Point Defects in Ionic Crystals. I. Methods of Calculating the Electronic Structure

Abstract

Methods which have been developed and employed for the calculation of point defects in ionic crystals are described. These methods involve a detailed Hartree-Fock-like treatment by way of angular-momentum-dependent exchange potentials of the ions within an inner region ${\tau }_1$ centered about the defect. In the outer region ${\tau }_2$, composed of the rest of the crystal, the ions are treated in two different approximations, the most successful of which involves an effective-mass formalism. Polarization effects are included by expressions of the form resulting from the work of Toyozawa, Haken, and Schottky. Although the main purpose of the paper is to describe the methods, applications are made to the calculation of the electronic energy levels in the optical absorption of the $F$ center in KCl and NaCl. Good agreement with experiment is found only if polarization effects, which are important even in the ground state, are included. Additional applications will be given in subsequent papers.