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Observation of Binding and Rotation of Methane and Hydrogen within a Functional Metal–Organic Framework

The key requirement for a portable store of natural gas is to maximize the amount of gas within the smallest possible space. The packing of methane (CH4) in a given storage medium at the highest possible density is, therefore, a highly desirable but challenging target. We report a microporous hydroxyl-decorated material, MFM-300(In) (MFM = Manchester Framework Material, replacing the NOTT designation), which displays a high volumetric uptake of 202 v/v at 298 K and 35 bar for CH4 and 488 v/v at 77 K and 20 bar for H2. Direct observation and quantification of the location, binding, and rotational modes of adsorbed CH4 and H2 molecules within this host have been achieved, using neutron diffraction and inelastic neutron scattering experiments, coupled with density functional theory (DFT) modeling. These complementary techniques reveal a very efficient packing of H2 and CH4 molecules within MFM-300(In), reminiscent of the condensed gas in pure component crystalline solids. We also report here, for the first time, the experimental observation of a direct binding interaction between adsorbed CH4 molecules and the hydroxyl groups within the pore of a material. This is different from the arrangement found in CH4/water clathrates, the CH4 store of nature.


■ INTRODUCTION
In recent years, natural gas, comprised primarily of methane, CH 4 (87−96%), 1 has become an important economic and technological target as a bridging fuel to a low carbon future. Although not renewable, large reserves (approximately twothirds of available fossil fuel reserves) and advances in recovery make natural gas an incredibly abundant energy source. This high availability, coupled with the lowest CO 2 emissions of any hydrocarbon fuel 2 and a low sulfur content, 3 ideally place natural gas as a replacement for coal and oil. Currently the widespread use of natural gas is restricted because under ambient conditions, gaseous CH 4 has a low energy density and therefore requires constant access to a pipeline. The energy density of bulk CH 4 can be increased by liquefaction or, to a lesser extent, compression, using either complex cryogenic tanks or heavy-walled high-pressure vessels with expensive compressors, precluding their use in mass-market applications. 4 An alternative approach to increasing the storage density of CH 4 is by adsorption on the surface of a porous material, reducing the intermolecular distance and therefore increasing the packing density. Metal−organic framework (MOF) materials have been widely investigated for their ability to store significantly higher volumes of gas than a conventional tank under the same conditions. 4−6 This has pronounced effects in a number of materials, which have been reported to adsorb gas species (upon saturation uptakes) at densities comparable to their respective liquid phase. To date, this effect has been observed primarily in MOFs showing high CO 2 or H 2 adsorption under extreme conditions, typically low temperatures, and/or high pressures. 7 13 all have significantly higher capacity than bulk CH 4 [33] under the same conditions. This approach offers promise for more efficient CH 4 storage. It is worth noting that, throughout this Article, the volumetric uptake is derived from the bulk material density on the basis of single crystals, and when the efficiency of powder packing is considered, the uptakes will be reduced accordingly. This is subject to the different compressibility and mechanical stability in different materials.
Variation of metal ions/clusters and organic ligands enables a multitude of design possibilities for MOF materials allowing incorporation of functional groups 14,15 and/or desirable metal binding sites 16−18 for specific guest binding interactions. To design future materials with improved gas adsorption properties, it is vital to understand the intermolecular contacts, location, and binding interactions of adsorbed guest molecules within the cavity of the host materials. Determination of the binding of molecular H 2 and CH 4 within porous materials is a very challenging proposition due the short scattering length of hydrogen in X-ray experiments. In addition, adsorbed H 2 and CH 4 molecules have low enthalpies of adsorption, resulting in them being highly disordered within the pores of MOFs. Indeed, H 2 and CH 4 have been shown to behave as a "freerotor" in the solid state when condensed at cryogenic temperatures. To date, determination of the location of adsorbed H 2 and CH 4 molecules has only been achieved in exceptional cases, 19 typically within MOF systems incorporating strong binding sites such as open metal sites 20,21 or geometrically confined pores in which the movement (translational motion) of adsorbed gas molecules is highly constrained. 