Förster resonance energy transfer, including transient coherent effects

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.