Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

Abstract

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

Calculation of coherences in Förster and modified Redfield theories of excitation energy transfer

“…where ρ g = e −βH ph / Tr e −βH ph is given in Ref. 17. However, if the bath relaxation is much faster than the population transfer, then the non-equilibrium corrections are negligible and we can still use Eq.…”

“…(14) with a non-equilibrium correction, which is calculated in Ref. 17. Here, for simplicity, we assume that the bath relaxes much faster than the population transfer occurs and this correction is negligible.…”

“…Here, for simplicity, we assume that the bath relaxes much faster than the population transfer occurs and this correction is negligible. Then p α (t) and p β (t) are well described by master equation (17) with the equilibrium transfer rates (18).…”

“…In Ref. 17 it is stressed that, despite of theoretical development of more advanced models (for example, with distinguished vibrational modes [18][19][20] ) and non-Markovian master equations (for example, the hierarchical equations of motions 21 or the polaron-representation master equation 22,23 ), these three theories will continue to play an important role for the description of EET for years to come.…”

Geometry Effects on Light‐Harvesting Complex's Light Absorption and Energy Transfer in Purple Bacteria

“…F€ orster resonance energy transfer and Dexter's electron exchange mechanism are the pioneering works dealing with the EET between the donors and acceptors (13,14). Recently, dynamical control and ultrafast energy transfer in the photonic system have also been studied (15)(16)(17)(18)(19). The twodimensional (2D) spectroscopy has been applied to study the coupling properties of the energy transfer process and the electronic excitation in photosynthetic complexes (20)(21)(22)(23).…”