Hierarchical Structure and Molecular Dynamics of Metal-Organic Framework as Characterized by Solid State NMR

Metal-organic framework (MOF) stands out as a promisingmaterial with great potential in application areas, such as gas separation and catalysis, due to its extraordinary properties. In order to fully characterize the structure ofMOFs, especially thosewithout single crystal, Solid State NMR (SSNMR) is an indispensable tool. As a complimentary analytical technique to X-ray diffraction, SSNMR could provide detailed atomic level structure information. Meanwhile, SSNMR can characterize molecular dynamics over a wide dynamics range. In this review, selected applications of SSNMR on various MOFs are summarized and discussed.


Introduction
Metal-organic framework, or MOF, consisting of metal ion center and organic ligand attracts numerous attention since 1990s [1].As an inorganic and organic hybrid, MOF owns extraordinary properties, such as ultrahigh internal surface area, tunable internal core size and high thermal stability.The modification of the organic ligand could further provide us with an excellent platform to adjust surface properties for proper applications.Due to these excellent characteristic features, MOFs own great potential in various application areas such as gas storage (i.e., CO 2 , CH 4 , and H 2 ) [2][3][4], separation [5], catalysis [6], and biomedicine [7].
The macroscopic performance of MOFs is highly related to microscopic structure and dynamics.The understanding of this relationship is crucial for us to optimize current MOFs or design new MOFs.For MOF structure, although the crystal structure of many MOFs can be determined through single crystal X-ray diffraction, for numerous MOF systems, such as the porous aluminum terephthalate (MIL-53) [8], it is difficult to obtain single crystal and the structural information always need to be refined based on powder Xray diffraction results.Therefore, other techniques that can access to molecular level atomic position are necessary to refine the existing crystal structure.For MOF dynamics, it is required to obtain molecular dynamics information of MOFs at elevated temperature or under different pressure for industrial application.For instance, in the case of the storage of CO 2 , it is necessary to obtain direct information about the interaction between CO 2 and MOFs and CO 2 adsorption dynamics [9].
Solid State NMR (SSNMR) technique stands out as an analytical technique to characterize both local structure and dynamics and the interplay between them [10][11][12].SSNMR is able to probe internuclear distance based on various interactions such as dipolar coupling, quadrupolar interaction, and chemical shift anisotropy (CSA).As a result, SSNMR could provide detailed local packing structure and short range ordering information, as a complimentary technique to Xray diffraction [13].This work provides a brief review of the application of SSNMR in characterizing both structure and dynamics of MOFs with selected examples.

