In this article, we present the radiative surface hopping algorithm, which enables modeling fluorescence within a semi-classical non-adiabatic molecular dynamics framework. The algorithm has been tested for the photodeactivation dynamics of trans-4-dimethylamino-4′-cyanostilbene (DCS). By treating on equal footing the radiative and non-radiative processes, our method allows us to attain a complete molecular movie of the excited-state deactivation. Our dynamics rely on a semi-empirical quantum mechanical/molecular mechanical Hamiltonian and have been run for hundreds of picoseconds, both in the gas phase and in isopropyl ether. The proposed approach successfully captures the first fluorescence processes occurring in DCS, and it succeeds in reproducing the experimental fluorescence lifetime and quantum yield, especially in the polar solvent. The analysis of the geometrical features of the emissive species during the dynamics discards the hypothesis of a twisted intramolecular charge transfer state to be responsible for the dual emission observed experimentally in some polar solvents. In a nutshell, our method opens the way for theoretical studies on early fluorescence events occurring up to hundreds of picoseconds in molecular systems.
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