  In this study, two different simple and intuitive semiempirical schemes for
computing approximate non-adiabatic coupling vectors (NACVs) between the ground
and excited electronic states are presented. The first approximation makes use
of Mulliken transition charges, while the second is based on derivative
coupling vectors between localized molecular orbitals. Both approximations lend
themselves easily to implementation within a whole spectrum of semiempirical
quantum-chemical semiempirical methods. Here we present the implementation
within the tight-binding DFT and benchmark its performance against analytical
TD-DFT NAC vectors for a range of planar fluorescent chromophores at the
Franck-Condon point. The pattern of the atomic NAC vectors is often reproduced,
but the relative magnitude and total length of the NAC vector are often in
serious error. Although quantitative predictions are not possible, these simple
and intuitive approximations allow to explain, in a qualitative way, trends in
the electronic coupling in extended molecular systems and complex materials. In
this context, we investigate how the non-adiabatic coupling depends on the
delocalization length of an excitation in chromophoric oligomers based on a
simple model. Finally, we make general qualitative predictions on the size
dependence of the fluorescence quantum yields in extended molecular systems,
and illustrate those on the example of triply fused porphyrin tapes with
increasing length.
