Detecting Molecular Rotational Dynamics Complementing the Low-Frequency Terahertz Vibrations in a Zirconium-Based Metal-Organic Framework

We show clear experimental evidence of cooperative terahertz (THz) dynamics observed below 3 THz ($\sim 100{\mathrm{cm}}^{-1}$), for a low-symmetry Zr-based metal-organic framework structure, termed MIL–140A [$\mathrm{ZrO}({\mathrm{O}}_2{\mathrm{C}\text{−}\mathrm{C}}_6{\mathrm{H}}_4\text{−}{\mathrm{CO}}_2)$]. Utilizing a combination of high-resolution inelastic neutron scattering and synchrotron radiation far-infrared spectroscopy, we measured low-energy vibrations originating from the hindered rotations of organic linkers, whose energy barriers and detailed dynamics have been elucidated via ab initio density functional theory calculations. The complex pore architecture caused by the THz rotations has been characterized. We discovered an array of soft modes with trampolinelike motions, which could potentially be the source of anomalous mechanical phenomena such as negative thermal expansion. Our results demonstrate coordinated shear dynamics (2.47 THz), a mechanism which we have shown to destabilize the framework structure, in the exact crystallographic direction of the minimum shear modulus ($G_{\min }$).

Figure 1

Three-dimensional (3D) framework structure of MIL-140A [ZrO(BDC); $\mathrm{BDC}={\mathrm{O}}_2\mathrm{C}-{\mathrm{C}}_6{\mathrm{H}}_4-{\mathrm{CO}}_2$] looking down the crystallographic (a) $b$ axis and (b) $c$ axis, respectively; it has the monoclinic $C2/c$ space group. The inorganic building units are ${\mathrm{ZrO}}_6$ coordination polyhedra, forming 1D chains along the $⟨001⟩$ zone axis. The black line represents one unit cell. Color scheme adopted: zirconium: light blue; carbon: gray; oxygen: red; hydrogen: white. Circled areas denote the type-$A$ and type-$B$ motions of the organic linkers.

Figure 2

Comparison of the experimental (black and green) and theoretical INS spectra (red: PBE; blue: PBE-D) in the region of $0–250{\mathrm{cm}}^{-1}$, measured at 5 K. Note that $1\mathrm{THz}\approx 33.3{\mathrm{cm}}^{-1}$. The experimental spectra excluding the MIL-140A sample (green trace) is included to confirm that the detected peaks are resulting from the framework vibrations of MIL-140A.

Figure 3

(a),(c) SR-FIR and (b),(d) offline Raman spectra in the region of 40-200 and $0–250{\mathrm{cm}}^{-1}$, respectively. Comparison of experimental (red) and theoretical spectra (blue and black) for MIL-140A. The blue theoretical spectra have a full-width-half-maximum (FWHM) Lorentzian line fit applied to aid in comparison with the experimental data ($2{\mathrm{cm}}^{-1}$ for FIR and $5{\mathrm{cm}}^{-1}$ for Raman). Theoretical Raman data were corrected for a laser frequency of 532 nm and a temperature of 293 K. High signal-to-noise SR-FIR spectrum was detected using a liquid helium-cooled bolometer. For the Raman spectra, it is noted that a discrepancy near the cutoff of $\sim 40{\mathrm{cm}}^{-1}$ is within the limit of such offline measurements.

Figure 4

Rotational dynamics of MIL–140A determined from DFT calculations, in accordance with experimental observations (Fig. 2). (a) Asymmetric and (b) symmetric type-$A$ rotorlike motions along with (inset) the energy barrier and change in SAV for the 180° ring rotations during the symmetric type-$A$ motion. (c) Asymmetric and (d) symmetric type-$B$ rotorlike motions. Blue circular arrowheads are used to mark the rotational directions.

Figure 5

Modification of the solvent accessible volume (SAV) of the (a) equilibrium geometry, with the structures obtained when the type-$A$ aromatic rings are rotated symmetrically by (b) $\varphi =30°$, resulting in an increased SAV, and (c) $\varphi =160°$, resulting in a decreased SAV and formation of purely 1D pore channels along the $c$ axis.

Figure 6

(a) Asymmetric type-$A$ and (b) asymmetric type-$B$ trampolinelike vibrational motions of MIL-140A.