Inertial solvent dynamics and the analysis of spectral line shapes: Temperature-dependent absorption spectrum of β-carotene in nonpolar solvent

Abstract

The influence of solvent dynamics on optical spectra is often described by a stochastic model which assumes exponential relaxation of the time-correlation function for solvent-induced frequency fluctuations. In contrast, theory and experiment suggest that the initial (subpicosecond) phase of solvent relaxation, resulting from inertial motion of the solvent, is a Gaussian function of time. In this work, we employ numerical and analytical calculations to compare the predicted absorption line shapes and the derived solvent reorganization energies obtained from exponential (Brownian oscillator) versus Gaussian (inertial) solvent dynamics. Both models predict motional narrowing as the ratio kappa = Lambda/Delta is increased, where Lambda and Delta are the frequency and variance, respectively, of the solvent-induced frequency fluctuations. However, the motional narrowing limit is achieved at lower values of kappa for the Brownian oscillator model compared to the inertial model. For a given line shape, the derived value of the solvent reorganization energy lambdasolv is only weakly dependent on the solvent relaxation model employed, though different solvent parameters Lambda and Delta are obtained. The two models are applied to the analysis of the temperature-dependent absorption spectrum of beta-carotene in isopentane and CS2. The derived values of lambdasolv using the Gaussian model are found to be in better agreement with the high temperature limit of Delta2/2kBT than are the values obtained using the Brownian oscillator model. In either approach, the solvent reorganization energy is found to increase slightly with temperature as a result of an increase in the variance Delta of the solvent-induced frequency fluctuations.