A molecular theory of the line shape: Inhomogeneous and homogeneous electronic spectra of dilute chromophores in nonpolar fluids

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Abstract
Kubo’s stochastic theory of the spectral line shape provides an elegant phenomenological description of inhomogeneous and homogeneous broadening and the transition between the two. This theory has been used profitably in the analysis of many experiments. In this paper we attempt to provide a microscopic foundation for the Kubo model by developing a completely molecular theory of the line shape. For definiteness we focus on the optical line shape of dilute chromophores in nonpolar fluids. Many of the features of the Kubo theory are found in the molecular theory; indeed, the molecular theory produces microscopic expressions involving the solvent structure and dynamics for Kubo’s phenomenological parameters, and provides some justification for the Gaussian assumption in the stochastic theory. On the other hand, the molecular theory produces a transition frequency time‐correlation function that is distinctly nonexponential, in contrast to the exponential assumption of the Kubo theory, and it is found that this nonexponentiality is necessary for the accurate description of line shapes in the regime intermediate between inhomogeneous and homogeneous broadening. For a model of Lennard‐Jones particles the molecular theory is compared with molecular dynamics computer simulations.