Identification of Complex State of Central Metal Ion.
The local environment of central metal ion is the crucial information to determine the MOFs' structure.Also, processes, such as absorption of gas and hydration/dehydration, could change the local structure of central metal ion.This leads to the change of metal ion NMR spectroscopy.Therefore, SSNMR of various metal ions will be first presented.Table 1 lists selected NMR active metal ions with basic NMR properties including spin number I, natural abundance, receptivity, Larmor frequency v 0 (at magnetic field strength B 0 = 11.7 T), and quadrupole moment Q.And detailed description of these properties of each nucleus and selected examples of application are discussed as follows. 27Al SSNMR. 27Al SSNMR is one of the most studied metal ions due to its high receptivity (relative to 1 H) and moderate quadrupolar interaction.Similar to other metal ions with spin  > 1/2, 27 Al (5/2) SSNMR spectrum is characterized by quadrupolar coupling constant (  ) and asymmetry parameter  representing the electric field gradient (EFG) of metal ion.Latter reflects the local environment close to the metal ion and can be used to determine the crystal structure or observe the structural change. 27Al SSNMR has been widely used to characterize inorganic materials such as cements [14][15][16][17].Following is selected literature related to Al based MOF systems.
The aluminum 1,4-benzenedicarboxylate (BDC) based MIL-53 is one of the attractive MOFs which has great potential in gas separation and hydrogen storage due to its very large breathe effect [18].As shown in Figure 1, there are three different forms of MIL-53 (Al) under different treatments: the as-synthesized MIL-53 (Al) (MIL-53as (Al)) contains two BDC molecules in each channel; when MIL-53as (Al) is annealed at high temperature (∼330 ∘ C) for three days, the MIL-53 ht (Al) will be obtained without any free BDC molecules in the channel; after cooling to ambient temperature, the MIL-53 lt (Al) is formed with water molecule absorbed inside [8].Loiseau et al. investigated the MIL-53 (Al) structure changes through 27 Al SSNMR as shown in Figure 2 [8]. Figure 2(a) shows 27 Al SSNMR spectra of MIL-53 (Al) in different phases.The MIL-53 as (Al) displays a broad shoulder originating from the amorphous Al(OH) 3 , and, after calcination, 27 Al SSNMR spectrum becomes shape suggesting more homogeneous systems.Due to large open space created in MIL-53 ht (Al), small molecules such as water are able to be absorbed.Because of well distinct NMR spectra of dehydrated and hydrated MIL-53 (Al), it is able to track the structural transition of MIL-53 (Al) during hydration process.After absorption of guest water molecule, a significant broad 27 Al SSNMR spectrum was obtained representing stronger quadrupolar coupling strength.Figure 2(b) shows the in situ observation of the hydration process of MIL-53 (Al), and the hydration ratio is increased from bottom to top as 0%, 30%, 50%, and finally 100%.A continuous increase of   could be obtained suggesting the break of local symmetry.
Later on, Jiang et al. changed the organic linker BDC into 2-aminobenzene-1,4-dicarboxylic acid (ABDC) and found that the quadrupolar coupling strength   decreases ∼ 1 MHz indicating more symmetric local structure and more homogeneous charge distribution [19].They also investigated the dehydration/rehydration process of this MOF.The evolution of 27 Al SSNMR spectra upon hydration process is similar to above results.And the broadening of 27   27 Al SSNMR was used to refined the crystal structure of these three phases, and it was found that MIL-118A and B display single 27 Al signal, while MIL-118C shows two resonance lines.This suggests Al is magnetically equivalent in MIL-118 A/B and has two inequivalent sites in MIL-118C, which is consistent with Xray diffraction results.The overlap of NMR signal of different Al sites induces dramatic difficulties in peak assignment and determination of the composition ratio of different Al.Due to well resolved NMR signal, the multiquantum (MQ) NMR is applied to obtain quadrupolar parameters and isotropic chemical shift of different sites [21][22][23].Figure 3 presents the contour plot of 3Q NMR spectrum of MIL-118A.The multiquantum coherences in one dimension are correlated with central transition (CT) coherence in another dimension. 27Al NMR signals of different sites are well resolved, and relative composition ratio of different species can also be obtained. 45Sc SSNMR.Scandium based materials own great potential in the application of catalyst, such as scandium(III) trifluoromethanesulfonate [Sc(OTf) 3 ], which can be used to catalyze the carbon-carbon bond-forming reaction in aqueous media [24,25].Due to its good receptivity and moderate quadrupolar interactions as listed in Table 1, 45 Sc has good NMR properties.Rossini et al. characterized the Sc(OTf) 3 structure through the combination of 45 Sc SSNMR and powder X-ray diffraction [26,27].For Sc(OTf) 3 it is difficult to obtain single crystal causing dramatic difficulties in structural determination.They chose Sc(OAc) 3 as a reference sample due to the well determined crystal structure.Meanwhile, the 45 Sc SSNMR spectra of both Sc(OTf) 3 and Sc(OAc) 3 are quite similar, and the obtained EFG tensor parameters are almost identical.This suggests that the Sc coordination states are almost the same in both samples.On the basis of the 3D structure of Sc(OAc) 3 , the crystal structure of Sc(OTf) 3 could be determined through the powder X-ray diffraction pattern.
