Pressure, relaxation volume, and elastic interactions in charged simulation cells

The ab initio calculation of charged supercells within density-functional theory is a necessary step to access several important properties of matter. The relaxation volume of charged point defects or the partial molar volume of ions in solution are two such examples. However, the total energy and therefore the pressure of charged systems is not uniquely defined when periodic boundary conditions are employed. This problem is tightly related to the origin of the electrostatic potential in periodic systems. This effect can be easily observed by modifying the electrostatic convention or modifying the local ionic potential details. We propose an approach to uniquely define the pressures in charged supercells with the use of the absolute deformation potentials. Only with such a definition could the ab initio calculations provide meaningful values for the relaxation volumes and for the elastic interactions for charged defects in semiconductors or ions in solution. The proposed scheme allows one to calculate sensible data even when charge neutrality is not enforced, thus going beyond the classical force-field-based approaches.