Lattice Dynamics of Metal-Organic Frameworks: Neutron Inelastic Scattering and First-Principles Calculations

By combining neutron inelastic scattering (NIS) and first-principles calculations, we have investigated the lattice dynamics of metal-organic framework-5 (MOF5). The structural stability of MOF5 was evaluated by calculating the three cubic elastic constants.We find that the shear modulus, c44=1.16 GPA, is unusually small, while two other moduli are relatively large (i.e., c11=29.42 GPa and c12=12.56 GPa). We predict that MOF5 is very close to structural instability and may yield interesting phases under high pressure and strain. The phonon dispersion curves and phonon density of states were directly calculated and our simulated NIS spectrum agrees very well with our experimental data. Several interesting phonon modes are discussed, including the softest twisting modes of the organic linker. Disciplines Engineering | Materials Science and Engineering Comments Suggested Citation: Zhou, W. and Yildirim, T. (2006). Lattice dynamics of metal-organic frameworks: Neutron inelastic scattering and first-principles calculations. Physical Review B 74, 180301. © 2006 American Physical Society http://dx.doi.org/10.1103/PhysRevB.74.180301 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/mse_papers/209 Lattice dynamics of metal-organic frameworks: Neutron inelastic scattering and first-principles calculations W. Zhou1,2 and T. Yildirim1,2 1NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 2Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Received 8 September 2006; revised manuscript received 24 October 2006; published 14 November 2006 By combining neutron inelastic scattering NIS and first-principles calculations, we have investigated the lattice dynamics of metal-organic framework-5 MOF5 . The structural stability of MOF5 was evaluated by calculating the three cubic elastic constants. We find that the shear modulus, c44=1.16 GPA, is unusually small, while two other moduli are relatively large i.e., c11=29.42 GPa and c12=12.56 GPa . We predict that MOF5 is very close to structural instability and may yield interesting phases under high pressure and strain. The phonon dispersion curves and phonon density of states were directly calculated and our simulated NIS spectrum agrees very well with our experimental data. Several interesting phonon modes are discussed, including the softest twisting modes of the organic linker. DOI: 10.1103/PhysRevB.74.180301 PACS number s : 63.20. e, 62.20.Dc, 61.82.Pv Metal-organic framework MOF compounds,1–5 which consist of metal-oxide clusters connected by organic linkers see Fig. 1 , are a class of nanoporous materials with very promising potential applications such as energy storage, gas separation, and template synthesis of nanoclusters and catalysts. There are an almost exponentially growing number of studies on MOF materials, mostly focusing on the optimization of the metal-oxide clusters and/or the organic linkers to improve the gas adsorption properties. Much less attention is paid to the fundamental properties of this interesting class of materials such as their structural stability and lattice dynamics. Understanding the stability and dynamical properties is clearly needed in order to optimize these materials for desired properties. For example, it was recently proposed that the MOF structure can encapsulate C60 molecules and result in superconductivity upon doping.6 In such hybrid structures, it is important to know the phonon spectrum of the MOF lattice and its coupling to the electronic structure. Furthermore, a lack of knowledge concerning MOFs lattice dynamics presents a significant obstacle in the quantum dynamics study of gas molecules H2, CH4, etc. adsorbed on MOFs.7,8 Here we report a detailed study of the structural stability and lattice dynamics of MOF5 the most widely studied MOF material from combined neutron inelastic scattering NIS and first-principles calculations. The structure of MOF5 Fig. 1 is highly symmetric space group Fm-3m and consists of ZnO4 clusters at the tetrahedral site of an fcc lattice, linked by 1,4-benzenedicarboxylate BDC to form the three-dimensional framework. Our first-principles calculations were performed within the plane-wave implementation of the local density approximation to density functional theory in the PWscf package.9 We used Vanderbilt-type ultrasoft potentials with PerdewZunger exchange correlation. A cutoff energy of 408 eV and a 1 1 1 k-point mesh were found to be enough for the total energy to converge within 0.5 meV/atom. We first describe the dependence of the structure on the cell volume i.e., external pressure . Figure 2 shows how the lattice parameter and the total energy of the cell changes with external pressure and the total volume, respectively. We optimized the atomic positions for each volume and did not find any structural instability over the pressure range studied. From −0.5 to 0.5 GPa, we find a linear pressure dependence of the lattice constant with a slope of 0.46 Å/GPa. Fitting the energy vs volume curve to the Murnaghan equation of state10 yields a bulk modulus of 18.2 