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).

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).