Monopole Dipole and Quadrupole Corrections: Difference between revisions

Revision as of 18:14, 31 August 2012

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 $L$ of the supercell. Using methods discussed in Ref. [55,56] VASP can correct for the leading errors, but one should stress, that in many details, we have taken a more general approach than the one outlined in Ref. [55].

For systems with a net dipole moment, the energy also converges slowly with respect to the size of the super cell. The dipole corrections (and quadrupole corrections for charged systems) fall off like $1/L^{3}$ . Both corrections, dipole and quadrupole for charged systems, will be calculated and added to the total energy if the IDIPOL flag is set.

Note: strictly speaking quadrupole corrections is not the proper wording. The relevant quantity is

\int d^{3}{\mathbf {r} }\rho (\mathbf {r} )\Vert \mathbf {r} \Vert ^{2}.

The following flags control the behaviour of VASP.

NELECT, total number of electrons
EPSILON, dielectric constant
IDIPOL, type of correction (monopole/dipole and quadrupole)
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 $1/L^{3}$ 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 (NELECT $>$ NELECT $_{\rm {neutral}}$ ) more reliable results can be obtained if the energy after correction of the linear error ( $1/L$ ) is plotted against $1/L^{3}$ to extrapolate results manually for $L\to \infty$ . 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).

@@ Line 1: / Line 1: @@
-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 $L$ of the supercell. Using methods discussed in Ref. [55,56] VASP can correct for the leading errors, but one should stress, that in many details, we have taken a more general approach than the one outlined in Ref. [55].
+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 <math>L</math> of the supercell. Using methods discussed in Ref. [55,56] VASP can correct for the leading errors, but one should stress, that in many details, we have taken a more general approach than the one outlined in Ref. [55].
-The following flags control the behaviour of VASP.
+For systems with a net dipole moment, the energy also converges slowly with respect to the size of the super cell. 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 the IDIPOL flag is set.
+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>
-* {{TAG|NELECT}}, charged systems:<br/> {{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 NELECT differs from the default, an additional neutralizing background charge is applied by VASP.
-* {{TAG|DIPOL}}='''R'''<sub>x</sub> '''R'''<sub>y</sub> '''R'''<sub>z</sub>
+The following flags control the behaviour of VASP.
-:where '''R'''<sub>x</sub>, '''R'''<sub>y</sub> and '''R'''<sub>z</sub> specify the center of the cell in direct, fractional coordinates.
+* {{TAG|NELECT}}, total number of electrons
+* {{TAG|EPSILON}}, dielectric constant
+* {{TAG|IDIPOL}}, type of correction (monopole/dipole and quadrupole)
+* {{TAG|DIPOL}}, center of the net charge of the cell
+* {{TAG|LDIPOL}} and {{TAG|LMONO}}, enable dipole and/or monopole corrections
+* {{TAG|EFIELD}}, applied electrostatic field
-This tag determines the center of the net charge distribution. The dipole is defined as
+For the current implementation, there are several restrictions; please read carefully:
-:<math>
+* Charged systems:<br/>Quadrupole corrections are only correct for cubic supercells (this means that the calculated <math>1/L^3</math> 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 ({{TAG|NELECT}}<math>></math>{{TAG|NELECT}} <math>_{\rm neutral}</math>) more reliable results can be obtained if the energy after correction of the linear error (<math>1/L</math>) is plotted against <math>1/L^3</math> to extrapolate results manually for <math>L\to \infty</math>. This is due to the uncertainties in extracting the quadrupole moment of systems with excess electrons.
-\int ({\mathbf r}-{\mathbf R}_{\rm center}) \rho_{\rm ions+valence}{\mathbf r} d^3 {\mathbf r}.
+* 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).
-</math>
-where <math>{\mathbf R}_{\rm center}</math> is the position as defined by the {{TAG|DIPOL}} tag. If the flag is not set, VASP determines, where the charge density averaged over one plane drops to a minimum and calculates the center of the charge distribution by adding half of the lattice vector perpendicular to the plane where the charge density has a minimum (this is a rather reliable approach for orthorhombic cells).