Besides catalysts, scandium based MOF can also be used in gas separation due to the porous structure.Miller et al. characterized the structure difference between scandium terephthalate, Sc 2 (BDC) 3 , and its derivatives, which is able to absorb CO 2 , through 45 Sc SSNMR [28]. 45Sc SSNMR spectrum of Sc 2 (BDC) 3 displays a characteristic second-order quadrupolar NMR line shape representing a single site for Sc.However, 45 Sc SSNMR spectra of its derivatives, aminoand nitro-BDC, display featureless resonance line indicating statistical disorder of the orientation of the functionalized derivatives.
69/71 Ga SSNMR.Gallium owns two NMR active nucleuses: 69 Ga and 71 Ga as listed in Table 1.As compared with 71 Ga, 69 Ga has larger   , which displays more broadened line shapes.Therefore, 71 Ga is favored in SSNMR experiment.Compared with 27 Al, 71 Ga owns larger second-order quadrupolar splitting (  = 3  /4(2 − 1)) due to its low spin number ( = 3/2).This leads to broader NMR resonance lineshape.Meanwhile, the natural abundance of 71 Ga is 40%, while that of 27 Al is 100%.Therefore, either NMR sensitivity or resolution of 71 Ga is lower than those of 27 Al.In order to overcome these deficiencies, several software (new pulse sequence) and hardware (fast magic angle spinning, MAS) techniques are utilized.Summary of these techniques can be found in relevant reviews [29].
Hajjar et al. investigated 71 Ga coordination environment in MIL-120 and MIL-124 through CT (central transition) MAS [30] NMR in conventional NMR probe [31].In combination of the NMR simulation SIMPSON [32] and 2D slow-CTMAS results, EFG parameters of different crystallographic Ga sites are determined; there are two distinct Ga sites in MIL-120 and one in MIL-124 with remaining site undetectable due to fast molecular motion.This paper shows that classical NMR probe without ultrahigh magnetic field and ultrahigh spinning rate can also be used to detect 71 Ga NMR signal and extract useful structural information.Ash and Grandinetti systematically investigated 69/71 Ga SSNMR in different coordination state [33].With the aid of ultrafast MAS spinning rate (30 kHz), the whole spectra of 69/71 Ga NMR are able to be obtained.The isotropic chemical shift of 69/71 Ga is found to be highly dependent on the coordination state: four coordinates lead to 50 ppm and six coordinates result in 225 ppm.Volkringer et al. studied gallium trimesate (MIL-96) through 71 Ga SSNMR in high magnetic field [34]. 71Ga SSNMR spectrum in the magnetic field strength B 0 = 14.1 T shows a featureless single resonance line.However, under the higher B 0 = 17.6 T, two distinct 71 Ga signals can be observed.This enable us to extract the isotropic chemical shift and EFG parameters to identify different Ga sites in MOF system. 25Mg/ 47/49 Ti/ 91 Zr/ 67 Zn SSNMR.Despite above nucleuses, other frequently used metal ions in MOFs such as 25 Mg, 47/49 Ti, 91 Zr, and 67 Zn in MOFs experience more severe problems in NMR signal and sensitivity.As shown in Table 1, the natural abundance of these nucleuses is quite low (<12%).This requires more NMR experiment time to get a NMR spectrum with an acceptable signal-to-noise ratio.Moreover, the low gyromagnetic ratio  (with corresponding Larmor frequency <50 MHz at 11.7 T) is beyond classical NMR probe sensitive range and large quadrupolar interactions ( > 150 MB) leads to broad quadrupolar lineshape.These unfavorable factors result in the low receptivity (<0.001).Therefore, both NMR sensitivity and resolution are extremely poor.To overcome these problems, ultrahigh magnetic field, ultrafast MAS spinning rate (≫10 kHz), and sensitivity enhancement techniques are necessary.
Huang's group used 25 Mg SSNMR to investigate the magnesium based MOF systems at high magnetic field (21.1 T) [35,36].The dehydration and rehydration process of CPO-27-Mg was in situ observed through 25 Mg SSNMR [35].The dehydration process leads to broadened 25 Mg SSNMR lineshape indicating that the system becomes more disordered.And the dehydrated MOF presents featureless 25 Mg NMR signal, which comes from the large   resulted from the distorted symmetry.
In literature, 47,49 Ti SSNMR was normally obtained through sensitivity enhancement pulse sequences, such as fast amplitude-modulated pulse trains [37] or high magnetic field [16,38,39].Due to almost the same Larmor frequency, 47 Ti and 49 Ti NMR signals always overlap with each other.Gervais et al. investigated the phase distribution of Titania nanoparticle through 47,49 Ti SSNMR.Due to different isotropic chemical shift and EFG parameters for different Ti, 47,49 Ti SSNMR can be used to get quantitative information of different Ti species with different local symmetry.Rossini et al. studied Titanocene Chlorides through the combination of 47,49 Ti SSNMR and quantum chemical calculation [39].In this case, 47 Ti and 49 Ti NMR spectra were observed separately at 21.1 T. The obtained NMR line shape together with EFG parameters and chemical shift (CS) tensors clarifies the Ti local structure and the symmetry.
91 Zr SSNMR was first reported in 1991 to investigate synthetic oxide materials [40]. 91Zr SSNMR line shape was found to be highly dependent on local symmetry.Zhu et al. investigated 91 Zr SSNMR in two zirconium silicates AM-2 and AV-3 [41].It was found that not only the local symmetry and distortion of the [ZrO 6 ] but also the second and third spheres of atoms could influence NMR line shape.This shows that the quadrupolar interaction and CS tensor could also reflect surrounding environment.Sutrisno et al. studied Zn-contained MOFs (zeolitic imidazolate frameworks ZIF-8, ZIF-14, ZIF-4, and ZIF-7) through 67 Zn SSNMR [42].The 67 Zn NMR line shape is determined not only by the local environment but also by the guest molecules.In combination with molecular dynamics, detailed information of the distribution and dynamics of guest molecules can be obtained.This paper, for the first time, shows the potential of 67 Zn SSNMR in determining the detailed structure of Zinc based MOFs as a powerful complimentary characterization tool to X-ray diffraction.

