Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

The need for operando modelling of 27Al NMR in zeolites: the effect of temperature, topology and water

Solid state (ss-) 27Al NMR is one of the most valuable tools for the experimental characterization of zeolites, owing to its high sensitivity and the detailed structural information which can be extracted from the spectra. Unfortunately, the interpretation of ss-NMR is complex and the determination of aluminum distributions remains generally unfeasible. As a result, computational modelling of 27Al ss-NMR spectra has grown increasingly popular as a means to support experimental characterization. However, a number of simplifying assumptions are commonly made in NMR modelling, several of which are not fully justified. In this work, we systematically evaluate the effects of various common models on the prediction of 27Al NMR chemical shifts in zeolites CHA and MOR. We demonstrate the necessity of operando modelling; in particular, taking into account the effects of water loading, temperature and the character of the charge-compensating cation. We observe that conclusions drawn from simple, high symmetry model systems such as CHA do not transfer well to more complex zeolites and can lead to qualitatively wrong interpretations of peak positions, Al assignment and even the number of signals. We use machine learning regression to develop a simple yet robust relationship between chemical shift and local structural parameters in Al-zeolites. This work highlights the need for sophisticated models and high-quality sampling in the field of NMR modelling and provides correlations which allow for the accurate prediction of chemical shifts from dynamical simulations.

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

Crystal structure of phenanthrenide salts stabilized by 15-crown-5 and 18-crown-6

Potassium 15-crown-5 phenanthrenide and potassium 18-crown-6 phenanthrenide were synthesized and characterized by powder X-ray diffraction and 39K solid state NMR spectroscopy. While the radical carbanion is very reactive in solution, the crystals are stable and storable under inert atmosphere. For 15-crown-5, a sandwich-like complex of potassium is formed with two molecules of crown ether per potassium resulting in a coordination number of 10. For the larger 18-crown-6 ligand, a 1:1 complex is obtained and a coordination number of 6 for the potassium cation. In neither crystal structure solvent molecules are incorporated. The 15-crown-5 compound crystallizes faster and is less soluble in THF as compared to the 18-crown-6 compound. Both compounds form solid phenanthrenide that is easy to handle and can be applied for reduction reactions.

Silanol defect engineering and healing in zeolites: opportunities to fine-tune their properties and performances

Zeolites have been game-changing materials in oil refining and petrochemistry over the last 60 years and have the potential to play the same role in the emerging processes of the energy and environmental transition. Although zeolites are crystalline inorganic solids, their structures are not perfect and the presence of defect sites - mainly Brønsted acid sites and silanols - influences their thermal and chemical resistance as well as their performances in key areas such as catalysis, gas and liquid separations and ion-exchange. In this paper, we review the type of defects in zeolites and the characterization techniques used for their identification and quantification with the focus on diffraction, spectroscopic and modeling approaches. More specifically, throughout the review, we will focus on silanol (Si-OH) defects located within the micropore structure and/or on the external surface of zeolites. The main approaches applied to engineer and heal defects and their consequences on the properties and applications of zeolites in catalysis and separation processes are highlighted. Finally, the challenges and opportunities of silanol defect engineering in tuning the properties of zeolites to meet the requirements for specific applications are presented.

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for ²⁷ Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that BR 2 2 1 outperforms the supercycled S₃ sequence and its pure double-quantum (DQ) (bracketed) version, [S₃ ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S₃ sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of BR 2 2 1 is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of BR 2 2 1 , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for BR 2 2 1 when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the BR 2 2 1 sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

A brief introduction to the basics of NMR spectroscopy and selected examples of its applications to materials characterization

Nuclear magnetic resonance (NMR) spectroscopy is an analytical technique that gives information on the local magnetic field around atomic nuclei. Since the local magnetic field of the nucleus is directly influenced by such features of the molecular structure as constitution, configuration, conformation, intermolecular interactions, etc., NMR can provide exhaustive information on the chemical structure, which is unrivaled by any other analytical method. Starting from the 1950s, NMR spectroscopy first revolutionized organic chemistry and became an indispensable tool for the structure elucidation of small, soluble molecules. As the technique evolved, NMR rapidly conquered other disciplines of chemical sciences. When the analysis of macromolecules and solids also became feasible, the technique turned into a staple in materials characterization, too. All aspects of NMR spectroscopy, including technical and technological development, as well as its applications in natural sciences, have been growing exponentially since its birth. Hence, it would be impossible to cover, or even touch on, all topics of importance related to this versatile analytical tool. In this tutorial, we aim to introduce the reader to the basic principles of NMR spectroscopy, instrumentation, historical development and currently available brands, practical cost aspects, sample preparation, and spectrum interpretation. We show a number of advanced techniques relevant to materials characterization. Through a limited number of examples from different fields of materials science, we illustrate the immense scope of the technique in the analysis of materials. Beyond our inherently limited introduction, an ample list of references should help the reader to navigate further in the field of NMR spectroscopy.

