Resonance energy transfer (RET) is a complex phenomenon where energy is transferred between two non-equivalent molecules. In the Förster picture, that applies to the weak coupling regime, RET occurs from the energy donor molecule in the relaxed excited state towards the acceptor, in an energy-conserving process. However, energy dissipation is crucial for a more general picture of RET that also applies to the strong coupling regime. Here we present a dynamical, non-adiabatic model for RET also accounting for energy relaxation. We exploit the essential state formalism to set up a model for the RET pair that yields an accurate picture of the relevant physics, accounting for just few electronic states and a single coupled vibrational coordinate per molecule. Molecular vibrations are treated in a non-adiabatic approach and energy dissipation is dealt within the Redfield formalism. The approach is first validated on an isolated dye, demonstrating that a very simple relaxation model, defined in terms of a single relaxation parameter, properly describes the different regimes of energy dissipation expected for a molecule, with a fast (fs time window) internal conversion to the lowest excited state and a slow relaxation towards the ground state (ns time window). The same approach is then applied to follow the real time dynamics of a RET pair. In line with the Förster model, in the weak coupling regime the internal conversion of the donor molecule is completed before energy transfer takes place. Our approach also applies to the strong coupling regime, where we observe ultrafast energy transfer occurring well before the internal relaxation of the energy donor is completed.
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