$
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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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* :c:data:`s_mo_coef`
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_one_e_integrals_from_mo`
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* :c:data:`fock_matrix_ao`
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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:: mo_to_ao_no_overlap:
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File : :file:`mo_one_e_ints/ao_to_mo.irp.f`
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.. code:: fortran
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subroutine mo_to_ao_no_overlap(A_mo,LDA_mo,A_ao,LDA_ao)
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$C.A_{mo}.C^\dagger$
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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:data:`d0tu_alpha_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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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:: orthonormalize_mos:
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File : :file:`mo_one_e_ints/orthonormalize.irp.f`
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.. code:: fortran
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subroutine orthonormalize_mos
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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:`lin_dep_cutoff`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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* :c:data:`mo_overlap`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`huckel_guess`
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* :c:func:`roothaan_hall_scf`
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* :c:func:`save_natural_mos`
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* :c:func:`save_natural_mos_canon_label`
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* :c:func:`save_natural_mos_no_ov_rot`
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* :c:func:`scf`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`ortho_lowdin`
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Touches:
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.. hlist::
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:columns: 3
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* :c:data:`mo_coef`
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