Identity of Organic
Linker.Despite the central metal ion, another important building block of MOFs is organic linker, or organic ligand.The organic linker is mostly constituted by carbon, proton, and oxygen. 13C and 1 H SSNMR are frequently used to identify the presence or absence of certain functional groups.As shown in Figure 4, 13 C and 1 H NMR spectra of MIL-53 in different phases display characteristic NMR line features [8]. 13C direct polarization (DP) MAS NMR spectrum could provide quantitative information of 13 C of different functional groups as the integrated intensity is proportional to the number of 13 C.As shown in Figure 4(a), MIL-53 as (Al) displays relatively broad NMR resonance line suggesting the heterogeneity of the system.However, after thermal treatment at high temperature, a narrow and sharp 13 C resonance line could be observed suggesting a highly ordered structure with high crystallinity.Further incorporation of guest molecules (i.e., water) broadens and shifts NMR resonance line indicating strong interaction between host (MIL-53) and guest (water) molecules. 13C cross polarization (CP) MAS NMR, most of the time, provides us with qualitative information about different 13 C species due to the cross polarization efficiency highly relying on the interaction between observed 13 C and neighboring 1 H, which can be modulated by various factors, such as internuclear distance and molecular motion.As shown in Figure 4(b), when incorporated with guest molecule (water), the carbonyl carbon NMR signal almost disappears as a result of lower CP efficiency caused by the enhanced molecular motions.
1 H SSNMR usually suffers from poor resolution resulting from the small chemical shift range and strong homonuclear dipolar coupling (∼60 kHz).With great advances in both hardware (i.e., fast MAS > 30 kHz) and software (new pulse sequence), the NMR resolution of proton spectrum has been largely increased.Nowadays, 1 H SSNMR has been widely used to study complicated systems, such as supramolecules [43][44][45] and biological areas [46][47][48][49].As shown in Some MOFs contain paramagnetic metal center such as Cu 3 (BTC) 2 (copper (II) benzene 1,3,5-tricarboxylate) [50].The introduction of paramagnetic ions could largely influence the local magnetic field [51].It will change the 1 H and 13 C chemical shift, broaden the NMR resonance line, and reduce the spin-lattice relaxation time [52].Gul-E-Noor et al. found that the proton signal of water absorbed by Cu 3 (BTC) 2 can shift downfield about 7.0 ppm [50].For 13 C SSNMR spectrum, signal of aromatic part shifts downfield of 98-92 ppm, while that of the carbonyl carbon shifts upfield of ∼300 ppm.The possible origin of such difference is ascribed to closer interaction of copper and carboxylic groups.
Oxygen is another frequently encountered atom in MOFs as organic carboxylate ligand is an important building block for many MOFs.Also, other functional groups such as hydroxyl (-OH-), oxygen anion (O 2− ) interacting with metal ions, and guest molecules (i.e., water) contain oxygen atom.
However, the only NMR active isotope is 17 O, whose natural abundance is 0.038%. 17

