# Green-function cellular method for the electronic structure of molecules and solids

## Abstract

A technique for obtaining rigorous solutions to the single-electron Schrödinger equation for solids and molecules, the Green-function cellular method (GFCM), is described. The technique is similar to full-potential multiple-scattering theory in that basis functions which are locally exact solutions to the Schrödinger equation within each potential cell are used to represent the wave function. Unlike multiple-scattering theory, however, the coefficients of expansion for the wave function are determined by a secular matrix which couples only nearest-neighbor cells. The matrix elements are Wronskian-like integrals over cell surfaces which may be chosen independently for each atomic cell. Similarly to multiple-scattering theory, the GFCM can be used to calculate the system Green function directly. As a special case, the GFCM formalism can be used to calculate the structure constants of Korringa-Kohn-Rostoker theory without using Ewald sums. Numerical calculations of the energy bands of fcc Cu illustrate the speed and flexibility of the method. A simple linearization scheme which allows the use of multiple energy panels without introducing discontinuities in the energy bands is used in these calculations. © 1992 The American Physical Society.