# Internal sums in full-potential multiple-scattering theory

## Abstract

Full-potential multiple-scattering theory for electrons can be derived from the variational principle of Kohn and Rostoker. The resulting equations differ from the standard Korringa-Kohn-Rostoker (KKR) formalism by a matrix multiplication, which introduces an intermediate sum that should in principle be carried out to completion. This implies that the usual site-diagonal square matrices S and C of KKR theory must be represented as rectangular matrices. In the limit of completeness of this internal sum, the resulting product of matrices can be represented in closed form as a Wronskian integral extended over the common interfaces of adjacent space-filling cells, as used in the variational cellular method (VCM), based on the variational principle of Schlosser and Marcus. The standard KKR method can be extended in two ways, either by direct use of rectangular matrices, or by using the VCM surface integral as a closure correction in the energy-linearized atomic-cell orbital method. Test calculations on an empty-lattice model (fcc three-dimensional space lattice) demonstrate the viability of these extensions. © 1992 The American Physical Society.