The Tight‐Binding Model and Embedded‐Atom Potentials

The tight-binding model is an approach to the electronic band structure from the atomic borderline case. It describes the electronic states starting from the limit of an isolated atom. It is assumed that the Fourier transform of the Bloch function can be approximated by the linear combination of atomic orbitals (LCAO). This simple model gives good quantitative results for energetic bands derived from strongly localized atomic orbitals. The embedded-atom method (EAM) overcomes the limitations of the pair potential technique. It is considered to be practical enough for calculations of defects, impurities, fractures, and surfaces in metals. In this model, an impurity is assumed to experience a locally uniform or only slightly nonuniform, environment. There are two ways of constructing the embedding function. One way is to describe it by an analytical function with adjustable parameters. Another way is to postulate an equation of state of the ground-state structure.