GPa. The minimum energy corresponds to lattice constant aC=25.58 Å, which is in excellent agreement with the experimental value11,1 of a =25.91 Å. The optimized atomic positions were also found to agree well with the experimental values. A better insight into the structural stability can be gained from the elastic constants, which we calculated following the standard scheme for a cubic crystal,12,13 starting from the fully optimized MOF5 structure. Three types of strains were applied to the conventional fcc cell of MOF5 see Fig. 3 . The first strain is a volume-conserving tetragonal deformation along the z axis, the second one refers to a uniform hydrostatic pressure, and the third one corresponds to a volume-conserving orthorhombic shear. For all three strains, FIG. 1. Color online The crystal structure of MOF5, which consists of BDC linkers connecting ZnO4 clusters located at the tetrahedral site of an fcc lattice. For clarity, some of the atoms were not shown. PHYSICAL REVIEW B 74, 180301 R 2006 RAPID COMMUNICATIONS 1098-0121/2006/74 18 /180301 4 ©2006 The American Physical Society 180301-1 there is only one variable, , in the strain tensor, reflecting the magnitude of the strain. All calculations were done on the strained primitive cell, which is structurally equivalent to the strained conventional cell. Atomic positions were fully optimized and E vs data were obtained. E /V was then fit to a polynomial in , where V is the unit cell volume. The results are summarized in Fig. 3. As expected, the calculated values satisfy the stability criteria i.e., c11 c12, c11+2c12 0, and c44 0 for a cubic crystal . However, the shear modulus c44 is very small 1.16 GPa , indicating that MOF5 is very close to structural instability. Besides, c11−c44 is significantly larger than zero and according to the Cauchy relation,14 this indicates a significant deviation from a central intermolecular potential, consistent with what was found previously.15 The small c44 also suggests that MOF5 could collapse into a potentially useful structure under certain shear stress. For example, the pristine MOF5 structure has a large pore volume but the pores are too open to hold hydrogen molecules at high temperatures; a collapsed MOF5 structure could have finer cavities connected by smaller channels, which are in principle better for H2 storage. Notably, the shear modulus c44 that we calculated is significantly different from a previously reported result.15 This is probably due to the very weak dependence of the energy on the shear strain applied, which requires very accurate total energy calculations. We note that we do get about the same value for c44 regardless of the magnitude of the strain used i.e., small or large , as evidenced from the perfect fit shown in Fig. 3. After having shown that the MOF5 structure is stable with a very small shear modulus, we now discuss the lattice dynamics properties at the zone center and along highsymmetry directions in the Brillouin zone. The phonon density of states DOS and dispersion curves were calculated using the supercell method with finite difference.16 The primitive cell was used and the full dynamical matrix was obtained from a total of 26 symmetry-independent atomic displacements 0.03 Å . The primitive cell of MOF5 contains two formula units Zn4O13− C8H4 3 giving rise to a total of 318 phonon branches. The phonon modes at are classified as q = 0 = 9A1g R + 3A1u + 3A2g + 9A2u + 12Eu + 12Eg R + 17T2u + 24T2g R + 24T1u IR + 17T1g, where R and IR correspond to Raman and infrared active, respectively. The crystal symmetry implies 105 Raman and 72 IR-active modes. In Table I, we list the calculated energies at . We hope that our calculations will initiate more experimental work such as Raman/IR measurements to confirm the gamma phonon energies that we calculated here. In the absent of such high-resolution data, we have performed neutron inelastic scattering measurements of the phonon DOS and compared it with our calculations. The experimental NIS spectrum shown in Fig. 4 was collected on a powder sample of MOF5 using the Filter Analyzer Neutron Spectrometer17 under conditions that provide full width at half maximum energy resolutions of 2–4.5 % of the incident energy over the range probed. To compare the NIS data with theory, the NIS spectrum was computed for a 10 10 10 q-point grid within the incoherent approximation,16,18 with instrumental resolution taken into account. As shown in Fig. 4, the agreement between calcuFIG. 3. Color online The three cubic elastic constants of MOF5. The dots are the actual calculations and the solid lines are the quadratic fit. The deformation matrices for each distortion are also shown. The right-bottom panel summarizes the calculated elastic moduli and the sound velocities. Here is the mass density of MOF5 0.59 g/cm3 . FIG. 2. Color online a The cubic lattice parameter of MOF5 versus pressure, indicating linear dependence near equilibrium structure. b The total energy versus primitive cell volume dots and the fit by the Murnaghan equation of state solid line . W. ZHOU AND T. YILDIRIM PHYSICAL REVIEW B 74, 180301 R 2006 RAPID COMMUNICATIONS