Singularly isostatic and geometrically unstable rigidity of metal-organic frameworks
Phys. Rev. B 114, 014317 – Published 24 July, 2026
DOI: https://doi.org/10.1103/hslc-s1jp
Abstract
Metal-organic frameworks (MOFs) combine high porosity with structural fragility, raising important questions about their mechanical stability. We develop a rigidity-based formalism in which spring networks parameterized by universal force field for metal-organic frameworks are used to construct rigidity and dynamical matrices. Large-scale analysis of 5682 MOFs from the computation-ready, experimental MOF 2019 database shows that most frameworks are formally overconstrained yet cluster sharply near the isostatic threshold, revealing accidental geometric modes and placing many MOFs near mechanical instability. In the representative case of UiO-66, we show that auxiliary long-range constraints introduced by tuning the neighbor cutoff lift these modes into soft, flat, finite-frequency bands. The results show that rigidity-matrix analysis can rapidly identify MOFs likely to remain mechanically stable. This near-criticality mirrors behavior known from topological mechanics and points to a deeper design principle in porous crystals.
