How to quantify long-time rotational motion in molecular systems

We show that all existing methods quantifying rotational motion in molecular fluids eventually have severe limitations in systems undergoing complex rotational motion characterized by slow, heterogeneous, or intermittent dynamics. This impacts, in particular, the study of rotational dynamics in molecular supercooled liquids near their glass transition, as well as discussions of the decoupling between rotational and translational motion and violations of the Debye-Stokes-Einstein relation. We present a brief overview of existing methods and explain why none of them can accurately capture the evolution of rotational dynamics from a diffusive fluid to an arrested solid, thus resolving inconsistent literature results. We then introduce an empirical method that efficiently solves all issues. We benchmark our method by devising a family of continuous-time random walk models for rotational dynamics. Our method correctly quantifies the statistics of free and caged rotational motion, as well as non-Gaussian and non-Fickian rotational dynamics, and should allow a better characterization of dynamic heterogeneity in the rotational motion of supercooled molecular fluids.