Electrostatic corrections

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 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, charged systems:

EPSILON, dielectric constant:

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/L^{3}

. 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

\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 $1/L^{3}$ 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).