Linear aspects of the Korringa–Kohn–Rostoker formalism

Abstract

We present the one-dimensional Korringa–Kohn–Rostoker (KKR) method with the aim ofelucidating its linear features, particularly important in optimizing the numericalalgorithms in energy band computations. The conventional KKR equations based onmultiple scattering theory as well as novel forms of the secular matrix with nearly linearenergy dependency of the eigenvalues are presented. The quasi-linear behaviour of theseeigenvalue functions appears after (i) re-normalizing the wavefunctions in such a way that‘irregular’ solutions vanish on the boundary of the ‘muffin-tin’ segments, and (ii)integrating the full Green function over the whole Wigner–Seitz cell. In addition, using theaforementioned approach we derive a one-dimensional analogue of the generalized Lloydformula.The novel KKR approach illustrated in one dimension can be almost directly applied tohigher dimensional cases. This should open prospects for the accurate KKR band structurecomputations of very complex materials.