Mapping of Multirotor Dynamics in Metal-Organic Frameworks

The amphidynamic nature of metal-organic frameworks (MOFs) arises from incorporated mobile rotors on organic linkers that connect metal or cluster building blocks into rigid crystalline networks. Quantifying such dynamics is crucial for advancing ultimate applications of MOFs in gas storage, separation, and molecular machinery. However, the lack of a versatile, label-free characterization technique capable of resolving the motions of multiple distinct rotors in a single framework results in an acute shortage of quantitative dynamical data sets, which hinders structure-property correlation. Here, we establish a high-resolution solid-state 13C MAS NMR (Magic Angle Spinning Nuclear Magnetic Resonance) method that employs a classic transverse relaxation theory, enabling quantitative mapping of multirotor dynamics in MOFs. This method is validated on a series of Zn4O(COO)6-based MOFs with increasing structural complexity. In particular, the rotor-specific phenylene motion of multiple linkers is simultaneously determined, yielding distinctive activation energies and motion frequencies spanning 102-107 Hz. DFT calculations of activation energies and known 2H NMR data, where available, corroborate the 13C dynamical analysis. The resulting dynamics maps correlate mobility with local structural features and sorption properties, revealing that higher porosity and weaker π-conjugation enhance rotation, and that high mobility reduces unusable methane uptake at low pressure, thereby enhancing deliverable methane capacity. This versatile methodology is broadly applicable to dynamic systems, providing site-specific insights into complex motional landscapes to establish structure-dynamics-property relationships.