A new formula of exciton coherence length in linear array of pigments

Abstract

By solving the generalized master equation with a memory function properly expressed by using the time-correlation function of the exciton-vibration interaction, we derived an empirical formula for the exciton coherence length Ncoh in the linear array of pigments as a function of exciton coupling U and the decay factor for excitation transfer g as follows: Ncoh = 1.40 + 1.32 (U/g ) Adopting the intermediate coupling theory of exciton in dimer (Kimura et al., J. Phys. Chem. B 104 (2000) 9276), we can express the decay factor g by using the reorganization energy l and energy gap D G due to the excitation transfer between neighboring pigments. Applying this general formula to the B850 ring of LH2 of photosynthetic purple bacteria (U = 350 cm-1, l = 80 cm-1 and so g = 140 cm-1), we obtain Ncoh = 4.7. When we evaluate g by considering the Gaussian inhomogeneous broadening (HWHM 200 cm-1), we obtain Ncoh = 3.2. Namely, the exciton domain extends only 3-4 BCl units among the 18 BCl units of B850 in LH2.