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The lineshape of spectroscopic transitions offer windows into the localenvironment of a system. Here, we present a novel approach for connecting thelineshape of a molecular exciton to finite-temperature lattice vibrationswithin the context of the Davydov soliton model (A. S. Davydov and N. I.Kislukha, Phys. Stat. Sol. {\bf 59},465(1973)). Our results are based upon anumerically exact, self-consistent treatment of the model in which thermaleffects are introduced as fluctuations about the zero-temperature localizedsoliton state. We find that both the energy fluctuations and the localizationcan be described in terms of a parameter-free, reduced description byintroducing a critical temperature below which exciton self-trapping isexpected to be stable. Above this temperature, the self-consistent ansatzrelating the lattice distortion to the exciton wavefunction breaks down. Ourtheoretical model coorelates well with both experimental observations onmolecular J-aggregate and resolves one of the critical issues concerning thefinite temperture stability of soliton states in alpha-helices and proteinpeptide chains.

Correlating exciton coherence length, localization, and its optical lineshape. I. a finite temperature solution of the Davydov soliton model