The Renaissance and Quantitative Development of the Tight-Binding Method

Abstract

The chapter presents a study on the renaissance and quantitative development of the tight-binding method. This chapter discusses the various methods available for the calculation of the electronic structure of molecular clusters and solids in a localized orbital basis. The chapter discusses those approximate techniques that can be applied to the aperiodic systems and large unit-cell crystals. This chapter discusses the use of a restricted atomic orbital basis set in otherwise first-principles applications, either at the Hartree-Fock level or making the local-density approximation for exchange and correlation. The chapter discusses semiempirical methods and the empirical interpolation schemes in which the linear-combination-of-atomic-orbitals (LCAO) integrals are regarded as free parameters in some unspecified basis. The underlying justifications for these models and the definitions of the localized basis orbitals involved are discussed. Methods by which a set of Wannier functions may be defined variationally without the former knowledge of the Bloch functions are discussed, together with the more general use of pseudopotential methods to define localized orbitals and nonhermitian representations. The chapter explains the extraction of tightbinding parameters from phase shifts, with particular reference to transition metals and their compounds and the use of “muffin-tin orbital” methods.