Investigation of Dynamics in MOF by SSNMR
Molecular dynamics is another key aspect for materials scientist to understand the correlation between microscopic and macroscopic properties.A thorough understanding of molecular dynamics requires characterization dynamics range of various techniques which can cover up to 14 orders of magnitude (10 −12 -10 2 s).SSNMR is one of the most frequently utilized techniques to characterize the molecule dynamics through relaxation or different anisotropic interactions (i.e., CSA and dipole-dipole interaction).Numerous reviews have been reported elsewhere [10-12, 54, 55].Here only selected literature is reported to show how SSNMR can be used to characterize different functional groups in MOFs.

Phase Transition as Investigated by Proton Spin-Lattice
Relaxation.Organic linker of MOFs always performs ultrafast dynamics (⟨  ⟩ < 10 −10 s) at ambient temperature.Proton spin-lattice relaxation (T 1 ) is able to probe such fast dynamics.Besara et al. investigate the phase transition and glassy behavior of [(CH 3 ) 2 NH 2 ] Zn(HCOO) 3 [56].This MOF takes an order-disorder transition at 156 K.The cationic ) is used as a probe to track the phase transition behavior.As shown in Figure 5, the minima of T 1 detected at 156 K is assigned to the order-disorder transition, and the shoulder observed at 40 K is attributed to the transition of the glassy phase to ferroelectric (FE) phase.Below 40 K, the motion of the methyl group is frozen.The "memory effect" was observed at the range of 65-150 K range as shown by T 1 difference resulted from different pathways.Morris et al. utilized proton spin-lattice relaxation method to probe dynamics of organic linkers in IRMOF-3 (Zn 4 O(BDC-NH 2 ) 3 ) [57].Besides 1 H T 1 , the spin-lattice relaxation in the rotating frame (T 1 ) under a fixed spinlocking field was also used to investigate dynamics of different groups.Different from T 1 , which is sensitive to ultrafast dynamics (∼MHz), T 1 could detect dynamics ∼10 kHz.Due to well resolved proton signal of amino and phenyl groups, molecular dynamics of each functional group can be determined.Their finding reveals that the amino group performs rotation with low activated energy and the central phenyl group (BDC) performs  flip motion with an activation energy of 21 kJ/mol.

Deuterium
( 2 H) NMR Spectroscopy.Deuterium ( 2 H) SSNMR is a versatile NMR technique to characterize the molecular dynamics with high resolution and sensitivity.Different from above metal ions, deuterium NMR is dominated by the first-order quadrupolar interaction.The quadrupolar echo pulse is used to obtain an undistorted anisotropic spectrum [58].Due to its simple pulse sequence and data acquisition, deuterium NMR owns wide application, even in industrial areas [59].Various 2 H NMR techniques, including 1D lineshape analysis and 2D exchange spectroscopy, have been applied to characterize segmental dynamics of glassy polymers (10 −6 -10 2 s) [59,60].Therefore, deuterium SSNMR could be used to investigate the dynamics of different functional groups in MOFs.
Bureekaew et al. investigated the aluminum MOFs with high conductivity through imidazole as a proton-carrier molecule [61].Two similar Al MOFs, [Al(2-OH)(1,4-ndc)]  (1) and [Al(2-OH)(1,4-bdc)]  (2), show dramatic conductivity difference; MOF 1 has higher proton conductivity than MOF 2. They used 2 H SSNMR to investigate the dynamics of imidazole in different porous systems.As shown in Figure 6, 2 H SSNMR spectrum of imidazole-d4 in MOF 2 at 20 ∘ C shows Pake-type doublet pattern suggesting anisotropic motion of adsorbed imidazole-d4, while that in MOF 1 displays an extra Lorentzian-type peak located at the middle positon.This indicates isotropic motion of imidazole-d4.The comparison between MOFs 1 and 2 shows that the adsorbed imidazole owns different dynamics characteristic especially at higher temperature; imidazole performs fast and isotropic motion in MOF 1 while it remains unchanged in MOF 2. Such dynamics difference is associated with the proton conductivity difference, and the proton conducting pathway is also determined to be proton-hopping mechanism.

