Identifying the Role of Terahertz Vibrations in Metal-Organic Frameworks: From Gate-Opening Phenomenon to Shear-Driven Structural Destabilization

We present an unambiguous identification of low-frequency terahertz vibrations in the archetypal imidazole-based metal-organic framework (MOF) materials: ZIF-4, ZIF-7, and ZIF-8, all of which adopt a zeolite-like nanoporous structure. Using inelastic neutron scattering and synchrotron radiation far-infrared absorption spectroscopy, in conjunction with density functional theory (DFT), we have pinpointed all major sources of vibrational modes. Ab initio DFT calculations revealed the complex nature of the collective THz modes, which enable us to establish detailed correlations with experiments. We discover that low-energy conformational dynamics offers multiple pathways to elucidate novel physical phenomena observed in MOFs. New evidence demonstrates that THz modes are intrinsically linked, not only to anomalous elasticity underpinning gate-opening and pore-breathing mechanisms, but also to shear-induced phase transitions and the onset of structural instability.

Figure 1

Nanoporous hybrid framework structures of (a) ZIF-4, (b) ZIF-7, and (c) ZIF-8, in which the inorganic building units are represented by the ${\mathrm{ZnN}}_4$ tetrahedra (purple). The middle panel shows the imidazole-based organic building units bridging the adjacent ${\mathrm{ZnN}}_4$ inorganic tetrahedra. The right panel depicts the complex pore morphologies and SAV (yellow surfaces). Hydrogen is omitted in the frameworks for clarity. The color scheme is zinc-purple, carbon-gray, nitrogen-blue, hydrogen-white.

Figure 2

INS spectra in the regions of (a) $0–200{\mathrm{cm}}^{-1}$ (linear scale), and for (b) $200–4000{\mathrm{cm}}^{-1}$ (log scale). Comparison of experimental (blue) and DFT theoretical spectra (red) for ZIFs-4, -7, and -8. The theoretical spectra simulate the purely inelastic response including overtones [24]. The four spectral regions are designated as I to IV (note $1\mathrm{THz}\approx 33.3{\mathrm{cm}}^{-1}$).

Figure 3

Far-infrared (FIR) spectra in the $25–700{\mathrm{cm}}^{-1}$ region. (a) Synchrotron FIR spectra. Comparison of experimental and theoretical DFT spectra for (b) ZIF-4, (c) ZIF-7, and (d) ZIF-8. An empirical $10{\mathrm{cm}}^{-1}$ FWHM Lorentzian line shape was applied to the DFT spectra to aid in comparison to the FIR data.

Figure 4

Low-energy THz vibrations of ZIF-4 viewed normal to the 4MR and 6MR orientations. (a) Soft mode facilitated by lattice distortion from shearing of 4MR, where negative shear stresses ($-\tau$) generate elongated 6MR, and vice versa. (b) Gate-opening mechanism, red arrows designate collective dynamics affecting pore cavity. Animated versions available in the Supplemental Material [24].

Figure 5

Low-energy lattice dynamics in ZIF-7. (a) Soft mode matching the experimentally determined phase transition [30]. (b) Breathing mode accommodated by collective 6MR spiral “screw” motion and 4MR shearing. (c) Breathing mode via synchronous flapping of organic linkages. Shear induced framework deformations are denoted by $\tau$. Animated versions available in the Supplemental Material [24].

Figure 6

Low-frequency lattice dynamics in a sodalite cage of ZIF-8. (a) Soft mode mechanism causing geometrical distortion of 6MR. (b) Shear deformation of 4MR. (c) Gate-opening mechanism of pore apertures. Animated versions available in the Supplemental Material [24].