Density-functional tight binding - an approximate density-functional theory method

In this paper, we review the foundations of the density-functional tight-binding (DFTB) method. The method is based on the density-functional theory as formulated by Hohenberg and Kohn. It introduces several approximations: First, densities and potentials are written as superpositions of atomic densities and potentials. Second, many-center terms are summarized together with nuclear repulsion energy terms in a way that they can be written as a sum of pairwise repulsive terms. For small distances, the nuclear repulsion dominates, whereas for large distances, these terms vanish. The KohnSham orbitals are expanded in a set of localized atom-centered functions. They are represented in a minimal basis of optimized atomic orbitals, which are obtained for spherical symmetric spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrices contain one- and two-center contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. In addition, we discuss a self-consistent charge extension, the treatment of weak interactions, and a linear response scheme in connection with the DFTB method. Finally, some practical aspects are presented. (c) 2012 John Wiley & Sons, Ltd.