Chapter 1: An Introduction to Solid-state NMR and Potential Applications for MOFs and COFs

The past two decades have given rise to a new era in porous materials, with innovations continually emerging. Metal–organic frameworks (MOFs) and covalent organic frameworks (COFs) are two of the most prominent families of porous materials, as they typically feature highly-ordered long-range structures and have exhibited promising performance in many applications,^1,2  including gas storage and separation,³  energy conversion and storage,⁴  chemical sensing,⁵  drug delivery,⁶  luminescence,⁷  proton conduction,⁸  and other fields (Figure 1.1). MOFs are crystalline organic and inorganic hybrid materials that contain metal ions or clusters connected by bound organic linkers. While COFs are also crystalline, they are composed wholly of organic materials and covalent bonds. Many MOFs and COFs exhibit exceptional porosity, with pore diameters that can be tuned from the microporous to mesoporous ranges; for example, IRMOF-74-XI has pores of 9.8 nm that can encapsulate proteins,⁹  and the 2D COF PyCOFamide contains 6.7 nm pores and also exhibits a high Brunauer–Emmett–Teller (BET) surface area of 1682 m² g⁻¹.¹⁰ 

MOFs and COFs are both exceptionally diverse families that feature a large and customizable set of functional groups and structural families or topologies. Both MOFs and COFs operate on the principle of reticular chemistry,^1,2  where extended crystalline structures are rationally constructed by connecting specifically selected nodes and linkers via strong bonds. The commonalities between MOFs and COFs not only result in outstanding performance for specific applications, but also mean that these materials can address the same types of scientific problems, owing to their wide-ranging structural motifs, highly crystalline nature, tailored pores, and controllable host–guest interactions, among others. The numerous similarities between MOFs and COFs naturally intertwine their development and applications. For example, the recently conceived field of metal–covalent organic frameworks (MCOFs) has seen rapid advances;¹¹  MCOFs exploit the principles underpinning MOFs and COFs to combine the unique advantages of each material, leading to a controllable blend of desirable properties such as high crystallinity, porosity, stability and functionality.

Currently, over 90 000 MOFs have been reported, making this the largest branch within the field of porous materials;¹²  the vast number of known and possible MOF configurations offers many potential applications. While MOFs and COFs share many common features, the inclusion of inorganic components in MOFs (i.e., the metal-based nodes) can confer unique properties that are not generally inherent to COFs. In situations when the metal centers in as-made MOFs are coordinated to solvent molecules, it is possible to remove some or all of the metal-coordinated solvent via activation at high temperature and/or under vacuum in order to generate open metal sites (OMSs).¹³  These coordinatively unsaturated metal centers can then significantly enhance MOF performance in gas adsorption or catalytic applications, owing to strong host–guest binding interactions between the OMSs and guest molecules. MOF-74(Mg) is a well-known example of a MOF that contains OMSs, featuring a five-coordinate Mg OMS that is generated by the removal of one coordinated solvent molecule. The MOF-74(Mg) system has exhibited excellent performance in adsorbing many simple gases such as CO₂, H₂, CO, and CH₄; for instance, the heat of adsorption (Q_st) values of CO₂ and H₂ in this material are −47.0 kJ mol⁻¹ and −10.3 kJ mol⁻¹, respectively, which are among the highest values reported for MOFs.¹³  OMSs in MOFs may also act as vacant Lewis acid sites for applications in catalysis and photocatalysis. A good example of this concept is the mesoporous MOF MIL-101(Cr), which contains Cr³⁺ OMSs that serve as strong Lewis acid sites and are linked to the exceptionally high 98.5% yield of this material in cyanosilylation reactions.¹⁴ 

A distinct advantage of MOFs is their intrinsic crystallinity and long-range order, making them promising targets for single-crystal X-ray diffraction (SCXRD) characterization. SCXRD-based techniques can yield the unambiguous atomic-level MOF structure and provide a foundation for establishing structure–property relationships.¹⁵  Unfortunately, growing single crystals of MOFs is often a trial-and-error process that sometimes cannot produce high-quality single crystals of sufficient size for SCXRD analysis. In such situations, the long-range order inherent to many MOFs still allows for structural investigation using powder XRD (PXRD) methods, particularly in cases involving the very common family of aluminum-based MOFs,¹⁶  although the PXRD route can be significantly more challenging than SCXRD. The ordered structures of MOFs can also be exploited through their use as crystalline sponges to solve crystal structures of smaller guest molecules that cannot be crystallized on their own; guests organize in a regular manner within the MOF pores, and the structure of the guests can then be solved either together or separately from that of the host MOF via XRD-based techniques.¹⁷ 

