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qp2/docs/source/modules/scf_utils.rst

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.. _module_scf_utils:
.. program:: scf_utils
.. default-role:: option
=========
scf_utils
=========
The scf_utils module is an abstract module which contains the basics to perform *Restricted* SCF calculations (the
spatial part of the |MOs| is common for alpha and beta spinorbitals) based on a single-determinant wave function.
This module does not produce any executable *and must not do*, but instead it contains everything one needs to perform an orbital optimization based on an Fock matrix.
The ``scf_utils`` module is meant to be included in the :file:`NEED` of the various single determinant SCF procedures, such as ``hartree_fock`` or ``kohn_sham``, where a specific definition of the Fock matrix is given (see :file:`hartree_fock fock_matrix_hf.irp.f` for an example).
All SCF programs perform the following actions:
#. Compute/Read all the one- and two-electron integrals, and store them in memory
#. Check in the |EZFIO| database if there is a set of |MOs|. If there is, it
will read them as initial guess. Otherwise, it will create a guess.
#. Perform the |SCF| iterations based on the definition of the Fock matrix
The main keywords/options are:
* :option:`scf_utils thresh_scf`
* :option:`scf_utils level_shift`
At each iteration, the |MOs| are saved in the |EZFIO| database. Hence, if the calculation
crashes for any unexpected reason, the calculation can be restarted by running again
the |SCF| with the same |EZFIO| database.
The `DIIS`_ algorithm is implemented, as well as the `level-shifting`_ method.
If the |SCF| does not converge, try again with a higher value of :option:`level_shift`.
To start a calculation from scratch, the simplest way is to remove the
``mo_basis`` directory from the |EZFIO| database, and run the |SCF| again.
.. _DIIS: https://en.wikipedia.org/w/index.php?title=DIIS
.. _level-shifting: https://doi.org/10.1002/qua.560070407
EZFIO parameters
----------------
.. option:: max_dim_diis
Maximum size of the DIIS extrapolation procedure
Default: 15
.. option:: threshold_diis
Threshold on the convergence of the DIIS error vector during a Hartree-Fock calculation. If 0. is chosen, the square root of thresh_scf will be used.
Default: 0.
.. option:: thresh_scf
Threshold on the convergence of the Hartree Fock energy.
Default: 1.e-10
.. option:: n_it_scf_max
Maximum number of SCF iterations
Default: 500
.. option:: level_shift
Energy shift on the virtual MOs to improve SCF convergence
Default: 0.
.. option:: scf_algorithm
Type of SCF algorithm used. Possible choices are [ Simple | DIIS]
Default: DIIS
.. option:: mo_guess_type
Initial MO guess. Can be [ Huckel | HCore ]
Default: Huckel
.. option:: energy
Calculated HF energy
.. option:: frozen_orb_scf
If true, leave untouched all the orbitals defined as core and optimize all the orbitals defined as active with qp_set_mo_class
Default: False
Providers
---------
.. c:var:: eigenvalues_fock_matrix_ao
File : :file:`scf_utils/diis.irp.f`
.. code:: fortran
double precision, allocatable :: eigenvalues_fock_matrix_ao (AO_num)
double precision, allocatable :: eigenvectors_fock_matrix_ao (AO_num,AO_num)
Eigenvalues and eigenvectors of the Fock matrix over the AO basis
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`fock_matrix_ao`
* :c:data:`s_half_inv`
.. c:var:: eigenvectors_fock_matrix_ao
File : :file:`scf_utils/diis.irp.f`
.. code:: fortran
double precision, allocatable :: eigenvalues_fock_matrix_ao (AO_num)
double precision, allocatable :: eigenvectors_fock_matrix_ao (AO_num,AO_num)
Eigenvalues and eigenvectors of the Fock matrix over the AO basis
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`fock_matrix_ao`
* :c:data:`s_half_inv`
.. c:var:: eigenvectors_fock_matrix_mo
File : :file:`scf_utils/diagonalize_fock.irp.f`
.. code:: fortran
double precision, allocatable :: eigenvectors_fock_matrix_mo (ao_num,mo_num)
Eigenvectors of the Fock matrix in the MO basis obtained with level shift.
