Optical spectra from Tight-Binding methods: Time dependent DFT
vs. Bethe-Salpether approaches

University of Paderborn, Warburger Str. 100, D - 33098 Paderborn, Germany and
Thomas Frauenheim, Department of Physics, Universität Paderborn, Warburger
Str. 100, 33098 Paderborn, Germany.

In recent years it was shown that the generalization of density functional
theory to time dependent problems (TDDFT) provides optical spectra with
predictive power at a moderate computational cost. However, also intolerable
failures have been reported for charge transfer excitations in molecules and
solid state applications. As an alternative to TDDFT, the solution of the
Bethe-Salpeter equation based on GW quasiparticle energies is expected to
overcome these problems. Focusing on molecular systems, we show how both
approaches can be implemented in the framework of density functional based
tight-binding methods. Special emphasis will be given on conceptual similarities
and differences in the treatment of the electron-hole interaction. Finally, some
benchmark studies will be presented to show which accuracy can be expected from
these approximate theories.