The COF family of materials was first documented in 2005 with an initial report by Yaghi and colleagues regarding a porous crystalline 2D COF termed COF-1.¹⁸  Following this groundbreaking account, the 3D COFs known as COF-102, COF-103, COF-105, and COF-108 were synthesized in 2007.¹⁹  Hundreds of different 1D, 2D, and 3D COFs have now been documented, and over 47 000 potential structures have been predicted to be stable.²⁰  In general, COFs are composed of lighter atoms such as C, H, O, Si, and B. COFs were initially synthesized using reversible polycondensation reactions involving boronate, imine, azine and squaraine linkages;²¹  however, many of these COFs were not sufficiently robust when exposed to harsh conditions. COFs based on irreversible polycondensation reactions, using groups such as phenazine and C═C linkages, have exhibited improved structural stability and have become increasingly popular in recent times.²²  The stronger covalent bonds associated with this approach can provide COFs with higher stability in aqueous, acidic, basic, oxidative, and reductive conditions, which are typically challenging environments for MOFs and COFs. For example, Donglin and co-workers prepared 2D sp² carbon-conjugated frameworks, sp²c-COF, sp²c-COF-2, and sp²c-COF-3, which exhibited promising luminescence properties and retained crystallinity after exposure to aggressive chemical environments such as 14 M NaOH and 12 M HCl.²³  Another illustrative case involves polyarylether-based covalent organic frameworks such as microporous JUC-505 and mesoporous JUC-506, which retain structural stability after exposure to boiling water, strong acids and bases (i.e., HCl, H₂SO₄, HF, NaOH, and MeONa), oxidizing chromic acid solution, and the reducing compound LiAlH₄.²⁴  An additional advantage of COFs is their low overall density due to the lack of metal ions, which makes them more practical adsorbents for gas storage.²⁵  The absence of metal ions in COFs is also useful for non-toxic applications in drug or biochemical delivery;²⁶  the JUC-505-COOH COF can adsorb antibiotics from water across pH values ranging from 1 to 13.²⁴  Characterization of COFs is not always straightforward, and often requires the use of several complementary methods. There are several documented methods for obtaining single crystals of 3D COFs suitable for SCXRD-based analysis that yield full structural solutions;²⁷  however, generating single crystals of 2D COFs suitable for SCXRD remains elusive, and even obtaining very small 2D COF crystals suitable for electron diffraction analysis is extremely challenging.²⁸  It is clear that a multi-pronged approach is necessary for in-depth COF studies.

Structural characterization is an essential step for understanding the origins of properties and applications in MOFs and COFs, and techniques such as XRD,^29,30  infrared spectroscopy,³¹  Raman spectroscopy,³²  electron microscopy (EM),^33,34  and density functional theory (DFT) calculations^35,36  have been proven to be very useful. Solid state NMR (SSNMR) is a powerful structural characterization tool that can provide element-specific information in both crystalline and amorphous MOFs and COFs. Information regarding the local chemical environment, bond connectivity, dynamics, local disorder, and host–guest interactions is often readily available from NMR experiments. The sensitivity and convenience of SSNMR, along with the depth of available information it provides and the non-destructive nature of this method, have made it an ideal tool in the portfolio of techniques for the study of MOFs and COFs.^37–41  In this chapter, a generalized and accessible description of NMR interactions and techniques is provided for non-experts, focusing on only essential details. We encourage readers interested in further details and equations regarding NMR to consult the cited references in this chapter and those that follow.

The CS interaction encodes information regarding bound chemical groups, bond lengths, local dynamics, and many other details. While many readers are familiar with solution NMR, there are many instances in which SSNMR CS measurements are more advantageous or the only choice available, such as when the sample is insoluble or dissociates in solution, when a particular phase must be examined, or when there are changes in the bonding environment between the solution and solid states. MOFs and COFs are often insoluble or rapidly deteriorate in solution, making SSNMR one of the few characterization methods that can intimately probe the local environment via the CS and the other interactions described below.

Many NMR interactions are directionally-dependent or anisotropic. Every unique orientation of the local nuclear environment with respect to the NMR magnetic field gives rise to a unique resonance frequency. This results in very broad SSNMR resonances with a low signal-to-noise ratio, called “powder patterns,” which can be challenging to acquire and interpret. In contrast, solution-state NMR involves rapidly tumbling sample molecules, allowing nuclei to sample all possible directions with respect to the NMR magnetic field within the time interval of an NMR experiment; this removes the anisotropic components of NMR interactions, resulting in motionally-averaged narrow resonances of high signal-to-noise ratios at well-defined frequencies.

While acquiring SSNMR spectra is not straightforward, there are various methods involving mechanical routes and pulse sequences to acquire high-resolution spectra within reasonable experimental times. A key method for removing the anisotropy of NMR interactions in the solid state is magic angle spinning (MAS).^42,43  The anisotropic component of many NMR interactions involves the (3 cos² θ − 1) term, where θ is the angle of interaction with respect to the NMR magnetic field. Spinning the sample at an angle of 54.74° (Figure 1.2a) makes the (3 cos² θ − 1) term equal to zero. MAS can thus completely remove the anisotropic portion of some NMR interactions and can partially remove the anisotropy of others; this results in a spectrum consisting of a relatively narrow central signal with a high signal-to-noise ratio that is governed by isotropic NMR interactions, flanked by one or a series of spinning sideband artefacts that are separated by the spinning frequency (Figure 1.2b–d). The spinning frequency versus the strength of the underlying interactions determines the number of spinning sidebands, with slower MAS frequencies giving rise to more sidebands. The effectiveness of MAS is limited when very strong NMR interactions are present. For instance, ¹H NMR spectroscopy is commonly employed in chemical systems due to the high gyromagnetic ratio and natural abundance of ¹H. Unfortunately, ¹H engages in strong homonuclear magnetic dipolar interactions with other ¹H nuclei, which poses a considerable challenge to obtaining high-resolution ¹H spectra at conventional MAS frequencies (i.e., <20–30 kHz). The advent of ultra-fast MAS hardware and advanced homonuclear decoupling pulse sequences (vide infra) in recent years has allowed researchers to obtain higher resolution SSNMR spectra.⁴⁴ 

