Theory of Excitation Energy Transfer in the Intermediate Coupling Case of Clusters

Abstract

Previously we presented a unified theory of excitation energy transfer (EET) in dimers, which is applicable to the intermediate coupling case by self-consistently solving the stochastic Liouville equation (Kimura, A.; Kakitani, T.; Yamato, T. J. Phys. Chem. B 2000 104, 9276). However, up to the present time, proper EET theory, which is applicable to the intermediate coupling case of clusters, was not established. In this paper, we contribute to such an intermediate coupling theory in cluster systems. We utilize the method of generalized master equations (GME). In the first step, we construct the memory function by the second-order perturbation theory of the excitonic interaction from a general point of view. Eventually, it is expressed by a Fourier transform of the overlap of the time-dependent fluorescence and the absorption spectra of the constituent molecules. We show that our new theory reduces to the Kenkre-Knox theory in the limit of fast vibrational relaxation and reduces to the Sumi theory of the hot transfer mechanism in the limit of fast decay of the memory function. In the next step, we introduce a renormalization function into this memory function. This renormalization includes a correction due to the contribution of powers of combination of the fourth- and the second-order correlation functions. By numerical calculations, we illustrate how the renormalization effect becomes significant as the excitonic coupling strength U becomes large. We applied this GME method to the EET between BChla molecules in B850 of the photosynthetic antenna system LH2. We found that the memory function calculated using the experimentally obtained optical spectra initially decays very rapidly (with time constant of about 5 fs) and has a plateau in the time region 10-25 fs. Because of this specific memory function, the calculated coherence length in the steady state was about 3. This GME method should be useful for the analysis of the mechanism of EET in many kinds of biological systems.