  Defects on surfaces of semiconductors have a strong effect on their
reactivity and catalytic properties. The concentration of different charge
states of defects is determined by their formation energies. First-principles
calculations are an important tool for computing defect formation energies and
for studying the microscopic environment of the defect. The main problem
associated with the widely used supercell method in these calculations is the
error in the electrostatic energy, which is especially pronounced in
calculations that involve surface slabs and 2D materials. We present an
internally consistent approach for calculating defect formation energies in
inhomogeneous and anisotropic dielectric environments, and demonstrate its
applicability to the cases of the positively charged Cl vacancy on the NaCl
(100) surface and the negatively charged S vacancy in monolayer MoS2.
