A Selfconsistent-Charge Density-Functional Tight-Binding Scheme

ABSTRACTWe present an extension to the tight-binding (TB) approach to improve total energies, forces and transferability in the presence of considerable long-range Coulomb interactions. We derive an approximate energy expression in terms of charge density fluctuations δn at a reference (input) density n0, which is a second order approximation to the total energy expression in density functional theory (DFT). With the choice of n0 as a superposition of densities of neutral atomic fragments, we can define a repulsive potential as in standard TB theory, which is pairwise, short ranged and transferable. The zero order terms in the total energy expression are recoverd as the standard terms of our density-functional based tight-binding (DF-TB). For the second order terms, the charge density fluctuations δn are approximated by the total charge fluctuation Δqα at atom α, which is qualitatively estimated by employing the Mullikan charge analysis. Within this approximations the total energy expression contains new parameters, which are related to ab-intio DFT calculations. Finally, by introducing localized basis functions and applying the variational principle we arrive at the Hamilton matrix elements, wich themselves depend on the charge fluctuations and, therefore, the general eigenvalue problem has to be solved self-consistently. To obtain forces for efficient geometry relaxation and molecular-dyamics, we calculated analytical derivatives of the total energy with respect to the atomic sites. In order to demonstrate the strenghts of our self-consistent-charge tight-binding (SCC-TB), we calculated reaction energies, geometries and vibrational frequencies for a large set of molecules and compare the results to semi-empirical methods, density-functional calculations and experiment.