Energy transfer, spectral diffusion, and fluorescence of molecular aggregates: Brownian oscillator analysis

The energy transfer rate and the time- and frequency-resolved fluorescence of molecular dimers is calculated. Spectral diffusion and the time-dependent Stokes shift are incorporated using the Brownian oscillator model for the solvent. The results generalize Fِrsterʹs energy transfer theory to the case when the energy transfer and spectral diffusion rates are comparable. Generalized rate equations for the excited state populations which contain time-dependent energy transfer rate W(t) are derived. This rate is expressed in terms of the overlap of the time-dependent fluorescence spectrum of the donor and the absorption spectrum of the acceptor.