Electronic absorption of Frenkel excitons in topologically disordered systems

A self-consistent effective medium theory of the electronic absorption spectra of tightly bound dipolar excitons in simple fluids is developed within the adiabatic picture. The theoretical approach is based on the isomorphism between the path-integral formulation of quantum theory and classical statistical mechanics and is an extension of previous work [D. Chandler, K. S. Schweizer, and P. G. Wolynes, Phys. Rev. Lett. 49, 1100 (1982)]. The consequences of fluid structural disorder on resonant excitation transfer and the statistical fluctuations of single molecule energy levels are simultaneously treated. Detailed numerical calculations are performed to establish the dependence of the absorption spectrum on fluid density, short range order, and the relative magnitude of the resonant transfer vs the single site disorder. The density dependence of the spectral features are found to be a sensitive function of fluid structure and the relative strength of the localizing vs the delocalizing interactions. By comparing the liquid state results with the corresponding crystalline solid behavior, the consequences of topological disorder on the exciton spectrum are identified. The relevance of the theoretical predictions to spectroscopic probes of exciton derealization in molecular liquids and glasses is discussed.