Energy calculations of charged point defects on surfaces

We present a virtual ionic crystal (VIC) method to calculate energies of charged point defects on surfaces. No artificial charge but an actual zero-dimensional (0D) species is introduced to charge a defect. Effect of dielectric substrate on lattice energy is depressed through suitable configuration of the unit cell. The lattice energy approximates to Madelung energy with defect and 0D species considered as point charges in vacuum. Energy required to charge the defect is derived from charge quantity on the defect in VIC, energy of unit cell, and energy required to charge the 0D species.