Origin of the Exceptional Negative Thermal Expansion in Metal-Organic Framework-5 Zn\u3csub\u3e4\u3c/sub\u3eO(1,4-benzenedicarboxylate)\u3csub\u3e3\u3c/sub\u3e

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 ≈−16×10−6 K−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 lowfrequency lattice vibrational modes (below ∼23 meV) involve the motion of the benzene rings and the ZnO4 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