# Ultrafast Energy Transfer with Competing Channels: Non-equilibrium Foerster and Modified Redfield Theories

## TL;DR

This paper develops non-equilibrium versions of Foerster and Modified Redfield theories to accurately describe ultrafast energy transfer in molecular systems where environmental relaxation is incomplete, especially in strong coupling regimes.

## Contribution

It introduces non-equilibrium rate theories applicable when environmental degrees of freedom do not relax fully before energy transfer occurs.

## Key findings

- Non-equilibrium theories better predict transfer rates in strong coupling regimes.
- Donor ground-state vibrational states are crucial for resonance conditions.
- Validates the importance of non-equilibrium effects in ultrafast energy transfer.

## 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 Foerster 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.