Characterization of Fast Restricted Librations of Terephthalate Linkers in MOF UiO-66(Zr) by ²H NMR Spin–Lattice Relaxation Analysis

2 H NMR spin–lattice relaxation was used to probe small-amplitude torsional vibrations (librations) of the organic terephthalate linkers in metal–organic framework (MOF) UiO-66(Zr) saturated with benzene molecules. In UiO-66 (Zr) the mobile phenylene fragments exhibit a complex rotational dynamics of the phenylene rings with fast librations and much slower π-flips around the C 2 symmetry axis. We show that due to the intrinsic broad distribution of the π-flips rate, the relaxation process for the deuterium in the C–D group of phenylene fragment is multiexponential. Two main modes of T 1 relaxation are clearly detected, corresponding to the fast T 1 fast and the slow T 1 slow relaxation. Based on the experimental observation of two-exponential relaxation, a computational model for this T 1 relaxation behavior capable to reproduce the peculiarities of the MOF linkers dynamics was built. Computational analysis allows to establish that the librational motion affects mostly the T 1 slow, while T 1 fast remains unaffected by this motion. Simulation of the T 1 slow dependence on the libration rate k lib shows that in the range of the librational frequencies of 10 6 –10 9 Hz the T 1 slow is not sensitive to the k lib variation, and therefore a precise correspondence between T 1 slow and k lib cannot be established. T 1 slow exhibits a specific “peak-like-shape” dependence of k lib in the range of 10 9 –10 12 Hz. In this range of libration frequencies an unambiguous relation between T 1 slow and k lib exists only in a very narrow frequency window of 0.1 × 10 10 –5 × 10 10 Hz. The best conditions to characterize the librational motion by means of T 1 relaxation analysis are met when the flipping motion is almost frozen ( k flip < 10 3 Hz) because T 1 slow becomes extremely sensitive to the variation of k lib .