Eqn (1.2) shows how δ_iso is simply the average value of the three principal CS tensor components. In practice, CSA does not broaden solution NMR resonances, as rapid tumbling in the liquid phase removes the anisotropic CS contributions, leaving the directionally-independent δ_iso value as the only discernible CS parameter. Similarly, for solid samples, MAS techniques can partially or completely remove the spectral effects associated with CSA. To obtain CSA information under MAS conditions, two methods are commonly used. The first method involves acquiring at least two MAS spectra using different spinning frequencies that are both significantly less than the magnitude of the CSA in order to identify the δ_iso value, and then extracting CS tensor information from the number and intensity of the MAS-generated spinning sidebands from one spectrum through techniques like Herzfeld–Berger analysis (HBA) simulations.⁴⁶  Static (i.e., non-spinning) SSNMR spectra can also be acquired to directly measure CSA; however simulating these spectra can be challenging when multiple signals are present, and acquiring them can also cost significant experimental time due to their wide resonance breadths. An alternate approach is to apply specialized pulse sequences that use radiofrequency (rf) energy to refocus the CSA;⁴⁷  however, this method can also be subject to resonance overlap from several unique signals. Various techniques have been developed,⁴⁸  including techniques such as cross-polarization phase-adjusted sideband separation (CPPASS),⁴⁹  recoupling of chemical shift anisotropy (ROCSA),⁵⁰  and separation of undistorted powder patterns by effortless recoupling (SUPPER),⁵¹  among many others.^52,53  Because CSA depends on the molecular orientation, it is also sensitive to any local motion occurring on the NMR timescale, and can thus yield additional information on dynamics of hosts or guests in MOFs and COFs.^54–56 

Nuclei of spin > 1/2 have an asymmetric distribution of positive charge within the nucleus, and thus have an intrinsic electric quadrupole moment (eQ). The anisotropic interaction between the quadrupole moment and the electric field gradient (EFG) at the nucleus is known as the quadrupolar interaction (QI). The EFG arises from the electric charge distribution surrounding the nucleus, which is in turn dependent on chemical bonds and nearby atoms; the QI thus encodes valuable information regarding aspects such as local structure, disorder, dynamics, defects, and other details relevant to MOF and COF researchers. The anisotropic nature of the QI means that each specific crystallite orientation gives rise to a unique resonant frequency (Figure 1.4). In a powdered MOF or COF sample, the NMR spectrum of a quadrupolar nucleus consists of a broad envelope because all possible crystallite orientations are present with respect to the magnetic field.

For spin 1/2 nuclei, the only possible spin transition occurs between the +1/2 ↔ −1/2 states. While NMR can probe transitions between other adjacent spin states, NMR spectroscopy of quadrupolar nuclei typically focuses solely on the +1/2 ↔ −1/2 “central transition.” The QI can be treated as a first- and second-order perturbation on the fundamental Zeeman NMR interaction. The first-order QI strongly perturbs the nuclear spin energy levels, significantly modifying the energy differences between all spin transitions except the +1/2 ↔ −1/2 central transition (CT, see the intense resonance in Figure 1.4a bottom); this spreads all transitions other than the CT over a wide frequency range, rendering them extremely challenging to acquire via SSNMR experiments (Figure 1.4a bottom, flanking features of low intensity). The CT is influenced by the less impactful second-order QI, resulting in SSNMR powder patterns that are subject to less severe broadening and can typically still be acquired within reasonable experimental times. For the remainder of this chapter and in future chapters, the CT will be the topic of discussion and will constitute the SSNMR spectra depicted in figures unless noted otherwise.

A η_Q value of zero represents an axially symmetric EFG tensor (i.e., local rotational symmetry ≥ C₃), while the other extreme value of one indicates an axially asymmetric EFG tensor with C₁ rotational symmetry. In a practical sense, η_Q values closer to one result in the characteristic quadrupolar “horns” that are located closer to the center of the SSNMR powder pattern, while η_Q values closer to zero move the “horns” towards the edges of the powder pattern perimeter (Figure 1.4c).⁵⁸  While the anisotropic portions of the CS and dipolar NMR interactions can be removed using MAS, the second-order QI can only be partially mitigated via standard MAS NMR experiments, which leaves residual spectral broadening that can complicate spectral assignment when multiple signals are present. Various NMR methods have been developed to eliminate the second-order quadrupolar interaction using strategies involving hardware or pulse sequences, such as multiple-quantum MAS (MQMAS),^59,60  satellite transition magic angle spinning (STMAS),⁶¹  double rotation (DOR),⁶²  and others.^63–66  The QI typically also reduces the longitudinal (T₁) and transverse (T₂) relaxation times of target nuclei along with nearby NMR-active nuclei, which allows for shorter pulse delays but can limit the effectiveness of some pulse sequences. Several additional details regarding the acquisition of quadrupolar NMR spectra and associated pulse sequences are provided in Chapter 2.

In principle, there are two fundamental spin–spin interactions that can occur between a pair of nuclear spins in a solid-state system. The direct magnetic dipolar interaction is an anisotropic through-space interaction of considerable strength, where the magnitude depends on the distance between the two NMR-active nuclei along with their respective gyromagnetic ratios. The most obvious effect of the direct dipolar interaction is the broadening of SSNMR linewidths, making spectra more difficult to acquire. The indirect dipolar interaction (i.e., J-coupling) is a through-bond coupling that is typically much weaker; in this chapter, the J-coupling contribution to SSNMR spectra of MOFs and COFs is often negligible, and J-coupling is not discussed in detail any further.

