Three-Center Tight-Binding together with Multipolar Auxiliary Functions

We present an ab initio tight-binding method that allows to improve on the effective potential and minimal basis approximations employed in semi-empirical calculations. Three-center expansions are used to evaluate the zeroth-order Hamiltonian matrix elements and repulsive energy terms in the spirit of the Horsfield method. Self-consistency is handled by expanding atomic orbital products in an auxiliary basis following the work of Giese and York, combined with a two-center expansion of the exchange-correlation kernels. Together with non-minimal main basis sets (double zeta plus polarization) we show that the resulting method trades a modest amount of accuracy for a significant gain in speed, compared to NAO-DFT, in calculations on small molecules, bulk compounds and metal nanoclusters.