Tight-binding molecular dynamics: A primer

Following the seminal paper by Slater and Koster (1954) the tight-binding model has been widely and successfully applied to investigate electronic properties of materials over several decades. Eventually the advent of efficiently computable ab initio methods, as well as the ever increasing power of digital computers, has obscured its relevance as a tool for electronic structure calculations. Nevertheless, in the last 15 years or so, the tight-binding description of electronic states has been resumed as a state-of-the-art research tool since it can provide a reliable semi-empirical total energy method suitable for large-scale molecular dynamics simulations at a comparatively small numerical effort. Under this respect, tight binding represents a conceptual bridge between superior (but expensive) ab initio simulations and model-potential ones, characterized both by a reduced computational workload and reduced transferability. In addition, the tight-binding approach is optimally tailored for training materials scientists to perform atomistic simulations: in fact, it is firmly rooted into an intuitive physico-chemical description of bonding and it does not necessarily require complex numerical tools. In this paper I review the tight-binding formalism and I discuss the key issues of the method as for its practical implementation as well as its underlying physical picture. I further extend the basic theory to the realm of molecular dynamics simulations and I discuss a linear scaling formulation of the method.