TIGHT-BINDING MODELING OF MATERIALS

The tight-binding method of modelling materials lies between the very accurate, very expensive, ab initio methods and the fast but limited e mpirical methods. When compared with ab initio methods, tight-binding is typically two to three orders of magnitude faster, but suffers from a reduction in transferability due to the approximations made; when c ompared with empirical methods, tight-binding is two to three orders o f magnitude slower, but the quantum mechanical nature of bonding is re tained, ensuring that the angular nature of bonding is correctly descr ibed far from equilibrium structures. Tight-binding is therefore usefu l for the large number of situations in which quantum mechanical effec ts are significant, but the system size makes ab initio calculations i mpractical. In this paper we review the theoretical basis of the tight -binding method, and the range of approaches used to exactly or approx imately solve the tight-binding equations. We then consider a represen tative selection of the huge number of systems which have been studied using tight-binding, identifying the physical characteristics that fa vour a particular tight-binding method, with examples drawn from metal lic, semiconducting and ionic systems. Looking beyond standard tight-b inding methods we then review the work which has been done to improve the accuracy and transferability of tight-binding, and moving in the o pposite direction we consider the relationship between tight-binding a nd empirical models.