It is possible to decouple or remove the effects of heteronuclear and homonuclear dipolar coupling to narrow linewidths and improve spectral resolution, while corresponding strategies for recoupling this interaction to obtain spatial information have also been developed. Fast MAS can partially or fully remove the effects of dipolar coupling, and dipolar decoupling is also achievable via pulse sequences, especially in heteronuclear situations. High-resolution ¹H SSNMR spectra have traditionally been very difficult to obtain due to ¹H–¹H homonuclear dipolar coupling, along with the prevalence of ¹H in many chemical systems, but this is now possible using modern hardware and very fast MAS conditions.⁴⁴  Further discussions of homonuclear and heteronuclear dipolar decoupling and recoupling methods are explored in the next section.

It is often prohibitively time-consuming to directly obtain SSNMR spectra of insensitive low-gyromagnetic ratio (γ) nuclei with poor natural abundance, such as ¹³C and ¹⁵N. Using a combination of MAS and cross polarization (CP) techniques, termed CPMAS, it is possible to obtain high-resolution SSNMR spectra of insensitive nuclei within reasonable experimental times.^67–69  In general, CP uses rf pulses to transfer spin polarization from an abundant nucleus (I), such as ¹H, to a dilute insensitive nucleus (S) via the dipolar coupling interaction (Figure 1.5); the enhanced polarization then allows for more rapid spectral acquisition of the NMR signal originating from the dilute nucleus.⁷⁰  The maximum theoretical CP signal enhancement is γ_I/γ_S. Another advantage of CP is that the NMR pulse delay depends only on the abundant nucleus, which typically relaxes much faster than the dilute nucleus.

CP NMR experiments are performed using rf pulses to transfer spin polarization and perform heteronuclear dipolar decoupling (Figure 1.5a). The sequence begins with a 90° pulse on the abundant spins. During the following mixing time or contact time, rf fields are applied to both the I and S spins, which permits magnetization exchange and the corresponding enhancement of S spin polarization. The last step involves detection of the S signal while the I spins are decoupled using rf pulses. The S signal enhancement from CP also depends on the magnitude of I–S dipolar coupling. Nuclear relaxation has a strong influence on the build-up of polarization transfer from I to S. In a very general sense, directly bound or immediately proximate I–S spin pairs (i.e., hydrogen directly bound to carbon) typically require only a short mixing time (Figure 1.5b), especially when one or both of I and S are mobile. In contrast, more distant I–S spin pairs (i.e., hydrogen and a nearby unprotonated carbon) and local molecular rigidity require longer CP mixing times (Figure 1.5c). CP experiments are thus non-quantitative, owing to the dependence of signal enhancement on the local environment, and integrated signal areas do not directly reflect the relative abundances of the associated nuclei. Many versions of the CP pulse sequence have been reported, including variants such as non-quaternary suppression (NQS), cross polarization with phase inversion (CPPI), variable-amplitude cross polarization (VACP)⁷¹  and cross polarization with total spinning sideband suppression (CPTOSS), which are designed for specific experimental scenarios.⁷² 

Heteronuclear dipolar coupling often results in significant broadening of SSNMR spectra, especially when ¹H is involved. A hydrogen–carbon bond length of 1.0 Å results in a ¹H–¹³C dipolar coupling of ca. 30 kHz, while a hydrogen–carbon bond length of 1.1 Å leads to a ca. 23 kHz dipolar coupling. There are two common approaches that can be used alone or in combination in order to mitigate dipolar coupling effects on NMR spectra. The first option is MAS, where the particular spinning frequency employed can partially or fully eliminate spectral effects of dipolar coupling. The second is heteronuclear decoupling using rf pulses; typical methods include continuous wave (CW) and two pulse phase modulation (TPPM),^73,74  although many other alternate rf-based strategies exist.

The broadening effects of ¹H–¹H homonuclear dipolar interactions in the ¹H SSNMR spectra of MOFs and COFs are often very strong and particularly challenging to address. From a mechanical perspective, MAS can be used to reduce spectral effects of ¹H–¹H coupling, but without access to extremely high MAS speeds, it is not possible to fully remove the homonuclear dipolar coupling in most MOF and COF systems using hardware alone. There are also rf-based decoupling techniques for homonuclear decoupling. CW decoupling of ¹H cannot be used, as the desired ¹H NMR signal will also be suppressed; however, rf pulses can be used to manipulate and reorient spin polarization in order to eliminate or strongly reduce homonuclear dipolar coupling. The mathematical result is that the NMR equation describing the anisotropic homonuclear dipolar interaction becomes equal to zero or nearly zero.

While the previous section discussed methods to remove or significantly reduce the spectral effects of dipolar coupling, the dipolar interaction also encodes valuable information regarding details such as internuclear distances, relative molecular orientation, and molecular-scale mobility, among others. It is possible to reintroduce dipolar coupling for both heteronuclear and homonuclear dipolar coupling using various pulse sequences; the heteronuclear case is discussed first.

