Symmetry-Based Analysis of the Effects of Random Energy Disorder on the Excitonic Level Structure of Cyclic Arrays: Application to Photosynthetic Antenna Complexes

We extend the work of Wu and Small who introduced symmetry-adapted basis defect patterns (BDPs) for systematic analysis of the effects of random static energy disorder (diagonal or off-diagonal) on the excitonic level structure of cyclic Cn arrays of chromophores. Examples include the B850 and B875 rings of bacteriochlorophyll (BChl) molecules associated with the LH2 and LH1 antenna complexes of purple bacteria for which, so far, n = 8, 9, and 16. Calculation of the localization/extendedness (chromophore occupation number) patterns and participation numbers of the exciton levels reveals that the effects of random disorder on the exciton levels that contribute to the critically important B850 or B875 absorption band can be understood in terms of a single BDP of e1 symmetry (“hidden correlation” effect). This is a consequence of the structures of the complexes, the complexes falling in the weak disorder regime and the strict symmetry selection rules that govern the couplings between zero-order exciton level...