Recent Progress in the Electron Theory of Solids and Their Surfaces: The Tight-Binding Moffin-Tin Orbital Method

Abstract

Publisher Summary The linear-muffin-tin orbital (LMTO) method, which is the linearized version of the Korringa–Kohn–Rostoker (KKR) method, is the fastest computationally, and its formalism is simple and transparent. Recently, the conventional LMTO-basis set has been transformed exactly into the orthogonal, tight-binding (TB) and minimal basis set, and this simplifies and generalizes the LMTO method considerably. Starting from first principles, TB Hamiltonians can be constructed whose hopping integrals factorize in potential parameters and short-ranged structure constants. The method combines the simplicity of TB approach with the accuracy of KKR method. This chapter gives a brief account of this method, and then concentrates on its application to random alloys and surfaces. The chapter defines first the envelope of the conventional MTO as a singular solution of the Laplace equation | K o RL (r−R)| ∞ = (|r−R|/w) −l−1 Y L (r−R), where R is the site index, L = lm is the orbital index, Y L is a spherical harmonic and w is the averaged Wigner-Seitz (WS) radius. The TB-MTO can be constructed with the help of slightly overlapping WS spheres instead of muffin-tin (MT) spheres. In this way the interstitial space effectively vanishes, and the theory simplifies significantly. This atomic sphere approximation (ASA) gives accurate information on the electronic structure of closed packed solids. The principal new feature of the theory is the existence of a whole class of MTOs specified by the matrices α, which is exploited to generalize theory to random alloys and surfaces.