Equivalence of dipole correction and Coulomb cutoff techniques in supercell calculations

In ab initio calculations of surfaces or nonperiodic systems, one frequently relies on the supercell approximation, where the periodic replicas of the system are separated by enough empty space to avoid spurious interactions between the successive images. However, a vacuum separation is not sufficient to screen the dipolar interaction that appears in asymmetrically charged or polar systems. The dipole correction and Coulomb cutoff methods are often used to eliminate such interactions between the periodic replicas. In this work, these methods are compared under the same conditions in the framework of plane-wave based density-functional theory. The dipole correction method is shown to be equivalent to the rigorous Coulomb cutoff formalism in the calculations of total energy, force, charge density, and self-consistent potential. We demonstrate that the band structures obtained by these methods coincide for the localized bound states and that the corrections have essentially no influence on the occupied energy bands, only substantially affecting the unoccupied bands. By comparing the results of the two methods, the localized bound states of interest can be easily distinguished from the highly delocalized unoccupied states using a relatively small supercell. This comparison offers substantial savings in the computational time when ascertaining convergence with supercell size. The accuracy of the dipole correction method is also confirmed by comparing the results for a model ferroelectric ${\text{BaTiO}}_{3}$ slab with a Berry-phase calculation of polarization for the bulk system.