22 The nature of the potential interaction(s) of pendant functional groups with adsorbed CH 4 within pores at a molecular level remains unclear. Herein, we report the high volumetric uptake of CH 4 in an In(III)-tetracarboxylate material, MFM-300(In) [202 v/v at 298 K and 35 bar; 328 v/v at 110 K and 0.6 bar]. The material also shows high volumetric uptake for H 2 (488 v/v at 77 K and 20 bar). Direct observation and quantification of adsorbed H 2 and CH 4 molecules within MFM-300(In) have been achieved using a combination of neutron diffraction and scattering techniques coupled with computational investigations. These complementary results suggest that the adsorbed CH 4 molecules form specific interactions with metal-bound hydroxyl groups within the pore, supplemented by intermolecular dipole interactions between adsorbed CH 4 molecules and the phenyl-ring lined walls of the pore. These cooperative supramolecular interactions allow packing of CH 4 to very high density upon saturation (0.37 g cm −3 ) reminiscent of liquid CH 4 (0.42 g cm −3 at 111 K) 23 and 71% of that of the solid (0.52 g cm −3 at 20.4 K). 24,25 Interestingly, to our best knowledge, the H 4 C guest ···H−O host interaction reported here represents the first example of such molecular contact in MOFs, and contrasts with the structures observed in CH 4 /water clathrate materials in which the CH 4 molecule is completely orientationally disordered and not observed to interact with the H···OH cageforming linkage. 26  Gas Adsorption Isotherms. Gravimetric isotherms (0−20 bar) were recorded at 77 and 87 K under liquid nitrogen and argon, respectively, for H 2 , and at 110, 215, and 245 K (liquid nitrogen cryofurnace), 195 K (dry ice/acetone), and 273, 283, 293, 303, and 308 K (temperature controlled water-bath) for CH 4 . Data were collected using an IGA-003 system (Hiden Isochema, Warrington, UK) equipped with a turbomolecular pumping system. Acetone exchanged samples were loaded into the system and degassed at 120°C and 1 × 10 −6 mbar for 20 h to give a dry, desolvated material of typical mass ca. 50 mg. 99.995+% grade H 2 and CH 4 were purchased from Air Liquide and used as received. High pressure (0−50 bar) gravimetric gas adsorption and desorption data were collected using a Xemis system (Hiden Isochema, Warrington, UK) equipped with a turbomolecular pumping system backed by a diaphragm pump. CH 4 isotherms (0−50 bar) were recorded at 273, 283, 293, 298, and 303 K by a temperature controlled water bath.
Neutron Powder Diffraction. Neutron powder diffraction experiments were undertaken at the WISH diffractometer at the ISIS facility. MFM-300(In) was loaded into a 6 mm diameter vanadium sample can and outgassed at 1 × 10 −7 mbar and 100°C for 1 day. The sample was loaded into a liquid helium cryostat and cooled to 7 K for data collection. D 2 and CD 4 gas were introduced by warming the samples to 50 and 150 K, respectively, and the gas was dosed volumetrically from a calibrated volume. The gas-loaded sample was then cooled to 7 K over a period of 2 h to ensure good mobility of adsorbed D 2 and CD 4 within the crystalline structure of MFM-300(In). The sample was kept at 7 K for an additional half an hour before date collection to ensure the thermal equilibrium.
Inelastic Neutron Scattering. Inelastic neutron scattering (INS) experiments were undertaken using the TOSCA spectrometer at the ISIS facility. MFM-300(In) was loaded into an 11 mm diameter vanadium sample can and outgassed at 1 × 10 −7 mbar and 100°C for 1 day. The sample was loaded into a helium closed cycle refrigerator (CCR) cryostat and cooled to 11 K for data collection. H 2 and CH 4 gas were introduced by warming the sample to 50 and 150 K, respectively, and the gas was dosed volumetrically from a calibrated volume. The gas-loaded sample was then cooled to 7 K over a period of 2 h to ensure good mobility of adsorbed D 2 and CD 4 within the crystalline structure of MFM-300(In). The sample was kept at 7 K for an additional half an hour before date collection to ensure the thermal equilibrium.
