Multiple-scattering theory for space-filling cell potentials

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Abstract
The multiple-scattering theory (MST) method of Korringa, and of Kohn and Rostoker for determining the electronic structure of solids, originally developed in connection with potentials bounded by non- overlapping spheres (muffin-tin potentials), is generalized to the case of space-filling potential cells of arbitrary shape. Both variational and nonvariational formalisms are used in effecting this generalization. In contrast to the case of muffin-tin potentials, different forms of MST exhibit different convergence rates for the energy and the wave function. Numerical results are presented that illustrate the differing convergence rates of the variational and nonvariational forms of MST for space-filling potentials. The generalized MST described here should be useful quite generally for constructing global solutions to linear partial differential equations from sets of locally exact solutions.