Förster resonance energy transfer, including transient coherent effects

Abstract

We formulate the weak intramolecular coupling Förster resonance energy transfer theory in a form suitable for calculating the ultrafast non-linear response of molecular systems. This is done through a formally exact factorization of the time-dependent molecular statistical operator into the system and bath components. Combining this factorization with unperturbed environment evolution, we generalize the traditional Förster master equation for the state population probabilities into a complete master equation for the system’s reduced statistical operator. The traditional Förster theory applies in the limit where the intermolecular coupling is weak and the system–bath coupling is strong. Our derivation explicitly yields a time-nonlocal Förster-type master equation that remains valid even in the limit of vanishing system–bath coupling. The theory predicts a rapid initial coherent evolution of populations arising from a transient initial coherence-dependent term, which induces a “slippage” of the initial condition that persists during subsequent rate-controlled transfer. Comparison with exact numerical results confirms the clear improvement of the present generalization over earlier formulations of the Förster theory and delineates its range of validity.