Density Functional Theory (DFT) Calculations. Density functional theory (DFT) calculations were performed using CA-STEP. 27 Three types of calculations were performed: geometry optimization (GO), lattice dynamics (LD), and molecular dynamics (MD). GO is used to determine the ground-state structure, binding energies of adsorbed CH 4 molecules, and rotational potentials for CH 4 molecules when combined with single point energy (SPE) calculations. LD was used to determine the molecular vibrations and thus the hydrogen vibrational density of states for comparison with the INS data. Physisorbed CH 4 is particularly problematic for LD methods due to the weak intermolecular interactions. MD simulations were, therefore, performed to determine the vibrational density of states from the velocity autocorrelation function. This analysis of the MD trajectories was performed with the nMoldyn code. 28 All calculations used the GGA-PBE functional, 29 and some tests were performed with semiempirical dispersive corrections (DFT-D) using the Grimme parametrization. 30 The calculations were performed on a single unit cell of size ∼15 × ∼15 × ∼12 Å 3 and therefore used a k-point set including only the Gamma point. Ultrasoft pseudopotentials were used to separate the core and (pseudo) valence electrons (1

Journal of the American Chemical Society
Article for H, 4 for C, 6 for O, and 13 for In were treated explicitly in the calculations), and the plane wave cutoff was set to 340 eV for all calculations except MD, for which a lower cutoff of 260 eV was used to reduce computational time. MD simulations were performed in the NVT ensemble using a time step of 1 fs and ran for 10 000 steps, therefore covering a time frame of 10 ps. For GO calculations, energy convergence was set to 10 −5 eV/atom, and the maximum residual force per atom was typically 0.02 eV/atom. LD calculations were limited to the Gamma point, Brillouin zone center modes.
■ RESULTS AND DISCUSSION Synthesis and Crystal Structure Analysis. The solvated framework complex [In 2 (OH) 2 (C 16 H 6 O 8 )]·1.28H 2 O· 2.87(DMF) [MFM-300(In)-solvate] was prepared via solvothermal reaction of H 4 L (H 4 L = biphenyl-3,3′,5,5′-tetracarboxylic acid) and In(NO 3 ) 3 ·5H 2 O in a 2:1 ratio mixture of dimethylformamide (DMF) and acetonitrile and was isolated as a microcrystalline powder. Structure solution by synchrotron powder X-ray diffraction confirmed that this material crystallizes in the tetragonal space group I4 1 22, and is isostructural to the related MFM-300(Al). 31,32 We note that this MOF has been previously reported in a different preparation, which yields large single crystals. 33 In our hands, these two forms of MFM-300(In) are equivalent despite the difference in morphology. MFM-300(In) exhibits an open structure comprising chains of [InO 4 (OH) 2 ] moieties bridged by tetracarboxylate ligands L 4− to afford a porous structure with channels formed by corner-sharing [InO 4 (OH) 2 ] octahedra linked via two mutually cis-μ 2 -OH groups. The [InO 4 (OH) 2 ] ∞ chain in MFM-300(In) is similar to that found in MIL-53(In), 34 although the latter features trans-μ 2 -OH groups, resulting in pronounced framework flexibility. The cis-μ 2 -OH groups in MFM-300(In) tie the framework into a rigid "winerack" arrangement. Desolvated MFM-300(In) displays a surface area of 1071 m 2 g −1 and a total pore volume of 0.419 cc g −1 as determined from the N 2 isotherm at 77 K. These values are consistent with the porosity derived from the single-crystal structure, and confirm the complete activation and phase purity of the material.
H 2 and CH 4 Sorption Analysis. H 2 and CH 4 sorption isotherms confirm that MFM-300(In) displays completely reversible uptake over a wide range of temperatures (77−308 K) and pressures ( Figure 1). The H 2 adsorption properties of this material are commensurate with the measured pore volume and BET surface area, reaching 275 v/v at 77 K and 1 bar, rising to 488 v/v at 20 bar, comparable with other MOF materials with similar BET surface areas. 35,36 The heat of adsorption at zero loading is estimated to be 6.8 kJ mol −1 , within the range (4−8 kJ mol −1 ) typically observed for MOF materials with comparable uptakes. 35,36 CH 4 adsorption in MFM-300(In) shows a maximum uptake of 328 v/v at 110 K and 0.6 bar, dropping gradually with increasing temperature, with uptakes at 20 bar of 266, 224, and 198 v/v at 195, 245, and 273 K, respectively. High pressure CH 4 adsorption isotherms revealed uptake capacities of 220 and 202 v/v at 273 and 298 K, respectively, at 35 bar, rising to 228 and 213 v/v, respectively, at 50 bar. Grand Canonical Monte Carlo (GCMC) simulations show excellent agreement with these experimental data ( Figure 1b). The CH 4 uptake of MFM-300(In) at 35 bar and 298 K is one of the highest values reported for a MOF to date, surpassed only by MOF-74(Ni, Co) 4 and HKUST-1 4 ( Table 1). The isosteric heat of adsorption of CH 4 was estimated using the van't Hoff isochore to be 16 kJ mol −1 , which gradually rises to 20 kJ mol −1 with increasing CH 4 loading (Figure 1), comparable to that of other MOFs with similar uptake capacities (12−21 kJ mol −1 ). 4 The steady increase in the heat of adsorption reflects the presence of intermolecular interactions between adsorbed CH 4 molecules within the pores.
