Theoretical study of a screened Hartree-Fock exchange potential using position-dependent atomic dielectric constants

Dielectric-dependent screened Hartree-Fock (HF) exchange potential and Slater-formula have been reported, where the ratio of the HF exchange term mixed into potentials is inversely proportional to the dielectric constant of the target semiconductor. This study introduces a position-dependent dielectric constant method in which the dielectric constant is partitioned between the atoms in a semiconductor. These partitioned values differ depending on the electrostatic environment surrounding the atoms and lead to position-dependent atomic dielectric constants. These atomic dielectric constants provide atomic orbital-based matrix elements for the screened exchange potentials. Energy band structures of several semiconductors and insulators are also presented to validate this approach.