The alignment of electrostatic potential between different atomic configurations is necessary for first-principles calculations of band offsets across interfaces and formation energies of charged defects. However, strong oscillations of this potential at the atomic scale make alignment challenging, especially when atomic geometries change considerably from bulk to the vicinity of defects and interfaces. We introduce a method to suppress these strong oscillations by eliminating the deep wells in the potential at each atom. We demonstrate that this method considerably improves the system-size convergence of a wide range of first-principles predictions that depend on the alignment of electrostatic potentials, including band offsets at solid-liquid interfaces, and formation energies of charged vacancies in solids and at solid surfaces in vacuum. Finally, we use this method in conjunction with continuum solvation theories to investigate energetics of charged vacancies at solid-liquid interfaces. We find that for the example of an NaCl (001) surface in water, solvation reduces the formation energy of charged vacancies by 0.5 eV: calculation of this important effect was previously impractical due to the computational cost in molecular-dynamics methods.

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