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`fock_matrix_mo`
* :c:data:`frozen_orb_scf`
* :c:data:`level_shift`
* :c:data:`list_inact`
* :c:data:`mo_coef`
* :c:data:`mo_num`
* :c:data:`n_core_orb`
.. c:function:: extrapolate_fock_matrix:
File : :file:`scf_utils/roothaan_hall_scf.irp.f`
.. code:: fortran
subroutine extrapolate_Fock_matrix( &
error_matrix_DIIS,Fock_matrix_DIIS, &
Fock_matrix_AO_,size_Fock_matrix_AO, &
iteration_SCF,dim_DIIS &
)
Compute the extrapolated Fock matrix using the DIIS procedure
Needs:
.. hlist::
:columns: 3
* :c:data:`max_dim_diis`
* :c:data:`ao_num`
Called by:
.. hlist::
:columns: 3
* :c:func:`roothaan_hall_scf`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`dsysvx`
.. c:var:: fock_matrix_ao
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision, allocatable :: fock_matrix_ao (ao_num,ao_num)
Fock matrix in AO basis set
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fock_matrix_mo`
* :c:data:`frozen_orb_scf`
* :c:data:`level_shift`
* :c:data:`mo_num`
* :c:data:`s_mo_coef`
Needed by:
.. hlist::
:columns: 3
* :c:data:`eigenvalues_fock_matrix_ao`
* :c:data:`fps_spf_matrix_ao`
.. c:var:: fock_matrix_diag_mo
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision, allocatable :: fock_matrix_mo (mo_num,mo_num)
double precision, allocatable :: fock_matrix_diag_mo (mo_num)
Fock matrix on the MO basis.
For open shells, the ROHF Fock Matrix is ::
| F-K | F + K/2 | F |
|---------------------------------|
| F + K/2 | F | F - K/2 |
|---------------------------------|
| F | F - K/2 | F + K |
F = 1/2 (Fa + Fb)
K = Fb - Fa
Needs:
.. hlist::
:columns: 3
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`fock_matrix_mo_alpha`
* :c:data:`fock_matrix_mo_beta`
* :c:data:`frozen_orb_scf`
* :c:data:`list_inact`
* :c:data:`mo_num`
* :c:data:`n_core_orb`
Needed by:
.. hlist::
:columns: 3
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`fock_matrix_ao`
.. c:var:: fock_matrix_mo
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision, allocatable :: fock_matrix_mo (mo_num,mo_num)
double precision, allocatable :: fock_matrix_diag_mo (mo_num)
Fock matrix on the MO basis.
For open shells, the ROHF Fock Matrix is ::
| F-K | F + K/2 | F |
|---------------------------------|
| F + K/2 | F | F - K/2 |
|---------------------------------|
| F | F - K/2 | F + K |
F = 1/2 (Fa + Fb)
K = Fb - Fa
Needs:
.. hlist::
:columns: 3
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`fock_matrix_mo_alpha`
* :c:data:`fock_matrix_mo_beta`
* :c:data:`frozen_orb_scf`
* :c:data:`list_inact`
* :c:data:`mo_num`
* :c:data:`n_core_orb`
Needed by:
.. hlist::
:columns: 3
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`fock_matrix_ao`
.. c:var:: fock_matrix_mo_alpha
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision, allocatable :: fock_matrix_mo_alpha (mo_num,mo_num)
Fock matrix on the MO basis
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`fock_matrix_mo`
.. c:var:: fock_matrix_mo_beta
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision, allocatable :: fock_matrix_mo_beta (mo_num,mo_num)
Fock matrix on the MO basis
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`fock_matrix_mo`
.. c:var:: fps_spf_matrix_ao
File : :file:`scf_utils/diis.irp.f`
.. code:: fortran
double precision, allocatable :: fps_spf_matrix_ao (AO_num,AO_num)
Commutator FPS - SPF
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_overlap`
* :c:data:`fock_matrix_ao`
* :c:data:`scf_density_matrix_ao`
Needed by:
.. hlist::
:columns: 3
* :c:data:`fps_spf_matrix_mo`
.. c:var:: fps_spf_matrix_mo
File : :file:`scf_utils/diis.irp.f`
.. code:: fortran
double precision, allocatable :: fps_spf_matrix_mo (mo_num,mo_num)
Commutator FPS - SPF in MO basis
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`fps_spf_matrix_ao`
* :c:data:`mo_coef`
* :c:data:`mo_num`
.. c:var:: scf_density_matrix_ao
File : :file:`scf_utils/scf_density_matrix_ao.irp.f`
.. code:: fortran
double precision, allocatable :: scf_density_matrix_ao (ao_num,ao_num)
Sum of :math:`\alpha` and :math:`\beta` density matrices
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`scf_density_matrix_ao_alpha`
* :c:data:`scf_density_matrix_ao_beta`
Needed by:
.. hlist::
:columns: 3
* :c:data:`fps_spf_matrix_ao`
.. c:var:: scf_density_matrix_ao_alpha
