Generalized KKR-theory for non-muffin-tin potentials

The author shows that the secular equation in KKR (Korringa, Kohn and Rostoker) theory retains its separable structure also in the case of non-muffin-tin potentials. This generalisation has been extensively discussed recently. During this discussion, in which the possible necessity of so-called near field corrections played an important role, it became more and more clear that attention should be concentrated on the basis functions used to represent the crystal wavefunction locally. The author discusses the concentration of reliable basis functions, and shows that several alternatives can be indicated, which are all theoretically sound. These different possibilities have quite different implications as far as their numerical evaluation is concerned, and he shows that the generalisation of the construction, which is already in use in 'classical' KKR theory, deserves preference. In the literature, it has been claimed that it is absolutely necessary to take into account the part of the crystal potential between the boundary of the Wigner-Seitz cell and its circumscribing sphere. The present derivations make it clear that basis functions, constructed from only the part of the crystal potential inside a Wigner-Seitz cell, may be satisfactory as well as those constructed from local potentials with larger support.