HFRCUT: Difference between revisions
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For details we refer to section IID4 of [Paier, Hirschl, Marsman, Kresse, J. Chem. Phys. 122, 23410 (2005)]. In periodic boundary conditions, the Coulomb energy and the Coulomb potential are usually evaluated under the assumption of a compensating background. This is justified for the Hartree energy (the compensation is stemming from the ions) but not for the Fock exchange. For the Fock exchange potential and energy, one can correct the resulting error by assuming that the density matrix is localized. The leading error is then given by the difference between the electrostatic energy of a localized model charge density in a homogeneous background periodically repeated and the same model charge density in isolation. | For details we refer to section IID4 of [Paier, Hirschl, Marsman, Kresse, J. Chem. Phys. 122, 23410 (2005)]. In periodic boundary conditions, the Coulomb energy and the Coulomb potential are usually evaluated under the assumption of a compensating background. This is justified for the Hartree energy (the compensation is stemming from the ions) but not for the Fock exchange. For the Fock exchange potential and energy, one can correct the resulting error by assuming that the density matrix is localized. The leading error is then given by the difference between the electrostatic energy of a localized model charge density in a homogeneous background periodically repeated and the same model charge density in isolation. | ||
For {{TAG|HFRCUT}}=0 and if regular automatic k-point grids and the standard Coulomb kernel are used, VASP calculates this correction using Ewald summations. If the k-point grid is not regular (for instance if the k-points are explicitly listed in the KPOINTS file) or if kernels different from the bare Coulomb kernel are used (HSE functions), the methods of Massida, Posternak and Baldereschi is used [S. Massida, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993)]. This approach assumes that the model charge density is an error-function-like charge distribution. Both methods, the Ewald summation and the method of Massida, Posternak and Baldereschi are strictly equivalent for regular k-point grids. However, the method of Massida, Posternak and Baldereschi requires to set a decay constant for the error function (tag {{TAG|HFALPHA}} in the INCAR file). The defaults used by VASP for {{TAG| HFALPHA}} depends of the energy cutoff and usually yields robust and accurate results (in agreement with the Ewald summation). | For {{TAG|HFRCUT}}=0 and if regular automatic k-point grids and the standard Coulomb kernel are used, VASP calculates this correction using Ewald summations. If the k-point grid is not regular (for instance if the k-points are explicitly listed in the KPOINTS file) or if kernels different from the bare Coulomb kernel are used (HSE functions), the methods of Massida, Posternak and Baldereschi is used [ S. Massida, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993), see also F. Gygi and A. Baldereschi, Phys. Rev. B 34, 4405 (1986)]. This approach assumes that the model charge density is an error-function-like charge distribution in real space. Both methods, the Ewald summation and the method of Massida, Posternak and Baldereschi, are strictly equivalent for regular k-point grids. However, the method of Massida, Posternak and Baldereschi requires to set a decay constant for the error function (tag {{TAG|HFALPHA}} in the INCAR file). The defaults used by VASP for {{TAG| HFALPHA}} depends of the energy cutoff and usually yields robust and accurate results (in meV agreement with the Ewald summation). | ||
{{TAG|HFRCUT}}=-1: An alternative recipe is to replace the 1/r Coulomb kernel by a truncated Coulomb kernel that is strictly zero beyond a certain cutoff radius. If {{TAG|HFRCUT}} is set to -1, the radial cutoff is chose to be equivalent to the volume of the specified cell times the total number of k-points in the full | {{TAG|HFRCUT}}=-1: An alternative recipe is to replace the 1/r Coulomb kernel by a truncated Coulomb kernel that is strictly zero beyond a certain cutoff radius. If {{TAG|HFRCUT}} is set to -1, the radial cutoff is chose to be equivalent to the volume of the specified cell times the total number of k-points in the full Brillouin zone (e.g. for a 4x4x4 k-point grid, 64 times the volume of the unit cell). Alternatively, the user can also specify the radial cutoff in Ångström ({{TAG| HFRCUT}}= cutoff radius). | ||
