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Non-adiabatic molecular dynamics of neutral chrysene and tetracene molecules is investigated using Tully's fewest switches surface hopping algorithm coupled to the time-dependent density functional based tight-binding (TD-DFT method for electronic structure calculations. We first assess the performance of two DFTB parameter sets based on the computed TD-DFTB absorption spectra. The main focus is given to the analysis of the electronic relaxation from the brightest excited state following absorption of a UV photon. We determine the dyn