The density of adsorbed CH 4 in MFM-300(In) can be estimated by using the total pore volume (0.419 cc g −1 ) derived from the N 2 isotherm at 77 K (assuming no distortion of the pore structure). At 110 K and 0.6 bar, the density of adsorbed CH 4 in MFM-300(In) was calculated to be 0.37 g cm −3 , comparable to that of liquid CH 4 (0.42 g cm −3 at 111 K), suggesting an ultraclose packing of the adsorbed CH 4 molecules in the pore, which could be a result of strong geometric confinement and/or specific host binding. Significantly, to our best knowledge, this density (0.37 g cm −3 ) found in MFM-300(In) represents the highest observed value in a porous MOF (Table 1). The density of adsorbed CH 4 in MFM-300(In) at 298 K and 35 bar is estimated as 0.231 g cc −1 (55% of the liquid density). Similarly, the density of adsorbed H 2 approaches that of the liquid, 0.069 g cc −1 at 77 K and 20 bar (liquid hydrogen density = 0.0708 g cc −1 at 20 K). The high density packing of the adsorbed gas molecules indicates that adsorbed CH 4 and H 2 molecules in MFM-300(In) pack very efficiently, resulting in a very high storage density in a given pore volume. This led us to study the packing of CH 4 and H 2

Journal of the American Chemical Society
Article molecules within MFM-300(In) at crystallographic resolution and investigate vibrational and rotational motions within the pore to determine the intermolecular interactions, which account for this observation.
Determination of the Binding Sites for Adsorbed Hydrogen and Methane Molecules. The locations of adsorbed H 2 and CH 4 molecules within MFM-300(In) were determined by in situ neutron powder diffraction (NPD) as a function of gas loading (Figure 2). NPD patterns were recorded at 7 K for the desolvated material and at loadings of 1.0, 1.5, 3.0, 4.5, and 6.0 D 2 /In and 1.0, 2.0, and 3.0 CD 4 /In. Fourier difference map analysis of the NPD data of the desolvated MOF indicates no residual nuclear density peaks within the pore, thus confirming the complete activation and structural stability of the desolvated sample. The bare material was then dosed volumetrically to the desired loading of D 2 at 50 K and CD 4 at 150 K, accompanied by significant changes in the relative peak intensities of the diffraction patterns. Sequential Fourier difference map analysis of the NPD patterns revealed the position of the center of gravity of the adsorbed D 2 and CD 4 molecules, which were further developed by Rietveld refinement of these data.
At the first loading of D 2 , two independent binding sites (D 2 I and D 2 II ) were located within the one-dimensional pore of   Table 2). The position of the newly observed D 2 IV site is shifted considerably toward the center of the pore channel at this loading, increasing the distances to D 2 V to 3.13(4) Å, accompanied by an increase in occupancy to 1.40 (2). At this saturation loading, a further adsorption site, D 2 VII , interstitial between D 2 II and D 2 III is observed [D 2 II ···D 2 VII = 2.95(3) Å] at an occupancy of 0.12. At this final loading, MFM-300(In) is saturated with D 2 , with a gas loading corresponding to an uptake of 689 cc cc −1 . This high uptake capacity indicates very close packing of molecular D 2 at 7 K. Quantum effects may also account for the high saturation uptake for deuterium in this MOF material. 11 Upon loading the regenerated material with methane, two independent CD 4 binding sites (CD 4 I and CD 4 II ) were located in MFM-300(In)·(CD 4 ) 2. 18 (Table 3) II is unchanged. The occupancy of CD 4 III increases to 0.478 (6), and its location moves slightly toward the pore center [4.629(10) Å from the edge of the 1D channel; C III ···C II distance of 5.649(11) Å]. Interestingly, a fourth site (CD 4 IV ) appears to accommodate the remaining CD 4 molecules. CD 4 IV is sandwiched between two CD 4 III sites with an intermolecular separation of 3.984(11) Å for C IV ···C III and an occupancy of 0.564 (14). Thus, the adsorbed molecules CD 4 I−IV form a 1D alternating molecular chain in the 1D channels of MFM-300(In) via intermolecular interactions (Figure 2b), consistent with the steady increase in the heat of adsorption on loading of CH 4 .
