Computational Insight into Free Molecular Rotors in Crystalline Solids: Inertial Rotation and Langevin Dynamics

Recent studies have shown that metal-organic frameworks (MOFs) can enable ultralow rotational barriers for molecular rotors in the solid state. In this near-free-rotor regime, elucidating how molecules behave within an ordered lattice becomes central to both a fundamental understanding and the design of crystalline molecular machines. Here, using a series of structurally simple, isoreticular MOF-5 homologues as a common platform, we present a systematic computational investigation of the rotational dynamics of five highly symmetric, rigid cage-like hydrocarbon rotators─bicyclo[1.1.1]pentane (BCP), cubane (CUB), bicyclo[2.2.2]octane (BCO), barrelene (BAR), and diamantane (DIA)─over a broad temperature range of 30-300 K. We show that under nearly barrierless conditions, these molecular rotators can exhibit inertia-dominated, continuous unidirectional rotations, which we quantify by the frequency of 360° turnover events. Temperature dependence of the 360° turnover frequency reveals clear differences among the rotors in how their dominant dynamical mechanisms transition with temperature. Furthermore, we introduce a Langevin description to quantitatively analyze the time evolution of the mean squared net angular displacement of the rotors in their rotational coordinate. We show that on long time scales all rotors enter the Brownian diffusion regime. The extracted rotational damping coefficients η reveal pronounced differences among the five rotors in both the strength of rotor-lattice coupling and its temperature dependence.