  We performed ab initio calculations of the elastic constants of five flexible
metal-organic frameworks: MIL-53(Al), MIL-53(Ga), MIL-47 and the square and
lozenge structures of DMOF-1. Tensorial analysis of the elastic constants
reveal a highly anisotropic elastic behavior, some deformation directions
exhibiting very low Young's modulus and shear modulus. This anisotropy can
reach a 400:1 ratio between the most rigid and weakest directions, in stark
contrast with the case of non-flexible MOFs such as MOF-5 and ZIF-8. In
addition, we show that flexible MOFs can display extremely large negative
linear compressibility (NLC). These results uncover the microscopic roots of
stimuli-induced structural transitions in flexible MOFs, by linking the local
elastic behavior of the material and its multistability.
