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 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 hartree_fock fock_matrix_hf.irp.f for an example).

All SCF programs perform the following actions:

  1. Compute/Read all the one- and two-electron integrals, and store them in memory
  2. 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.
  3. Perform the SCF iterations based on the definition of the Fock matrix

The main keywords/options are:

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 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.

EZFIO parameters

max_dim_diis

Maximum size of the DIIS extrapolation procedure

Default: 15

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.

thresh_scf

Threshold on the convergence of the Hartree Fock energy.

Default: 1.e-10

n_it_scf_max

Maximum number of SCF iterations

Default: 500

level_shift

Energy shift on the virtual MOs to improve SCF convergence

Default: 0.

scf_algorithm

Type of SCF algorithm used. Possible choices are [ Simple | DIIS]

Default: DIIS

mo_guess_type

Initial MO guess. Can be [ Huckel | HCore ]

Default: Huckel

energy

Calculated HF energy

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

eigenvalues_fock_matrix_ao

File : scf_utils/diis.irp.f

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:

  • ao_num
eigenvectors_fock_matrix_ao

File : scf_utils/diis.irp.f

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:

  • ao_num
eigenvectors_fock_matrix_mo

File : scf_utils/diagonalize_fock.irp.f

double precision, allocatable   :: eigenvectors_fock_matrix_mo  (ao_num,mo_num)

Eigenvector of the Fock matrix in the MO basis obtained with level shift.

Needs:

extrapolate_fock_matrix:()

File : scf_utils/roothaan_hall_scf.irp.f

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:

  • max_dim_diis
  • ao_num

Called by:

  • roothaan_hall_scf()

Calls:

  • dgemm()
  • dsysvx()
fock_matrix_ao

File : scf_utils/fock_matrix.irp.f

double precision, allocatable   :: fock_matrix_ao       (ao_num,ao_num)

Fock matrix in AO basis set

Needs:

  • ao_num
  • elec_alpha_num
  • elec_beta_num

Needed by:

fock_matrix_diag_mo

File : scf_utils/fock_matrix.irp.f

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:

Needed by:

fock_matrix_mo

File : scf_utils/fock_matrix.irp.f

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:

Needed by:

fock_matrix_mo_alpha

File : scf_utils/fock_matrix.irp.f

double precision, allocatable   :: fock_matrix_mo_alpha (mo_num,mo_num)

Fock matrix on the MO basis

Needs:

Needed by:

fock_matrix_mo_beta

File : scf_utils/fock_matrix.irp.f

double precision, allocatable   :: fock_matrix_mo_beta  (mo_num,mo_num)

Fock matrix on the MO basis

Needs:

Needed by:

fps_spf_matrix_ao

File : scf_utils/diis.irp.f

double precision, allocatable   :: fps_spf_matrix_ao    (AO_num,AO_num)

Commutator FPS - SPF

Needs:

Needed by:

fps_spf_matrix_mo

File : scf_utils/diis.irp.f

double precision, allocatable   :: fps_spf_matrix_mo    (mo_num,mo_num)

Commutator FPS - SPF in MO basis

Needs:

scf_density_matrix_ao

File : scf_utils/scf_density_matrix_ao.irp.f

double precision, allocatable   :: scf_density_matrix_ao        (ao_num,ao_num)

S^{-1}.P.S^{-1} where P = C.C^t

Needs:

  • ao_num
  • elec_alpha_num

Needed by:

scf_density_matrix_ao_alpha

File : scf_utils/scf_density_matrix_ao.irp.f

double precision, allocatable   :: scf_density_matrix_ao_alpha  (ao_num,ao_num)

S^{-1}.P_alpha.S^{-1}

Needs:

  • ao_num
  • elec_alpha_num

Needed by:

scf_density_matrix_ao_beta

File : scf_utils/scf_density_matrix_ao.irp.f

double precision, allocatable   :: scf_density_matrix_ao_beta   (ao_num,ao_num)

S^{-1}.P_beta.S^{-1}

Needs:

  • ao_num
  • elec_beta_num

Needed by:

scf_energy

File : scf_utils/fock_matrix.irp.f

double precision        :: scf_energy

Hartree-Fock energy

Needs:

threshold_diis_nonzero

File : scf_utils/diis.irp.f

double precision        :: threshold_diis_nonzero

If threshold_DIIS is zero, choose sqrt(thresh_scf)

Needs:

  • thresh_scf
  • threshold_diis

Subroutines / functions

damping_scf:()

File : scf_utils/damping_scf.irp.f

subroutine damping_SCF

Needs:

  • mo_label
  • n_it_scf_max
  • thresh_scf
  • frozen_orb_scf

Calls:

  • ezfio_set_hartree_fock_energy()
  • initialize_mo_coef_begin_iteration()
  • mo_as_eigvectors_of_mo_matrix()
  • reorder_core_orb()
  • save_mos()
  • write_double()
  • write_time()

Touches:

huckel_guess:()

File : scf_utils/huckel.irp.f

subroutine huckel_guess

Build the MOs using the extended Huckel model

Needs:

Called by:

  • create_guess()

Calls:

  • save_mos()

Touches:

roothaan_hall_scf:()

File : scf_utils/roothaan_hall_scf.irp.f

subroutine Roothaan_Hall_SCF

Roothaan-Hall algorithm for SCF Hartree-Fock calculation

Needs:

Called by:

  • run()

Calls:

  • extrapolate_fock_matrix()
  • initialize_mo_coef_begin_iteration()
  • mo_as_eigvectors_of_mo_matrix()
  • reorder_core_orb()
  • save_mos()
  • write_double()
  • write_time()

Touches: