Convergence of internal sums

This problem can be avoided by expressing the MST equations in terms of the square matrix S C = CVS, Hermitian in consequence of the surface-matching theorem. This matrix has full rank because it is contracted over the larger index lg. From the definitions of the C and S matrices, the matrix product S C is a specific integral involving the Helmholtz Green function [281], 

In a matrix notation omitting L indices and summations, the KKR/MST equation is 

The coefficients ft = Sy are the expansion coefficients of the global matching function (cr) = Jft, l nl (G ) l - Defining t = —SiSUjy Sft which reduces to t = —SC l for square matrices [281], EIIV takes the standard MST form I — tg, without implying inversion of a rectangular matrix. Using these closed forms, the coefficients ft and y are related by 

In alloy theory, this equation determines the variational wave function for an atomic cell I/, embedded in a statistical medium defined by the vector of coefficients ft for all other cells [157, 281]. 

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