On the flexibility of metal-organic frameworks

Occasional, large amplitude flexibility in metal-organic frameworks (MOFs) is one of the most intriguing recent discoveries in chemistry and material science. Yet, there is at present no theoretical framework that permits the identification of flexible structures in the rapidly expanding universe of MOFs. Here, we propose a simple method to predict whether a MOF is flexible, based on treating it as a system of rigid elements, connected by hinges. This proposition is correct in application to MOFs based on rigid carboxylate linkers. We validate the method by correctly classifying known experimental MOFs into rigid and flexible groups. Applied to hypothetical MOFs, the method reveals an abundance of flexibility phenomena, and this seems to be at odds with the proportion of flexible structures among experimentally known MOFs. We speculate that the flexibility of a MOF may constitute an intrinsic impediment on its experimental realization. This highlights the importance of systematic prediction of large amplitude flexibility regimes in MOFs.