  A derivation of non-adiabatic coupling vectors for the density functional
based tight binding method (DFTB) between ground and excited states is
presented. The analytical result is valid both for semi-local and long-range
corrected DFTB and includes all required Pulay terms. Electron-translation
factors lead to a conceptual simplification of the Slater-Koster scheme for
precomputed integrals. Compared to scalar couplings obtained from numerical
derivatives, the present approach is computationally more efficient and can be
applied to systems with hundreds of atoms. The accuracy of DFTB derivative
couplings is assessed by comparison to full density functional theory (DFT)
calculations using semi-local and hybrid exchange-correlation functionals with
promising results. As exemplified by a case study of furan, DFTB provides
non-adiabatic coupling vectors that are close to DFT counterparts in size and
direction also in the vicinity of conical intersections.