Chemical Shift Anisotropy.
The NMR signal in solid state is orientation dependent [62].For certain nucleus, such as 13 C, this interaction is named chemical shift anisotropy (CSA) and can be used to probe molecular dynamics (10 −3 -10 2 s).For MOFs, as mentioned in the introduction, one of the most promising applications is the capture and storage of guest molecules, such as CO 2 .A molecular level understanding of the binding and dynamics of these guest molecules is necessary to refine current MOFs.
Kong et al. for the first time uses SSNMR to characterize the binding and molecular dynamics of CO 2 in Mg-MOF-74 (Mg2(dobdc) (H4dobdc = 2,5-dihydroxyterephthalic acid) [9].CO 2 is 13 C enriched in order to obtain good signal-tonoise ratio.The temperature dependence of CSA patterns is acquired together with CSA simulation in order to obtain quantitative information about the molecular orientation of CO 2 .CO 2 is found to perform uniaxial rotation close to Despite porous MOF systems, the host-guest interaction also exists in some nonporous crystal at high temperature.The CO 2 sorption process in these crystals is difficult to be observed due to its rapid motion.Bin et al. use synchrotron powder X-ray diffraction and SSNMR to investigate the restrained motion of CO 2 in the small cages within the crystal [64].The interaction between the host and guest molecules is characterized by 1 H-13 C HETCOR.The CO 2 molecules are found to be located between the outer phenyl rings of host molecule H 3 BTB and the DMF molecules.Similar to above mentioned MOFs, the incorporation and molecular dynamics of CO2 are investigated through 13 C CSA.

Conclusion
In this review, we briefly summarize different SSNMR work on MOFs.SSNMR is a powerful analytical technique to characterize metal ion center, organic linker, and host-guest interaction as a complimentary technique to X-ray diffraction.Meanwhile, SSNMR can characterize molecular dynamics over a broad range with site specific advantage at a molecular level.Such information can in turn help us understand the origin of some macroscopic performances of MOFs.This could rationalize the molecular design of MOFs.Summary of different MOFs characterized by different SSNMR techniques is shown in Table 2. Admittedly, limited by article length, there is numerous pieces of SSNMR literature of MOFs which is not included in current review.With the increment of applications of MOFs and the great achievement of SSNMR techniques, it will be more convenient for us to obtain molecular information of different functional groups of MOFs, and SSNMR would become an indispensable analytical tool to characterize both structure and dynamics of MOFs.
O enrichment is necessary to do 17 O SSNMR leading to high cost.As a result, little literature about 17 O SSNMR of MOFs has been reported.He et al. reported an innovative method to prepare 17 O enriched MOFs and characterize 17 O of different sites through SSNMR [53].

17
O enriched MOFs are prepared through incorporating 17 O atom from H 2 17 O.The EFG parameters and chemical shift tensor information can be obtained through 17 O SSNMR.Thus providing detailed structural information and identification of different oxygen contained species.

Figure 5 :
Figure 5: The proton T 1 as a function of the inverse temperature T −1 .A, B, and C refer to glassy, ferroelectric (FE), and paraelectric (PE) states.And two characteristic temperatures are 40 K and 156 K. Reprinted with permission from Ref. [56].Copyright 2011 PNAS.

Table 1 :
Selected metal ions with different NMR properties b .

Table 2 :
Application of SSNMR in various MOFs with different techniques.