Single molecule spectroscopy of disordered circular aggregates: A perturbation analysis

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Abstract
Analytical expressions for various spectroscopic observables are derived for 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 levels that are degenerate in the absence of disorder, and the distribution of intensity of levels that are forbidden in the absence of disorder are derived. For simplicity only diagonal disorder is considered here. The approach, however, can be extended to include other types of disorder. Expressions are written in terms of standard deviations of Gaussian disorder, the symmetry number of the aggregate, and in some cases intermolecular couplings. The approach is compared to numerical simulations and shows excellent agreement 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 of the expressions for quantifying disorder and intermolecular couplings from single molecule experiments is also demonstrated.

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