In MFM-300(In)·(CD 4 ) 6.22 , the material is saturated with a total CD 4 occupancy corresponding to an uptake of 340 v/v a D 2 is refined as a single atom with occupancy 2.0 because the orientation could not be determined from the NPD data. After taking into account the site multiplicity, the occupancies are shown as D 2 molecule per indium ion.

Journal of the American Chemical Society
Article and with an adsorbed CD 4 density of 0.63 g cm −3 , 92% of that of solid deuterated CH 4 (0.68 g cm −3 ). 31 This result is in excellent agreement with the measured CH 4 isotherm uptake (328 v/v) at 110 K. The slightly higher value observed for CD 4 adsorption is probably due to a quantum effect as observed in H 2 /D 2 adsorption studies. 11 Comparison of the densities of adsorbed and solid CD 4 indicates a very efficient intermolecular packing of CH 4 molecules in MFM-300(In), considering that the density of adsorbed CD 4 may be underestimated by the use of the pore volume derived from N 2 isotherm at 77 K, as the total void space of MFM-300(In) as measured and determined by the N 2 BET experiment may not be entirely accessible to the bulkier CH 4 molecules. The high packing efficiency is also evidenced by the observation of the comparable intermolecular distance between the adsorbed CD 4 molecules at different sites when compared to that in solid CH 4 (3.95−4.28 Å). 37,38 This NPD study confirms that the free bridging hydroxyl group within the pore of MFM-300(In) is the primary binding site for adsorbed H 2 and CH 4 molecules, leading to high occupancy at low gas loadings. This suggests that adsorbed H 2 and CH 4 molecules populate at site D 2 I /CD 4 I at low surface coverage as a direct result of a C x D y guest ···H−O host binding interaction. D 2 I forms a direct binding interaction with the bridging hydroxyl group in the pore, and the binding distance is slightly longer than that observed in MOFs with open metal sites, 9 consistent with the nature of the different binding mechanisms. Upon higher loadings of D 2 , multiple sites appear at the center of the pore, forming a 3D intermolecular binding network similar to that observed in solid H 2 . At higher loadings of CD 4 , the occupancy of this initial site CD 4 I increases in occupancy from 0.796(4) to 0.872(4), reaching a maximum of 1.008 (12) 26 Closer examination reveals an interesting structural difference between the D 4 C guest ···H−O host binding in MFM-300(In) and that in CH 4 /water clathrates. In the latter case, water molecules form two different types of cages via intermolecular hydrogen bonds: (i) six large cages having 12 pentagonal and 2 hexagonal faces (denoted by 5 12 6 2 ) formed by 24 water molecules and (ii) two small cages having 12 pentagonal faces (denoted by 5 12 ) formed by 20 water molecules. The large and small cages have an average cavity size of 4.33 and 3.95 Å, respectively, and host one CH 4 molecule per cage, giving a stoichiometry of (CH 4 ) 0.174 ·H 2 O (Figure 3). The distance between two trapped CH 4 molecules in the adjacent cages is ca. 5 Å, 26 and this is very similar to the intermolecular distance observed for adsorbed CD 4 molecules in MFM-300(In), confirming the high packing efficiency in the MOF. The stoichiometries for adsorbed CD 4 molecules in MFM-300(In) with respect to the HO-M group are (CD 4 ) 1.09 · HO-M, (CD 4 ) 2.09 ·HO-M, and (CD 4 ) 3.11 ·HO-M for the first, second, and third loadings, respectively. Although these numbers are much higher than that observed for clathrates, it is worth noting that the nature of the host−guest complexes (clathrate and MOF) is not strictly comparable. Indeed, this result suggests that, in addition to the HO-M group, the geometrical confinement due to the phenyl rings in the pore also plays a significant role in trapping CH 4 in the pore. On both cages of the clathrate, the protons on water molecules all point toward each other, assembling cage "edges" with a fully disordered CH 4 molecule at the center. Thus, the dominating binding interaction in clathrates will be H 3 C−H guest ···O host −H.

