Atomistic simulation studies of complex carbon and silicon systems using environment-dependent tight-binding potentials

The use of tight-binding formalism to parametrize electronic structures of crystals and molecules has been a subject of continuous interests since the pioneer work of Slater and Koster [1] more than a half of a century ago. Tight-binding method has attracted more and more attention in the last 20years due to the development of tight-binding potential models that can provide interatomic forces for molecular dynamics simulations of materials [2–7]. The simplicity of the tight-binding description of electronic structures makes the method very economical for large-scale electronic calculations and atomistic simulations [5,9]. However, studies of complex systems require that the tight-binding parameters be “transferable”, [4] i.e., to be able to describe accurately the electronic structures and total energies of a material in different bonding environments. Although tight-binding molecular dynamics has been successfully applied to a number of interesting systems such as carbon fullerenes and carbon nanotubes, [10,11] the transferability of tight-binding potentials is still the major obstruction hindering the wide spread application of the method to more materials of current interest. There are two major approximations made in a typical tight-binding representation of effective one-electronHamiltonianmatrix or band structure based on the Slater-Koster theory