In the limit of many k-points, both methods ({{TAG|HFRCUT}}=-1 and {{TAG|HFRCUT}}=0) should yield identical results. In our experience, the second method HFRECUT=-1 converges more rapidly for systems with a gap as well as molecules and atoms, whereas {{TAG|HFRCUT}}=0 | In the limit of many k-points, both methods ({{TAG|HFRCUT}}=-1 and {{TAG|HFRCUT}}=0) should yield identical results. In our experience, the second method HFRECUT=-1 converges more rapidly for systems with a gap as well as molecules and atoms, whereas {{TAG|HFRCUT}}=0 converges faster for metallic systems. It is expedient to first converge the energies with respect to the number of k-points for both methods and then select for subsequent calculations the method that converges more rapidly ({{TAG|HFRCUT}}=-1 or {{TAG|HFRCUT}}=-0). | ||
== Related Tags and Sections == | == Related Tags and Sections == | ||
Revision as of 06:47, 27 April 2021
HFRCUT = [real]
Default: HFRCUT = 0
Description: HFRCUT specifies how the Coulomb kernel is approximated at G=0 when the Fock energy and the exchange potential are evaluated.
For details we refer to section IID4 of [Paier, Hirschl, Marsman, Kresse, J. Chem. Phys. 122, 23410 (2005)]. In periodic boundary conditions, the Coulomb energy and the Coulomb potential are usually evaluated under the assumption of a compensating background. This is justified for the Hartree energy (the compensation is stemming from the ions) but not for the Fock exchange. For the Fock exchange potential and energy, one can correct the resulting error by assuming that the density matrix is localized. The leading error is then given by the difference between the electrostatic energy of a localized model charge density in a homogeneous background periodically repeated and the same model charge density in isolation.
For HFRCUT=0 and if regular automatic k-point grids and the standard Coulomb kernel are used, VASP calculates this correction using Ewald summations. If the k-point grid is not regular (for instance if the k-points are explicitly listed in the KPOINTS file) or if kernels different from the bare Coulomb kernel are used (HSE functions), the methods of Massida, Posternak and Baldereschi is used [ S. Massida, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993), see also F. Gygi and A. Baldereschi, Phys. Rev. B 34, 4405 (1986)]. This approach assumes that the model charge density is an error-function-like charge distribution in real space. Both methods, the Ewald summation and the method of Massida, Posternak and Baldereschi, are strictly equivalent for regular k-point grids. However, the method of Massida, Posternak and Baldereschi requires to set a decay constant for the error function (tag HFALPHA in the INCAR file). The defaults used by VASP for HFALPHA depends of the energy cutoff and usually yields robust and accurate results (in meV agreement with the Ewald summation).
HFRCUT=-1: An alternative recipe is to replace the 1/r Coulomb kernel by a truncated Coulomb kernel that is strictly zero beyond a certain cutoff radius. If HFRCUT is set to -1, the radial cutoff is chose to be equivalent to the volume of the specified cell times the total number of k-points in the full Brillouin zone (e.g. for a 4x4x4 k-point grid, 64 times the volume of the unit cell). Alternatively, the user can also specify the radial cutoff in Ångström (HFRCUT= cutoff radius).
In the limit of many k-points, both methods (HFRCUT=-1 and HFRCUT=0) should yield identical results. In our experience, the second method HFRECUT=-1 converges more rapidly for systems with a gap as well as molecules and atoms, whereas HFRCUT=0 converges faster for metallic systems. It is expedient to first converge the energies with respect to the number of k-points for both methods and then select for subsequent calculations the method that converges more rapidly (HFRCUT=-1 or HFRCUT=-0).
Related Tags and Sections
AEXX, AGGAX, AGGAC, ALDAC, LTHOMAS, hybrid functionals, range separated hybrid functionals, settings for specific hybrid functionals