File : :file:`scf_utils/scf_density_matrix_ao.irp.f`
.. code:: fortran
double precision, allocatable :: scf_density_matrix_ao_alpha (ao_num,ao_num)
:math:`C.C^t` over :math:`\alpha` MOs
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`elec_alpha_num`
* :c:data:`mo_coef`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`hf_energy`
* :c:data:`scf_density_matrix_ao`
* :c:data:`scf_energy`
.. c:var:: scf_density_matrix_ao_beta
File : :file:`scf_utils/scf_density_matrix_ao.irp.f`
.. code:: fortran
double precision, allocatable :: scf_density_matrix_ao_beta (ao_num,ao_num)
:math:`C.C^t` over :math:`\beta` MOs
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`elec_beta_num`
* :c:data:`mo_coef`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`hf_energy`
* :c:data:`scf_density_matrix_ao`
* :c:data:`scf_energy`
.. c:var:: scf_energy
File : :file:`scf_utils/fock_matrix.irp.f`
.. code:: fortran
double precision :: scf_energy
Hartree-Fock energy
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_one_e_integrals`
* :c:data:`extra_e_contrib_density`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`nuclear_repulsion`
* :c:data:`scf_density_matrix_ao_alpha`
* :c:data:`scf_density_matrix_ao_beta`
.. c:var:: threshold_diis_nonzero
File : :file:`scf_utils/diis.irp.f`
.. code:: fortran
double precision :: threshold_diis_nonzero
If threshold_DIIS is zero, choose sqrt(thresh_scf)
Needs:
.. hlist::
:columns: 3
* :c:data:`thresh_scf`
* :c:data:`threshold_diis`
Subroutines / functions
-----------------------
.. c:function:: damping_scf:
File : :file:`scf_utils/damping_scf.irp.f`
.. code:: fortran
subroutine damping_SCF
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_coef`
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`scf_energy`
* :c:data:`scf_density_matrix_ao_beta`
* :c:data:`fock_matrix_mo`
* :c:data:`ao_num`
* :c:data:`scf_density_matrix_ao_alpha`
* :c:data:`fock_matrix_ao`
* :c:data:`mo_label`
* :c:data:`n_it_scf_max`
* :c:data:`thresh_scf`
* :c:data:`frozen_orb_scf`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_hartree_fock_energy`
* :c:func:`initialize_mo_coef_begin_iteration`
* :c:func:`mo_as_eigvectors_of_mo_matrix`
* :c:func:`reorder_core_orb`
* :c:func:`save_mos`
* :c:func:`write_double`
* :c:func:`write_time`
Touches:
.. hlist::
:columns: 3
* :c:data:`scf_density_matrix_ao_alpha`
* :c:data:`scf_density_matrix_ao_beta`
* :c:data:`mo_coef`
.. c:function:: huckel_guess:
File : :file:`scf_utils/huckel.irp.f`
.. code:: fortran
subroutine huckel_guess
Build the MOs using the extended Huckel model
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_one_e_integrals`
* :c:data:`mo_coef`
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`ao_overlap`
* :c:data:`ao_num`
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fock_matrix_ao_alpha`
Called by:
.. hlist::
:columns: 3
* :c:func:`create_guess`
Calls:
.. hlist::
:columns: 3
* :c:func:`save_mos`
Touches:
.. hlist::
:columns: 3
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`mo_coef`
.. c:function:: roothaan_hall_scf:
File : :file:`scf_utils/roothaan_hall_scf.irp.f`
.. code:: fortran
subroutine Roothaan_Hall_SCF
Roothaan-Hall algorithm for SCF Hartree-Fock calculation
Needs:
.. hlist::
:columns: 3
* :c:data:`max_dim_diis`
* :c:data:`mo_occ`
* :c:data:`ao_md5`
* :c:data:`mo_coef`
* :c:data:`level_shift`
* :c:data:`fps_spf_matrix_mo`
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`scf_energy`
* :c:data:`mo_num`
* :c:data:`thresh_scf`
* :c:data:`scf_algorithm`
* :c:data:`fock_matrix_mo`
* :c:data:`ao_num`
* :c:data:`fock_matrix_ao`
* :c:data:`mo_label`
* :c:data:`n_it_scf_max`
* :c:data:`threshold_diis_nonzero`
* :c:data:`frozen_orb_scf`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fps_spf_matrix_ao`
Called by:
.. hlist::
:columns: 3
* :c:func:`run`
Calls:
.. hlist::
:columns: 3
* :c:func:`extrapolate_fock_matrix`
* :c:func:`initialize_mo_coef_begin_iteration`
* :c:func:`mo_as_eigvectors_of_mo_matrix`
* :c:func:`reorder_core_orb`
* :c:func:`save_mos`
* :c:func:`write_double`
* :c:func:`write_time`
Touches:
.. hlist::
:columns: 3
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`fock_matrix_ao_alpha`
* :c:data:`mo_coef`
* :c:data:`level_shift`
* :c:data:`mo_coef`
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