Under MAS conditions, sample spinning has a significant influence on the effective heteronuclear dipolar coupling at any given point in the rotor (i.e., sample container) period. By applying rf pulses at specific times in the MAS-based pulse sequence, the heteronuclear dipolar coupling interaction is no longer equal to zero over a rotor period, thus re-introducing it into the measured SSNMR spectrum. The rotational echo double resonance (REDOR) technique is a classic example of this strategy, and has been widely used to determine the heteronuclear dipolar coupling strength between proximate spin-1/2 nuclides, such as ¹³C and ¹⁵N, in various materials.⁷⁹  REDOR is broadly applicable to a variety of situations, such as the measurement of weak heteronuclear dipolar couplings in systems where significant CSA is present,⁸⁰  but it can also be applied to many local environments in MOFs and COFs. A generalized description of the REDOR experiment is provided below, and the reader is directed towards other resources for further details and practical applications.^79,81–85 

The two nuclei targeted in a REDOR experiment are termed I and S, which are not necessarily synonymous with the I and S terms used to denote spins in a CP experiment. A REDOR experiment (Figure 1.7a) generally involves acquiring two separate spectra of S: a reference spectrum (S₀) and a dipolar dephased spectrum (S). Obtaining the S₀ reference spectrum involves a simple spin–echo pulse sequence on S. This means there is first a π/2 pulse on S, followed by some time interval τ, a π pulse on S, another τ interval, and then S₀ signal acquisition. Acquiring the dipolar dephased spectrum S is more complicated; while the spin-echo pulse sequence on the S channel remains the same, additional pulses are now applied on the I channel. After the initial π/2 pulse on S, a train of rotor-synchronized π pulses is applied on the I channel that are separated by an interval equal to half of the sample rotor rotational period; the entire pulse train on I must run for a period of time equal to τ, which is an integer multiple of the rotor period. There is no π pulse on I when the mid-sequence S-channel π pulse is applied. Following the π pulse on S, another series of rotor-synchronized π pulses are applied on the I channel for the same time period τ, where the π pulses on I are again spaced apart by half of the sample rotor rotational period. The S signal is then observed. S is inherently less intense than the S₀ reference signal, owing to the reintroduction of the signal-reducing heteronuclear dipolar interaction via the π pulse train on I.

Using the SSNMR spectral intensities obtained from the S and S₀ spectra, a REDOR dephasing curve can then be generated, which plots the normalized difference of (S₀ − S)/S₀ versus the dipolar dephasing time (Nτ_r) used. The REDOR curve depends solely on the heteronuclear dipolar coupling between the two spins and can be quantitively analyzed using simulations to obtain information such as internuclear distance constraints (Figure 1.7b). An example of a REDOR curve involving a ¹³C and ¹⁵N spin pair in isotopically-labelled glycine is shown in Figure 1.7c.

There are limitations to REDOR experimental capabilities. Both the signal intensities of S and S₀ decrease as the I echo train period of τ is increased, owing to the transverse relaxation time (T₂) of the S magnetization. There is also a maximum measurable distance that depends on the gyromagnetic ratios of the I and S spins. The effectiveness and signal-to-noise ratio of REDOR experiments are also decreased by rf field inhomogeneities, pulse imperfections, and resonance offsets from the irradiation frequency; in practice, using phase cycling strategies such as xy-8 and xy-16 can be employed to compensate for some of these issues.⁸⁶ 

When dealing with spin-1/2 nuclei (S) dipolar-coupled to quadrupolar nuclei (I), standard REDOR experiments are no longer applicable due to the additional significant influences of the quadrupolar frequency and the orientation of the EFG tensor. Application of a π pulse results in incomplete dipolar dephasing of the quadrupolar nuclei, and hardware limitations render it unfeasible to generate strong tailored π pulses to completely irradiate the entire quadrupolar NMR signal and invert the spin state. To overcome these excitation bandwidth limitations, various pulse sequences have been developed, including TRAPDOR,⁸⁷  REAPDOR,⁸⁸  and RESPDOR.^89–91  These and other similar methods leverage the fact that adiabatic population transfer between spin states can be achieved through rf irradiation of the quadrupolar nucleus, bypassing the need for an extremely strong π pulse on the quadrupolar nucleus to target the entire CT.

Homonuclear dipole–dipole coupling can reveal detailed information regarding the distance and orientation of spin pairs; however, MAS methods are often required to achieve appreciable resolution in SSNMR spectra involving homonuclear dipolar coupling. In MAS experiments, rf pulses can be used to effectively reintroduce some degree of homonuclear coupling, similar to heteronuclear dipolar recoupling experiments.^92,93  Homonuclear recoupling NMR experiments generally utilize some arrangement of π/2 and π pulses in order to invert the sign of the homonuclear dipole–dipole coupling.^94,95  In situations involving modern (i.e., fast) MAS frequencies, the sample is typically treated as an averaged powder containing all possible molecular orientations, and the experimental focus is on obtaining information relevant to internuclear distances.

A classic example of a pulse sequence designed for homonuclear dipole–dipole recoupling is termed dipolar recovery at the magic angle (DRAMA), which uses rf pulses synchronized with the MAS frequency and sample rotation period (τ_R).⁹⁶  In the basic DRAMA pulse sequence, two π/2 pulses are applied during each τ_R (Figure 1.8a), which results in a non-zero homonuclear dipolar coupling. In order to eliminate CSA and isotropic CS-related resonance offset effects in a DRAMA experiment, π pulses can be added (Figure 1.8b), which only results in a minimal reduction of the dipolar recoupling. It is also possible to determine internuclear distances from a DRAMA-based experiment in a manner similar to a REDOR experiment, since the magnetization of the recoupled nuclei decays during the mixing period due to homonuclear dipolar coupling; a S₀ spectrum is first obtained using a traditional 90°-acquire pulse sequence with the homonuclear dipolar coupling averaged to zero by MAS, and then the S spectrum can be obtained with the dipolar coupling reintroduced using a DRAMA-based experiment. It is also possible to use DRAMA in 2D NMR pulse sequences (Figure 1.8c) to investigate the spatial proximity of two spins with different chemical shifts via the observation of cross peaks. Figure 1.8d illustrates a practical application of DRAMA for the investigation of ¹³C–¹³C distances in a (carbonyl-¹³C) polycarbonate.⁹⁷  Several other pulse schemes have been developed based on DRAMA. One example is dipolar recovery with a windowless sequence (DRAWS), which incorporates an additional π pulse between the two basic π/2 pulses in order to compensate for CSA and isotropic CS offsets. DRAWS-based NMR experiments can be used to determine specific internuclear proximity, such as ¹³C–¹³C distances in materials and torsional angles in biomolecules.^98–102 

