Collective Buckling in Metal-Organic Framework Materials

Metal-Organic Frameworks (MOFs) are crystalline materials consisting of metallic coordination centers connected by organic linkers, forming porous lattices. Under compressive stress, the molecular linkers can adopt deformed configurations while spontaneously breaking a spatial symmetry. This is known as buckling. We develop a microscopic theory of collective buckling in MOFs. We define a buckling coordinate that captures the buckling of a single linker and derive an effective interaction between neighboring linkers within a dipolar approximation. This leads to a lattice Hamiltonian, which we analyze within a mean-field framework to identify collective behaviour such as ferrobuckling and antiferrobuckling. In these ordered phases, neighbouring linkers tend to buckle in the same or in opposite directions, respectively. To make contact with real systems, we focus on MOF-5, using parameters obtained from density functional theory to estimate the relevant energy scales and transition temperatures. Our results establish a quantitative route to describe mechanically driven order in framework materials.