In this paper we propose an extension of the self-consistent charge-density
-functional tight-binding (SCC-DFTB) method [M. Elstner et al., Phys. Rev.
B 58, 7260 (1998)], which allows the calculation of the optical properties
of finite systems within time-dependent density-functional response theory
(TD-DFRT). For a test set of small organic molecules low-lying singlet exci
tation energies are computed in good agreement with first-principles and ex
perimental results. The overall computational cost of this parameter-free m
ethod is very low and thus it allows us to examine large systems: we report
successful applications to C-60 and the polyacene series.