Designing Geared Molecular Rotors in Flexible Metal-Organic Frameworks

Translating macroscopic mechanical concepts such as gears to the molecular scale offers a route to precise control over nanoscale motion, inspired by the efficiency of biological machines. In this work, we explore two-dimensional interlocked linker rotations in the flexible metal-organic framework NU-2002. The volume-dependent free energy landscape is mapped using bias-deletion metadynamics to identify six characteristic phases, ranging from very closed to very open pore. We then perform unbiased molecular dynamics simulations at each phase to track rotation events and evaluate co-rotation statistics, calculate free energy barriers, and measure pairwise radial force transfer between neighbouring linkers. We show that the free energy barrier acts as a rotational-speed filter, where rare rotational transitions lead to higher speeds on average. Across the volume profile, we classify four distinct geared regimes: sterically restricted rotations at small volumes (Jammed Gear), rotational coupling extending to third neighbour linkers (First Gear), in-plane partnered linker coupling (Second Gear), and uncoupled, independent rotation at large volumes (Neutral Gear). Together, these results establish framework breathing as a molecular gearbox that switches both the speed and collective coupling of linker rotation. Framework flexibility therefore offers a handle for programming collective motion in solid-state molecular machines.