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 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).