The tight-binding (TB) model is a kind of counterpart of the nearly-free electron approximation for which the plane wave basis is the most suited to the delocalized characacter of the elecrons. The approximation of the TB method is to assume that the restricted Hibert space, spanned by atomic-like orbitals is sufficient to describe the wave functions solution of the Schrodinger equation (at least in restricted energy range). Such an atomic-like basis provides a natural, physically motivated description of electronic states in matter. In practice there are many versions of TB, depending on the degree of "ab-initio". Some methods are using true atomic-like orbitals and are calculating all the terms of the Hamiltonian leading to an LCAO method, but there exist a semi-empirical version using fitted parameters. This semi-empirical tight-binding method is particularly simple and instructive since the localized basis is not explicitely specified and one needs only the matrix elements of the overlap and the hamiltonian.
If you want to know more about tight-binding method, have a look at the course given at Cargèse Winter School: Tight-Binding in Cargèse.
Maj : 07/10/2009 (309)