A Case Study in the Molecular Interpretation of Optical Kerr Effect Spectra: Instantaneous-Normal-Mode Analysis of the OKE Spectrum of Liquid Benzene

Abstract

The ease with which optical Kerr effect (OKE) spectroscopy manages to sample dynamics in the far-infrared would seem to makes it a rather attractive way of doing intermolecular spectroscopy on liquids. However, molecular-level calculations of such spectra are still far less common than microscopically ill-defined phenomenological fits. As a result, there are comparatively few liquids whose OKE spectra have ever been interpreted in any genuinely molecular fashion. In this paper we explore the OKE spectrum of an experimentally well-studied liquid, liquid benzene, at a fully microscopic level by making use of molecular dynamics simulation and an instantaneous-normal-mode analysis. As has often been noted, the long-time tail of the OKE signal is quantitatively accounted for by rotational diffusion (albeit a collective diffusion). Moreover, consistent with the usual expectations, the interaction-induced portion of the remaining signal (which we show to arise almost entirely from center-of-mass translation in this example) appears only at low frequency. However, contrary to the common assumptions, rotational dynamics, often strongly coupled with translational dynamics, contributes over the entire spectral range. The unusual shape of the experimental benzene OKE spectra is shown to arise from the presence of an especially large ratio of rotational to translational bandwidths, an explanation that may account for the similar spectra seen with numerous other planar molecules. Having a molecular-level picture also allows us to point out that there is no need to invoke any kind of hypothetical benzene aggregates in order to explain benzene's OKE spectrum. Benzene and related aromatics are simple liquids whose dynamics, as well as structure, depend largely on repulsive forces and molecular shape.