  The time-dependent density functional based tight-binding (TD-DFTB) approach
is generalized to account for fractional occupations. In addition, an on-site
correction leads to marked qualitative and quantitative improvements over the
original method. Especially, the known failure of TD-DFTB for the description
of \sigma -> \pi* and n -> \pi* excitations is overcome. Benchmark calculations
on a large set of organic molecules also indicate a better description of
triplet states. The accuracy of the revised TD-DFTB method is found to be
similar to first principles TD-DFT calculations at a highly reduced
computational cost. As a side issue, we also discuss the generalization of the
TD-DFTB method to spin-polarized systems. In contrast to an earlier study
[Trani et al., JCTC 7 3304 (2011)], we obtain a formalism that is fully
consistent with the use of local exchange-correlation functionals in the ground
state DFTB method.
