Electrostatic corrections: Difference between revisions

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The following flags control the behaviour of VASP:
The following flags control the behaviour of VASP:
* {{TAG|NELECT}}, charged systems:
* {{TAG|NELECT}}, charged systems:
:{{TAG|NELECT}} determines the total number of electrons in the system. The value may deviate from the default value, which is calculated assuming charge neutrality in the system. If {{TAG|NELECT}} differs from the default, an additional neutralizing background charge is applied by VASP. In this case, however, the energy converges very slowly with respect to the size ''L'' of the super cell. The required first order correction to the energy is given by
::<math>\frac{e^2q^2\alpha}{L\epsilon}</math>
:where ''q'' is the net charge of the system, &alpha; the Madelung constant of a point charge ''q'' placed in a homogeneous background charge ''-q'', and &epsilon; the dielectric constant of the system. For atoms or molecules surrounded by vacuum, &epsilon; takes on the vacuum value &epsilon;=1. VASP can automatically correct for the leading error, by setting the {{TAG|IDIPOL}} and {{TAG|EPSILON}} tags in the {{FILE|INCAR}} file (see below).
:It is important to emphasize that the total energy can not be corrected for charged slabs, since a charged slab results in an electrostatic potential that grows linearly with the distance from the slab (corresponding to a fixed electrostatic field). It is fairly simple to show that as a result of the interaction between the charged slab and the compensating background, the total energy depends linearly on the width of the vacuum. Presently, no simple ''a posteriori'' correction scheme is known or implemented in VASP. ''Total energies from charged slab calculations are hence useless, and can not be used to determine relative energies.''
:'''Note''': If you are not convinced, simply vary the vacuum width and draw the energy versus the vacuum width.


* {{TAG|EPSILON}}, dielectric constant:
* {{TAG|EPSILON}}, dielectric constant:


* {{TAG|IDIPOL}}, type of correction (monopole/dipole and quadrupole):
* {{TAG|IDIPOL}}, type of correction (monopole/dipole and quadrupole):
:For systems with a net dipole moment, the energy converges slowly with respect to the size of the super cell as well. The dipole corrections (and quadrupole corrections for charged systems) fall off like <math>1/L^3</math>. Both corrections, dipole and quadrupole for charged systems, will be calculated and added to the total energy if {{TAG|IDIPOL}} is set.
:For systems with a net dipole moment, the energy converges slowly with respect to the size of the super cell as well. The dipole corrections (and quadrupole corrections for charged systems) fall off like 1/''L''<sup>3</sup>. Both corrections, dipole and quadrupole for charged systems, will be calculated and added to the total energy if {{TAG|IDIPOL}} is set.


:There are four possible settings for {{TAG|IDIPOL}} (= 1 {{!}} 2 {{!}} 3 {{!}} 4).
:There are four possible settings for {{TAG|IDIPOL}} (= 1 {{!}} 2 {{!}} 3 {{!}} 4).
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:'''Note''': strictly speaking quadrupole corrections is not the proper wording. The relevant quantity is
:'''Note''': strictly speaking quadrupole corrections is not the proper wording. The relevant quantity is
:<math> \int d^3{\mathbf r} \rho(\mathbf r) \Vert \mathbf r\Vert^2.</math>
::<math> \int d^3{\mathbf r} \rho(\mathbf r) \Vert \mathbf r\Vert^2.</math>


* {{TAG|DIPOL}}, center of the net charge of the cell
* {{TAG|DIPOL}}, center of the net charge of the cell

Revision as of 16:22, 10 March 2013

For charged cells or for calculations of molecules and surfaces with a large dipole moment, the energy converges very slowly with respect to the size Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): L of the supercell. Using methods discussed by Makov et al.[1] and Neugebauer et al.[2], VASP can correct for the leading errors (in many details, we have taken a more general approach, though).

The following flags control the behaviour of VASP:

NELECT determines the total number of electrons in the system. The value may deviate from the default value, which is calculated assuming charge neutrality in the system. If NELECT differs from the default, an additional neutralizing background charge is applied by VASP. In this case, however, the energy converges very slowly with respect to the size L of the super cell. The required first order correction to the energy is given by
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\frac {e^{2}q^{2}\alpha }{L\epsilon }}
where q is the net charge of the system, α the Madelung constant of a point charge q placed in a homogeneous background charge -q, and ε the dielectric constant of the system. For atoms or molecules surrounded by vacuum, ε takes on the vacuum value ε=1. VASP can automatically correct for the leading error, by setting the IDIPOL and EPSILON tags in the INCAR file (see below).
It is important to emphasize that the total energy can not be corrected for charged slabs, since a charged slab results in an electrostatic potential that grows linearly with the distance from the slab (corresponding to a fixed electrostatic field). It is fairly simple to show that as a result of the interaction between the charged slab and the compensating background, the total energy depends linearly on the width of the vacuum. Presently, no simple a posteriori correction scheme is known or implemented in VASP. Total energies from charged slab calculations are hence useless, and can not be used to determine relative energies.
Note: If you are not convinced, simply vary the vacuum width and draw the energy versus the vacuum width.
  • IDIPOL, type of correction (monopole/dipole and quadrupole):
For systems with a net dipole moment, the energy converges slowly with respect to the size of the super cell as well. The dipole corrections (and quadrupole corrections for charged systems) fall off like 1/L3. Both corrections, dipole and quadrupole for charged systems, will be calculated and added to the total energy if IDIPOL is set.
There are four possible settings for IDIPOL (= 1 | 2 | 3 | 4).
For IDIPOL=1-3, the dipole moment will be calculated only parallel to the direction of the first, second or third lattice vector, respectively. The corrections for the total energy are calculated as the energy difference between a monopole/dipole and quadrupole in the current supercell and the same dipole placed in a super cell with the corresponding lattice vector approaching infinity. This flag should be used for slab calculations.
For IDIPOL=4 the full dipole moment in all directions will be calculated, and the corrections to the total energy are calculated as the energy difference between a monopole/dipole/quadrupole in the current supercell and the same monopole/dipole/quadrupole placed in a vacuum, use this flag for calculations for isolated molecules.
Note: strictly speaking quadrupole corrections is not the proper wording. The relevant quantity is
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \int d^{3}{{\mathbf r}}\rho ({\mathbf r})\Vert {\mathbf r}\Vert ^{2}.
  • DIPOL, center of the net charge of the cell
  • LDIPOL and LMONO, enable dipole and/or monopole corrections
  • EFIELD, applied electrostatic field

For the current implementation, there are several restrictions; please read carefully:

  • Charged systems:
    Quadrupole corrections are only correct for cubic supercells (this means that the calculated Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 1/L^{3} corrections are wrong for charged supercells if the supercell is non cubic). In addition, we have found empirically that for charged systems with excess electrons (NELECTFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): > NELECT Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): _{{{\rm {neutral}}}} ) more reliable results can be obtained if the energy after correction of the linear error (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 1/L ) is plotted against Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 1/L^{3} to extrapolate results manually for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): L\to \infty . This is due to the uncertainties in extracting the quadrupole moment of systems with excess electrons.
  • Potential corrections are only possible for orthorhombic cells (at least the direction in which the potential is corrected must be orthogonal to the other two directions).

Related Tags and Sections

NELECT, EPSILON, DIPOL, IDIPOL, LDIPOL, LMONO, EFIELD

References

  1. ↑ G. Makov and M. C. Payne, Phys. Rev. B 51, 4014 (1995).
  2. ↑ J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067 (1992).

Contents

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