  Bridging the gap between first principles methods and empirical schemes, the
density functional based tight-binding method (DFTB) has become a versatile
tool in predictive atomistic simulations over the past years. One of the major
restrictions of this method is the limitation to local or gradient corrected
exchange-correlation functionals. This excludes the important class of hybrid
or long-range corrected functionals, which are advantageous in thermochemistry,
as well as in the computation of vibrational, photoelectron and optical
spectra. The present work provides a detailed account of the implementation of
DFTB for a long-range corrected functional in generalized Kohn-Sham theory. We
apply the method to a set of organic molecules and compare ionization
potentials and electron affinities with the original DFTB method and higher
level theory. The new scheme cures the significant overpolarization in electric
fields found for local DFTB, which parallels the functional dependence in first
principles density functional theory (DFT). At the same time the computational
savings with respect to full DFT calculations are not compromised as evidenced
by numerical benchmark data.
