Full-potential revision of coherent-potential-approximation alloy theory

Korringa-Kohn-Rostoker (KKR) multiple-scattering theory has recently been extended from the traditional muffin-tin model to a valid full-potential theory. This implies that the coherent-potential-approximation (CPA) theory of substitutional alloys can be similarly generalized without revising its logical basis. Model calculations, however, have shown that internal sums that occur in matrix products in the full-potential theory must be carried to completion, requiring the use of rectangular matrices. These matrices are square in the muffin-tin model, and standard KKR-CPA theory implicitly requires inversion of such a matrix. Since this inversion is invalid for rectangular matrices, derivations of KKR-CPA alloy theory need to be revised to avoid it. An appropriate revision is considered here. © 1992 The American Physical Society.