  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.