Article
In contrast, adsorbed CD 4 molecules bind to the hydroxyl groups along the H−O bond in MFM-300(In), and thus the dominating binding interaction is H 3 C−H guest ···H−O host . Indeed, the position of the proton on the hydroxyl group was refined in the NPD data, and no distortion of the HO-M group was observed upon CD 4 inclusion, as is also evidenced by further neutron spectroscopic studies and corresponding modeling (see below). Thus, this study may open new investigations of binding interactions in clathrate materials when strong space confinement is considered.
Studies of the Rotational Motion of Adsorbed H 2 and CH 4 Molecules by INS/DFT/MD. The absolute orientation for all of the adsorbed D 2 and CD 4 molecules cannot be unambiguously determined from the NPD data due to the thermal motion of the host−guest system, despite data collection at 7 K. It is widely accepted that both of these adsorbates (H 2 and CH 4 ) act as a "free rotor" in bulk phase, 39 Upon loading this material with para-H 2 , there is no distortion of the vibrational modes arising from the internal modes of the bare material, confirming the absence of structural change, consistent with the NPD analysis and the low enthalpy of adsorption. At a low H 2 loading (1.0 H 2 /In) (Figure 4), a new peak was observed at 9.5 meV, lower than that of the solid H 2 (14.7 meV), corresponding to the rotational motion of the adsorbed H 2 . 41,42 In addition, a broad peak was observed at ca. 25 meV, corresponding to the liquid recoil motion of molecular H 2 . 43 The appearance of this recoil motion indicates that there is little interaction between the adsorbed H 2 and host material.
The almost-free rotation of adsorbed H 2 within this material is consistent with the crystal structure of pure solid H 2 , in which the molecular positions can be discerned, but the atoms are spherically disordered, even at temperatures as low as 2 K. 40 At a higher H 2 loading of 2.0 H 2 /In, there is an increase in the area of the peaks relating to the rotational and recoil motion of the adsorbed H 2 , consistent with the H 2 binding at the low loading. Further increasing the H 2 loading to 4.0 and 6.0 H 2 /In results in the consistent growth of the rotational and recoil peaks, accompanied by an additional peak at 14.7 meV, consistent with the formation of "solid-hydrogen-like" material within the pores of the MOF. This observation is in excellent agreement with the insight gained from the in situ crystallographic study, which reveals that at this loading, the intermolecular bond length between adsorbed H 2 molecules (3−5 Å) is of an order similar to that observed in solid H 2 (3.75 Å). 44−46 INS spectra of CH 4 -loaded MFM-300(In) show a considerable increase in intensity with a broad peak at low energy transfer (below 40 meV) as a result of adsorbed CH 4 molecules (Figures S44). Difference INS spectra exhibit an intense and broad peak at 10−30 meV as the dominating signal. No significant change to the vibrational peaks arising from the internal modes of the bare MOF was observed, indicating that there is no strong distortion of the local H modes from the porous material upon CH 4 adsorption. This result suggests that adsorbed CH 4 molecules in MFM-300(In) have a wide amplitude, weakly hindered rotational motion, even at a temperature that is well below its melting point (90.7 K). This is consistent with the structure of solid CH 4 -I that is shown to have well-defined molecular positions, but spherically disordered protons. 33 Geometry optimization (GO) calculations were performed with both fixed and variable cell parameters, with an observed increase of the unit cell dimensions of 2−3%. However, we

Journal of the American Chemical Society
Article found this did not affect the calculated binding energies, rotational potentials, or vibrational spectra. Binding energies were calculated for the two most stable sites (CD 4 I and CD 4 II ), which are populated with adsorbed CH 4 molecules at low surface coverage. Density functional theory (DFT) calculations determine the binding energies to be 20.5 and 19.7 kJ mol −1 for CD 4 I and CD 4 II , respectively, in excellent agreement with that determined experimentally from the adsorption isotherms (16− 20 kJ mol −1 ). The similarity of the calculated binding energies at two different sites also explains the absence of any marked steps in the adsorption profiles (even in logarithmic view as shown in Figure S12) that would be indicative of the presence of adsorption sites of significantly different stabilities. 34 Rotating the CH 4 molecule on the most stable site (CD 4 I ) about a C−H bond aligned with the O−H group ( Figure 5) and performing a series of single point energy (SPE) calculations enabled the rotational potential of adsorbed CH 4 molecules to be determined. In this case, the rotational barrier is 5 meV (0.48 kJ mol −1 ), and therefore the rotation of adsorbed CH 4 molecules is almost free, consistent with the observed strong recoil motion at low energy transfer in the INS spectra.
