Metal-organic frameworks (MOFs) are crystalline materials consisting of metal centers and organic linkers forming open and porous structures. They have been extensively studied because of various possible applications exploiting their large amount of internal surface area. Phonon properties of MOFs are, however, still largely unexplored, despite their relevance for thermal and electrical conductivities, thermal expansion, and mechanical properties. Here, we use quantum-mechanical simulations to provide an in-depth analysis of the phonon properties of isoreticular MOFs. We consider phonon band structures, spatial confinements of modes, projected densities of states, and group velocity distributions. Additionally, the character of selected modes is discussed based on real-space displacements, and we address how phonon properties of MOFs change when their constituents are altered, in terms of mass and spatial extent, bonding structure, etc. We find that more complex linkers shift the spectral weight of the phonon density of states toward higher frequencies, while increasing the mass of the metal atoms in the nodes has the opposite effect. As a consequence of the high porosity of MOFs, we observe a particularly pronounced polarization dependence of the dispersion of acoustic phonons with rather high group velocities for longitudinal acoustic modes (around $6000\mathrm{m}{\mathrm{s}}^{-1}$ in the long-wavelength limit). Interestingly, also for several optical phonon modes group velocities amounting to several thousand meters per second are obtained. For heterogeneous systems such as MOFs, correlating group velocities and the displacement of modes is particularly relevant. Here we find that high group velocities are generally associated with delocalized vibrations, while the inverse correlation does not necessarily hold. To quantify anharmonicities, we calculate mode Grüneisen parameters, which we find to be significant only for phonons with frequencies below $\sim 3$ THz. The presented results provide the foundations for an in-depth understanding of the vibrational properties of MOFs and, therefore, pave the way for a future rational design of systems with well-defined phonon properties.

• Received 5 July 2019
• Revised 10 September 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.116003