  We propose a new method of calculating electronically excited states that
combines a density functional theory (DFT) based ground state calculation with
a linear response treatment that employs approximations used in the
time-dependent density functional based tight binding (TD-DFTB) approach. The
new method termed TD-DFT+TB does not rely on the DFTB parametrization and is
therefore applicable to systems involving all combinations of elements. We show
that the new method yields UV/Vis absorption spectra that are in excellent
agreement with computationally much more expensive time-dependent density
functional theory (TD-DFT) calculations. Errors in vertical excitation energies
are reduced by a factor of two compared to TD-DFTB.
