Energy correction for isolated impurities under periodic boundary conditions

The Coulomb energy of aperiodic systems was investigated. To treat completely isolated disorder in infinite systems, energy correction for a supercell method is presented. We discuss a definition of the correction term, and then consider a direct approach taking into account interactions between charge distribution and an indirect approach based on a multipole expansion. In test calculations for isotropic-charged, anisotropic-charged, and neutral impurities, impurity energies independent of supercell sizes were obtained. The present energy correction can be applied to arbitrary systems and is expected to realize more practical simulations for aperiodic systems.