Alternative local approach to nonorthogonal tight-binding theory: Environment dependence of the interaction parameters in an orthogonal basis

A method is presented for determining locally the environment dependent single- and two-particle matrix elements Tij and Vijkl between orthogonal basis states, in terms of the corresponding matrix elements Tij and Vijkl between nonorthogonal orbitals having overlaps Sij. Coupled linear equations are derived for Tij and Vijkl which take into account the local environment and overlap effects self-consistently. It is shown that these equations always have a unique solution, which can be efficiently obtained by iterative procedures. The method is applied to electronic structure calculations within the tight-binding approximation, and its accuracy is demonstrated for transition-metal and semiconductor systems, having both three-dimensional and low-dimensional structures. The formulation is exploited to analyze, from a local point of view, the overlap effects on the interaction parameters and the resulting changes in the electronic structure. The calculated modifications of Tij are of limited spatial extension, even for infinite systems, which is of considerable practical importance. The present approach allows us to combine efficiently the simplicity of the orthogonal representation with transferability of the nonorthogonal approach, and thus should be useful for the study of complex systems. © 1995 The American Physical Society.

VIVO