Electrostatic treatment of charged interfaces in classical atomistic simulations

Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for model systems of increasing complexity, both neutral and charged, and with either open or periodic boundary conditions. This allows to correctly interpret results of classical atomistic simulations which are directly affected by the appearance of these potentials. We demonstrate our approach at the example of a strontium titanite (SrTiO$_3$) supercell containing an asymmetric tilt grain boundary. The formation energies of charged oxygen vacancies and the relaxed interface structure are calculated based on an interatomic rigid-ion potential, and the results are analyzed in consideration of the electrostatic effects.