HFRCUT: Difference between revisions

Revision as of 11:28, 28 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.

In systems with periodic boundary conditions, the Coulomb energy and the Coulomb potential are usually evaluated under the assumption of a compensating background by introducing a compensation charge density. This is well-justified for the Hartree energy, where the compensation charge density stems from the ions. Yet, this assumption is not valid for the Fock exchange, which causes an error. For the Fock exchange potential and energy, one can correct the resulting error by assuming that the density matrix is local. The leading order correction is 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 J. Paier et al., Section II. D. 4^[1].

HFRCUT = 0: Ewald summation or method of Massida, Posternak, and Baldereschi depending on k-mesh

If a regular automatic k-mesh and the standard 1/r Coulomb kernel are used, the correction is computed using Ewald summations. If the k-mesh is not regular (e.g., if the k-points are explicitly listed in the KPOINTS file) or if kernels different from the bare Coulomb kernel are used (e.g., HSE functional), the method of Massida, Posternak, and Baldereschi^[2]^[3] is used. This approach assumes that the model charge density is an error-function-like charge distribution in real space in order to handle the long-range nature of the potential in reciprocal space. It requires setting a decay constant for the error function, see HFALPHA. Both methods, the Ewald summation and the method of Massida, Posternak, and Baldereschi, are strictly equivalent for regular k-mesh.

HFRCUT = -1: Automated cutoff radius

An alternative recipe is to replace the 1/r Coulomb kernel with a truncated Coulomb kernel that is strictly zero beyond a certain cutoff radius. If HFRCUT is set to -1, the radial cutoff is chosen to be equivalent to the radius of the sphere with a volume of the unit cell times the total number of k-points in the full Brillouin zone. For instance, for a 4x4x4 k-point grid, that yields 64 times the volume of the unit cell.

HFRCUT = [cutoff radius]: Manually set cutoff radius in Ångström.

In the limit of many k-points, both methods (HFRCUT=-1 and HFRCUT=0) should yield identical results. In our experience, the HFRCUT=-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.

References

[paier:jcp:05-1] J. Paier, R. Hirschl, M. Marsman, and G. Kresse, J. Chem. Phys. 122, 234102 (2005).

[gygi:prb:86-2] F. Gygi and A. Baldereschi, Phys. Rev. B 34, 4405(R) (1986).

[massidda:prb:93-3] S. Massidda, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993).

[1]

[2]

[3]

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 Description: {{TAG|HFRCUT}} specifies how the Coulomb kernel is approximated at G=0 when the Fock energy and the exchange potential are evaluated.
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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 it is not valid 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 (e.g. HSE functional), the method 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  Gygi and Baldereschi, are strictly equivalent for regular k-point grids. However, the method of Gygi and Baldereschi  requires to set a decay constant for the error function (tag {{TAG|HFALPHA}} in the INCAR file). The default 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).
+In systems with periodic boundary conditions, the Coulomb energy and the Coulomb potential are usually evaluated under the assumption of a compensating background by introducing a compensation charge density. This is well-justified for the Hartree energy, where the compensation charge density stems from the ions. Yet, this assumption is not valid for the Fock exchange, which causes an error. For the Fock exchange potential and energy, one can correct the resulting error by assuming that the density matrix is local. The leading order correction is 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 J. Paier ''et al.,'' Section II. D. 4{{cite|paier:jcp:05}}.
-{{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 radius of the sphere with a volume of the unit 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).
+*{{TAG|HFRCUT}} = 0: Ewald summation ''or'' method of Massida, Posternak, and Baldereschi depending on k-mesh
+:If a regular automatic k-mesh and the standard 1/r Coulomb kernel are used, the correction is computed using Ewald summations. If the k-mesh is ''not'' regular (e.g., if the k-points are explicitly listed in the {{FILE|KPOINTS}} file) or if kernels different from the bare Coulomb kernel are used (e.g., HSE functional), the method of Massida, Posternak, and Baldereschi{{cite|gygi:prb:86}}{{cite|massidda:prb:93}} is used. This approach assumes that the model charge density is an error-function-like charge distribution in real space in order to handle the long-range nature of the potential in reciprocal space. It requires setting a decay constant for the error function, see {{TAG|HFALPHA}}. Both methods, the Ewald summation and the method of Massida, Posternak, and Baldereschi, are strictly equivalent for regular k-mesh.
-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).
+*{{TAG|HFRCUT}} = -1: Automated cutoff radius
+:An alternative recipe is to replace the 1/r Coulomb kernel with a truncated Coulomb kernel that is strictly zero beyond a certain cutoff radius. If {{TAG|HFRCUT}} is set to -1, the radial cutoff is chosen to be equivalent to the radius of the sphere with a volume of the unit cell times the total number of k-points in the full Brillouin zone. For instance, for a  4x4x4 k-point grid, that yields 64 times the volume of the unit cell.
-== Related Tags and Sections ==
+*{{TAG| HFRCUT}} = [cutoff radius]: Manually set cutoff radius in Ångström.
+In the limit of many k-points, both methods ({{TAG|HFRCUT}}=-1 and {{TAG|HFRCUT}}=0) should yield identical results. In our experience, the {{TAG|HFRCUT}}=-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.
+== Related tags and articles ==
 {{TAG|AEXX}},
 {{TAG|AGGAX}},
@@ Line 23: / Line 28: @@
 {{sc|HFSCREEN|Examples|Examples that use this tag}}
+== References ==
+<references/>
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