Advances and applications in the FIREBALL ab initio tight-binding molecular-dynamics formalism

One of the outstanding advancements in electronic-structure density-functional methods is the Sankey-Niklewski (SN) approach [Sankey and Niklewski, Phys. Rev. B 40, 3979 (1989)]; a method for computing total energies and forces, within an ab initio tight-binding formalism. Over the past two decades, several improvements to the method have been proposed and utilized to calculate materials ranging from biomolecules to semiconductors. In particular, the improved method (called FIREBALL) uses separable pseudopotentials and goes beyond the minimal sp(3) basis set of the SN method, allowing for double numerical (DN) basis sets with the addition of polarization orbitals and d-orbitals to the basis set. Herein, we report a review of the method, some improved theoretical developments, and some recent application to a variety of systems.