Secular equation of Korringa, Kohn, and Rostoker for the case of non-muffin-tin, space-filling potential cells

Abstract

Proof is provided that the secular equation proposed by Korringa, Kohn, and Rostoker for determining the electronic structure of collections of muffin-tin potentials, i.e., potentials bounded by nonoverlapping spheres, remains valid in the completely general case of nonoverlapping, arbitrarily shaped, and particularly space-filling potential cells. Consequently, this secular equation leads to the proper coefficients for determining the wave function of the system as a linear combination of cell wave functions.