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