In homonuclear dipolar-coupled two-spin systems of spin-1/2 nuclei, it is possible to exploit double quantum (DQ) coherences that encode data relevant to spin–spin distances. Spiess and co-workers designed the back-to-back (BABA) pulse sequence in order to excite and reconvert multiple-quantum coherences in homonuclear dipolar coupled systems,^103,104  and it has been utilized to investigate homonuclear distances and connectivity in various inorganic and organic crystalline materials.^105–113  The basic 2D BABA NMR pulse sequence (Figure 1.9a) begins with a pulse to introduce a double quantum spin state; after an increased evolution time of t₁, a reconversion pulse is applied to convert the coherence to a single quantum state for detection. This type of NMR experiment gives rise to cross peaks in the 2D NMR spectrum that yield information regarding the spatial proximity of two spin-1/2 nuclei via the homonuclear dipolar–dipolar interaction (Figure 1.9b).¹¹⁴  Additional data regarding internuclear distances can be obtained by simulating the cross peak intensity across a range of recoupling times.¹¹⁵  When this method is applied to ¹H nuclei, the resulting spectral resolution is typically quite limited due to strong homonuclear dipolar coupling. However, by combining higher MAS spinning frequencies with homonuclear decoupling sequences such as POST-C7, it is possible to obtain very high resolution 2D ¹H BABA NMR spectra.¹¹⁶  These advancements have allowed NMR spectroscopists to use such double quantum experiments to investigate hydrogen bonding and packing arrangements in organic and inorganic materials.^106,117 

The 2D heteronuclear correlation (HETCOR) NMR experiment involves using dipolar coupling to correlate a pair of unlike nuclei.¹¹⁸  In a HETCOR spectrum, both directly bound and spatially proximate nuclei will give rise to correlation peaks. HETCOR can be used for a variety of purposes in MOFs and COFs, including the assignment of chemical shifts to structural sites, understanding host–guest interactions and proximity, and elucidating guest dynamics, among others.^119–122  A general schematic of the HETCOR pulse sequence and the resulting 2D SSNMR spectrum is shown in Figure 1.10 for two nuclei denoted I and S; as in CP terminology, I is typically the more abundant nucleus (e.g., ¹H). The HETCOR sequence can be divided into four distinct subsections (Figure 1.10a): preparation, evolution, mixing, and detection. HETCOR begins with a preparation period where I spin magnetization is generated, followed by an evolution period of t₁ during which the I spins evolve for some time under the effect of chemical shift or heteronuclear couplings. During the evolution period, homonuclear I–I dipolar interactions are typically suppressed using a pulse sequence on the I channel such as FSLG,¹²³  DUMBO,¹²⁴  and MREV-8,^125,126  in order to achieve high resolution spectra in the indirect (F₁) dimension. The following mixing period involves the transfer of I spin magnetization to the S spins, which is typically accomplished using a CP-based pulse sequence. The final period is known as detection (t₂), during which the S signal is detected while heteronuclear decoupling is applied to I.

In practice, the HETCOR experiment is performed by acquiring successive spectra in the direct F₂ dimension at evenly spaced increments of the evolution time t₁. The 2D HETCOR NMR spectrum is then obtained by performing a Fourier transform of both the F₁ and F₂ dimensions (Figure 1.10b). By varying the I–S CP mixing time, it is also possible to investigate spatial proximity; for example, directly bound atoms undergoing a strong dipolar interaction can be distinguished from unbound spatially close atoms exhibiting weak dipolar interactions. The wide versatility and applicability of HETCOR makes it especially well-suited to investigate a variety of environments in MOFs and COFs.^{110,111,122,127} 

MQMAS is a 2D NMR experiment that can yield high-resolution NMR spectra of half-integer-quadrupolar nuclei (I ≥ 3/2) by correlating multiple quantum spectra and single quantum spectra.⁵⁹  The MQMAS experiment utilizes MAS to mitigate the effects of CSA, heteronuclear dipolar coupling, and a portion of the second order QI, while rf pulses are used to eliminate the remaining second-order QI. In an MQMAS experiment, a high-resolution MQ isotropic spectrum free of quadrupolar broadening is obtained in the indirect dimension (F₁), while traditional 1D NMR experimental spectra with lower signal-to-noise that are influenced by the QI can be extracted from individual “slices” in the direct dimension (F₂). A common strategy is to extract QI parameters from the F₁ dimension of a MQMAS spectrum, which can then be used as fixed values to successfully simulate a separate high-resolution 1D NMR spectrum of the same sample. The MQMAS F₂ slices can alternately be used for simulations of all other NMR parameters instead of conducting a separate 1D NMR experiment, provided that the slices have sufficiently high resolution and signal-to-noise ratio.

A general MQMAS pulse sequence selecting the triple quantum coherence (i.e., 3QMAS) is shown in Figure 1.11a. In this case, the first pulse of phase ϕ₁ is used to achieve the desired 3Q coherence. There is then an evolution time (t₁), after which a second “conversion” pulse of phase ϕ₂ is applied to convert the MQ coherence to a single quantum (SQ) coherence that is detectable via NMR. The SQ signal echo then refocuses through a second evolution time (t₂) and can be detected. It should be noted that many variations of MQMAS also include an additional π/2 or π pulse after the conversion pulse for various reasons, and this additional pulse is omitted from Figure 1.11a for clarity.

