Single molecule spectroscopy of disordered circular aggregates: A perturbation analysis

Analytical expressions for various spectroscopic observables are derived fo r statically disordered circular aggregates using first order perturbation theory. Quantities relevant to single molecule spectroscopy experiments on circular aggregates such as the distribution of energy splittings between l evels that are degenerate in the absence of disorder, and the distribution of intensity of levels that are forbidden in the absence of disorder are de rived. For simplicity only diagonal disorder is considered here. The approa ch, however, can be extended to include other types of disorder. Expression s are written in terms of standard deviations of Gaussian disorder, the sym metry number of the aggregate, and in some cases intermolecular couplings. The approach is compared to numerical simulations and shows excellent agree ment over a large range of parameters. The expressions, however, provide a more direct framework to examine and understand the effects of disorder on spectroscopy of aggregates than do the simulations. The potential utility o f the expressions for quantifying disorder and intermolecular couplings fro m single molecule experiments is also demonstrated. (C) 2001 American Insti tute of Physics.