Lattice dynamics (LD) calculations of the bare MFM-300(In) enable the hydrogen density of states to be determined, which can be compared to the experimental spectrum. Above 18 THz or 74 meV, there are pronounced vibrational peaks, which show a good match between LD calculations of MFM-300(In) and the measured spectrum ( Figure 5). The vibrational spectrum is a fingerprint of the solid-state structure, and reproducing the measured spectrum from the experimental structure using a high level of theory (DFT) validates the structural model. Molecular dynamics (MD) simulations were performed at temperatures ranging from 50 to 250 K. The simulation at 250 K gave the most appropriate sampling of the potential energy surface (PES). The hydrogen vibrational density of states from this run was in good agreement with the LD calculation and INS experiment ( Figure 5). MD simulations of CH 4 -loaded MFM-300(In) allowed the vibrational density of states of the CH 4 molecules to be determined, and this calculated spectrum for CH 4 was compared to the experimental difference spectrum ( Figure S43). In the low frequency part of the spectrum, where signals are related to whole molecule vibrations and low frequency liberational/rotational modes, the spectra are in good agreement. At higher frequency, the calculated spectrum shows the internal modes (bending and stretching) of CH 4 , but these are not observed in the experimental INS spectrum. The experimentally observed modes are attenuated by a Debye− Waller factor (exp(−Q 2 u 2 )), which is stronger for CH 4 than for the MOF host, revealing a higher mean square displacement (u 2 ) for the CH 4 because it is relatively weakly bound and can undergo almost free rotations as suggested from SPE calculations.
Thus, this neutron spectroscopic study of MFM-300(In) has investigated the rotational modes and packing of adsorbed H 2 and CH 4 within this material. INS spectra of H 2 loaded MFM-300(In) confirm the appearance of two types of adsorbed H 2 : one with reduced rotational energy and one with "almost-free" rotations; the latter is a reminiscent of solid H 2 . This study further confirms that the bridging hydroxyl is the strongest binding site for methane within MFM-300(In), forming H 3 C− H guest ···H−O host binding interactions, with the adsorbed CH 4 molecules having wide amplitude, weakly hindered rotational motion in the confined cavity of the MOF, even at 11 K. To improve the CH 4 storage capacity, further efforts are required to "immobilize" adsorbed CH 4 molecules in the pore by increasing the binding energies and reducing their rotational motion via introduction of more specific host−guest interactions.

■ CONCLUSIONS
Several key insights into the binding of H 2 and CH 4 within the hydroxyl-decorated material MFM-300(In) have been revealed from the direct visualization and quantification of the host− guest interactions of these gases within the porous host at crystallographic resolution. This has implications for the design and discovery of future materials capable of storing H 2 and CH 4 at high capacity. The binding of H 2 within this material is mediated by a combination of a number of weak intermolecular interactions at low loadings and a combination of adsorbate− adsorbent and adsorbent−adsorbent interactions at high loadings. The very high density of adsorbed CH 4 molecules observed in MFM-300(In) was found to be dominated by a specific H 4 C guest ···H−O host interaction, which is supplemented further by CH 4 guest ···CH 4 guest intermolecular dispersion interactions. The phenyl rings on the linker play a further role in providing space confinement for the adsorbed CH 4 molecules, thereby inducing a change from the H 3 C−H guest ···O host −H binding mode observed in clathrates. These multiple relatively weak binding interactions are aligned in the pore with an optimal geometry, offering a highly cooperative binding environment for the adsorbed H 2 and CH 4 molecules. As a result, the adsorption and binding modes of H 2 and CH 4 within this material have been observed and rationalized by both experimental and theoretical investigations. We hope that the strategy developed here will help the development of improved materials with optimized pore environment for natural gas storage and separation.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.6b01323.