An isotropic 2D spectrum can be obtained from the MQMAS data by performing a shearing transformation along the indirect dimension. In an MQMAS NMR spectrum, the lineshapes are typically clearly resolved in the indirect dimension (Figure 1.11b, left of the vertical axis), and the overall spectrum in the F₂ direct dimension (Figure 1.11b, above horizontal axis) is simply the sum of each individual slice. The ¹⁷O MQMAS NMR spectrum of [3,5,6-¹⁷O]-α-d-glucose in Figure 1.11b exhibits clear resolution of several crystallographically unique oxygen sites; this data permitted extraction of the corresponding quadrupolar parameters.¹²⁸  A small example of the information available from this MQMAS data is provided in Figure 1.11b for the O6A oxygen sites, where δ_iso = −6 ppm, C_Q = 8.8 MHz, and η_Q = 0.9.

The diverse framework composition and functionalities of MOFs and COFs pose significant challenges for structural characterization and performance evaluation. Several techniques can be used to characterize these materials and elucidate structure–property relationships, including X-ray diffraction (XRD), SSNMR, scanning/transmission electron microscopy (SEM/TEM), and adsorption–desorption isotherms. Among the various accessible characterization routes, XRD and SSNMR are particularly important, as XRD provides information regarding long-range structure while SSNMR can investigate the short-range local environment. The blend of these complementary techniques with first-principles calculations constitutes an approach termed “NMR crystallography,”¹²⁹  which has been proven very useful for investigations of porous materials and MOFs.^130–132  XRD provides only limited information regarding materials of low crystallinity, yet SSNMR can investigate environments of local disorder,^133,134  and first principles calculations can relate experimental observations to predicted parameters for both techniques.

The field of SSNMR spectroscopy has advanced tremendously in recent decades, and characterization of many porous materials is now routinely feasible, including zeolites, MOFs, COFs, PIMs (polymers of intrinsic microporosity) and CMPs (conjugated microporous polymers).^{39,55,135–138}  Information on the chemical composition, local environment, pore dimensions, pore connectivity, and guests in porous materials can be obtained from various NMR parameters. Detailed information on the dynamic behaviour of frameworks and host–guest interactions in porous materials across various timescales is also available. For example, 2D HETCOR SSNMR experiments can probe the spatial connectivity and proximity between two distinct nuclei,^139,140  while pulsed field gradient (PFG) NMR experiments are an effective route to investigate the self-diffusion coefficients and diffusion pathways of guest molecules within the pores of MOFs and COFs.¹⁴¹  In situ SSNMR approaches are well-established for examining catalytic mechanisms in porous materials, and can observe reactive intermediates trapped in porous structures.^142,143  Variable temperature (VT) SSNMR can also be used to investigate framework flexibility and the dynamic behaviour of guests by probing molecular motions in porous materials.^{144  129}Xe NMR spectroscopy offers an ideal probe for detecting the size and shape of the pores or channels in porous materials.¹⁴⁵  In this book, we focus on how practical scientific issues relevant to structures and host–guest interactions of MOFs and COFs have been addressed by SSNMR spectroscopy. For further information regarding applications of SSNMR in microporous materials, the readers are directed to additional resources cited here.^{41,130,136,137,146} 

SSNMR spectroscopy provides three primary types of structural information from MOFs and COFs (Figure 1.12). SSNMR can provide local information at the atomic level in MOFs and COFs. Metal sites in MOFs and metal doping in MOFs and COFs, local structure of organic linkers, and confirmation of covalent bond formation in COFs can be investigated using SSNMR. SSNMR can also be used for studying host–guest interactions in MOFs and COFs. Both the framework dynamics and the motion of guests can be examined, along with any structural changes or interactions upon guest adsorption and desorption. SSNMR has also been proven very useful for probing the porous structure of MOFs and COFs, including the pore size and pore connectivity.

In Chapter 2, we summarize and review studies over the previous 15 years that have employed SSNMR to investigate framework metal centers and dopant metals in MOFs and COFs. It is apparent that a broad range of information, including the number of unique metal sites, the metal oxidation state, and the local metal coordination geometry, can be obtained via SSNMR. Studies focusing on metals with a spin number of 1/2 (e.g., ¹¹¹Cd and ²⁰⁷Pb) and I > 1/2 (quadrupolar nuclei, e.g., ²⁵Mg, ⁴³Ca, and ⁶⁷Zn) are included. All NMR-active metal nuclei are influenced by the CS, dipolar, and J-coupling interactions, but quadrupolar nuclei are additionally subject to the QI, which renders spectral acquisition particularly challenging. Acquisition strategies for spin-1/2 and quadrupolar metal SSNMR experiments on MOFs and COFs are discussed, including the use of modern pulse sequences and NMR hardware. Characterization of the metal nodes and doped metals in MOFs and COFs is an integral step toward understanding structure–property relationships and facilitating the rational design of new functional materials.

