Origin of the exceptional negative thermal expansion in metal-organic framework-5Zn4O(1,4−benzenedicarboxylate)3

Metal organic framework-5 (MOF-5) was recently suggested to possess an exceptionally large negative thermal-expansion coefficient. Our direct experimental measurement of the thermal expansion of MOF-5 using neutron powder diffraction, in the temperature range of 4 to 600 K, shows that the linear thermal-expansion coefficient is $\ensuremath{\approx}\ensuremath{-}16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }{\text{K}}^{\ensuremath{-}1}$. To understand the origin of this large negative thermal-expansion behavior, we performed first-principles lattice dynamics calculations. The calculated thermal-expansion coefficients within quasiharmonic approximation agree well with the experimental data. We found that almost all low-frequency lattice vibrational modes (below $\ensuremath{\sim}23\text{ }\text{meV}$) involve the motion of the benzene rings and the ${\text{ZnO}}_{4}$ clusters as rigid units and the carboxyl groups as bridges. These so-called ``rigid-unit modes'' exhibit various degrees of phonon softening (i.e., the vibrational energy decreases with contracting crystal lattice) and thus are directly responsible for the large negative thermal expansion in MOF-5. Initial efforts were made to observe the phonon softening experimentally.