In Chapter 3, recent applications of SSNMR for the characterization of organic linkers in MOFs and COFs are examined. The organic ligands serve two important roles in MOFs and COFs, acting as structural linkers and also as possible sites for tailoring functionality. Multinuclear SSNMR offers a unique opportunity to examine the local linker structure and chemical environment in MOFs and COFs from the perspective of several different nuclei. ¹H–¹³C and ¹H–¹⁵N CPMAS NMR approaches are commonly used in this field, and serve as a straightforward method to characterize the functional groups in various MOFs and COFs. Isotopic labelling of ¹³C and ¹⁵N is also widely used in order to enhance sensitivity and target specific sites. Direct comparison of the ¹H, ¹³C, and ¹⁵N NMR chemical shifts between the starting monomers and final product can verify the introduction of linkers and functional groups in MOFs and COFs. More advanced strategies, such as combining ¹H–¹³C CPMAS and NQS solid-state NMR techniques, can verify formation of specific carbon centers (i.e., quaternary) in COFs; REDOR-based experiments may be used to measure the distance between a specific spin pair. Establishing the specific coordination and functional groups present on MOF and COF linkers is a well-suited task for NMR.

In Chapter 4, we detail how SSNMR can be applied to investigate host–guest relationships in MOFs and COFs. It is possible to probe both the host and guest to directly confirm the incorporation of guest molecules, while also obtaining information regarding the short-range structure and local order. SSNMR also provides insight regarding guest binding site locations, guest molecular orientations, host–guest interaction strengths and dynamics of guest molecules. Multinuclear and multidimensional SSNMR experiments provide even more data; we review studies in which the location and dynamics of guest molecules in MOFs and COFs are available from SSNMR methods such as T₂-based experiments and 2D ¹H–¹H DQ-MAS NMR. We also examine reports in which in situ hyperpolarized ¹²⁹Xe NMR experiments at variable temperatures and pressures were used to investigate dynamic changes in the framework structure and pore accessibility. ²H isotopic labelling along with ²H SSNMR spectroscopy also permits measurement of guest dynamics. Taken as a whole, these approaches hold promise for future routine measurements involving local structure, chemical reactions, guest mobility, and quantitative assessments of interactions in MOFs and COFs.

SSNMR is a powerful technique for the structural characterization of MOFs and COFs, but the intrinsically low sensitivity of this route can limit applications. High-value avenues such as ²⁷Al–¹³C 2D NMR experiments, ultra-wideline metal NMR spectroscopy, and natural-abundance ¹⁷O NMR approaches can be very challenging or outright unfeasible. While future sensitivity gains may be achieved through new hardware and pulse sequences, the most promising route to sensitivity enhancement lies in polarization enhancement techniques. In Chapter 5, dynamic nuclear polarization (DNP), which transfers spin polarization from unpaired electrons to the surrounding nuclei, is introduced. DNP techniques offer a tremendous boost in sensitivity, enabling many NMR experiments that were previously considered too challenging or impractical. We provide a brief history of DNP NMR, describe common DNP instrumentation, and discuss the development and implementation of several different polarizing agents (PAs) that provide unpaired electrons. The Overhauser effect, solid effect and cross effect mechanisms of DNP are also reviewed. Published applications of DNP-enhanced SSNMR in the research areas of MOFs and COFs are summarized and discussed, illustrating how NMR sensitivity issues can be mitigated. DNP NMR under moderate to high magnetic fields, particularly when combined with MAS and MQMAS techniques, holds tremendous promise for future characterization of MOFs and COFs.

3Q

Triple quantum

BABA

Back-to-back

BET

Brunauer–Emmett–Teller

CMPs

Conjugated microporous polymers

COFs

Covalent organic frameworks

CP

Cross-polarization

CPPASS

Cross-polarization phase-adjusted sideband separation

CPPI

Cross-polarization with phase inversion

CPTOSS

Cross-polarization with total spinning sideband suppression

CRAMPS

Combined rotational and multiple pulse spectroscopy

CS

Chemical shift

CSA

Chemical shift anisotropy

CT

Central transition

CW

Continuous wave

DFT

Density functional theory

DNP

Dynamic nuclear polarization

DOR

Double rotation

DQ

Double quantum

DRAMA

Dipolar recovery at the magic angle

DRAWS

Dipolar recovery with a windowless sequence

EFG

Electric field gradient

EM

Electron microscopy

eQ

Electric quadrupole moment

HBA

Herzfeld–Berger analysis

HETCOR

Heteronuclear correlation

MAS

Magic angle spinning

MCOFs

Metal–covalent organic frameworks

MOFs

Metal–organic frameworks

MQMAS

Multiple-quantum magic angle spinning

NMR

Nuclear magnetic resonance

NQS

Non-quaternary suppression

Nτ_r

N times rotor period

OMSs

Open metal sites

Pas

Polarizing agents

PFG

Pulsed field gradient

PIM

Polymers of intrinsic microporosity

PXRD

Powder X-ray diffraction

QI

Quadrupolar interaction

REDOR

Rotational echo double resonance

rf

Radiofrequency

ROCSA

Recoupling of chemical shift anisotropy

SCXRD

Single-crystal X-ray diffraction

SEM

Scanning electron microscopy

SQ

Single quantum

SSNMR

Solid state nuclear magnetic resonance

STMAS

Satellite transition magic angle spinning

SUPPER

Separation of undistorted powder patterns by effortless recoupling

TEM

Transmission electron microscopy

TPPM

Two pulse phase modulation

VACP

Variable-amplitude cross polarization

VT

Variable temperature

WAHUHA

Waugh–Huber–Haeberlen

XRD

X-ray diffraction

τ_R

Rotation period

This work was financially supported by the National Key R&D Program of China (no. 2022YFA1503300) and the National Natural Science Foundation of China (no. 92056202, 22105091, and 22301115). S. C. is grateful for support from Fundamental Research Funds for the Central Universities (lzujbky-2021-sp26).