Indirect detection of broad spectra in solid-state NMR using interleaved DANTE trains

We analyze the performances and the optimization of ¹H-{I} HMQC experiments using basic and interleaved DANTE schemes for the indirect detection of nuclei I = 1/2 or 1 exhibiting wide lines dominated by chemical shift anisotropy (CSA) or quadrupole interaction, respectively. These sequences are first described using average Hamiltonian theory. Then, we analyze using numerical simulations (i) the optimal lengths of the DANTE train and the individual pulses, (ii) the robustness of these experiments to offset, and (iii) the optimal choice of the defocusing and refocusing times for both ¹H-{I} J- and D-HMQC sequences for ¹⁹⁵Pt (I = 1/2) and ¹⁴N (I = 1) nuclei subject to large CSA and quadrupole interaction, respectively. These simulations are compared to ¹H-{¹⁴N} D-HMQC experiments on γ-glycine and L-histidine.HCl at B₀ = 18.8 T and MAS frequency of 62.5 kHz. The present study shows that (i) the optimal defocusing and refocusing times do not depend on the chosen DANTE scheme, (ii) the DANTE trains must be applied with the highest rf-field compatible with the probe specifications and the stability of the sample, (iii) the excitation bandwidth along the indirect dimension of HMQC sequence using DANTE trains is inversely proportional to their length, (iv) interleaved DANTE trains increase the excitation bandwidth of these sequences, and (v) dephasing under residual ¹H-¹H and ¹H-I dipolar couplings, as well as ¹⁴N second-order quadrupole interaction, during the length of the DANTE scheme attenuate the transfer efficiency.

Uniform signal enhancement in MAS NMR of half-integer quadrupolar nuclei using quadruple-frequency sweeps

We introduce two MAS schemes that allow manipulating the satellite-transition (ST) populations of half-integer quadrupolar nuclei, and which both exhibit improved robustness to the quadrupolar coupling constant (C_Q). These schemes, called quadruple frequency sweep (QFS) or quadruple WURST (QWURST) are the sums of two DFS or four WURST to efficiently invert the ST populations of nuclei subject to large or small quadrupole interactions, simultaneously. These quadruple sweeps methods only require 6% more rf-power than the double sweeps ones. We demonstrate, both numerically and experimentally, that the QFS and QWURST schemes benefit from robustness to C_Q and rf amplitude and offset and hence achieve uniform enhancement of the CT signal for ²⁷Al nuclei subject to different quadrupole interactions. Although the version of QFS with repetitive accumulation can achieve higher enhancement in the S/N of the ²⁷Al MAS spectrum, the final sensitivity gains mainly depend on the longitudinal relaxation time of different ²⁷Al sites. We also confirm that these schemes provide an improved acceleration of the ³¹P-{²⁷Al} coherence transfer in PT-J-HMQC experiments.

24 T High-Resolution and -Sensitivity Solid-State NMR Measurements of Low-Gamma Half-Integer Quadrupolar Nuclei 35Cl and 37Cl

Solid-state NMR observations of low-gamma half-integer quadrupolar nuclei, ³⁵Cl and ³⁷Cl, were demonstrated using a 24 T hybrid magnet (¹H resonance frequency of 1.02 GHz) comprised of the high-temperature (HTS) and low-temperature (LTS) superconductors, and compared with results using a 14.1 T standard NMR magnet. While at 24 T the linewidth is 1.7 times narrower than that at 14.1 T, the gain in the sensitivity is 7.0 times because of enhanced polarization, reduced linewidth, and the use of larger rotor. A simple theoretical model was used to rationalize the sensitivity enhancements. The ratio of ³⁵Cl and ³⁷Cl quadrupolar couplings agrees well with the ratio of quadrupolar moments, and no isotope-dependent chemical shift has been observed. In addition, the 3QMAS spectrum of ³⁵Cl is shown to demonstrate the high sensitivity rendered by the 24 T spectrometer.

Satellite and central transitions selective 1H/{27Al} D-HMQC experiments at very fast MAS for quadrupolar couplings determination

Recent study has demonstrated the application of the proton-detected heteronuclear multi-quantum coherence (HMQC) at ultrafast Magic Angle Spinning (MAS) to probe quadrupolar nuclei including ¹⁴N and ³⁵Cl. In addition, for half-integer quadrupolar nucleus like ³⁵Cl, the quadrupolar product can be calculated based on the shift difference between the center band of satellite transition (ST) and the central transition (CT) peaks. The applicability of this technique is further investigated on spin I=5/2, namely ²⁷Al nucleus, and kaolin is chosen as the testing sample. However this study is not straightforward owing to a spin quantum number I=5/2 of ²⁷Al nucleus and a small quadrupolar coupling of kaolin. Furthermore, very fast MAS, which is mandatory for proton-detected experiment to suppress ¹H-¹H homonuclear dipolar interactions, introduces additional complexities. It induces the partial overlap of CT and the center band of inner ST (ST1) resonance in addition to the insufficiency of CT-selective excitation by soft-pulse irradiation. In the current work, we employ the constant-time D-HMQC experiment, in which the duration between two recoupling blocks is fixed to a constant value and the arbitrary t₁ increment can be used within this duration. This constant-time D-HMQC enables the precise determination of CT and ST resonance shifts through CT- and ST-selective observations by the indirect spectral width (i) with asynchronized sampling to the top of rotational-echoes for STs and (ii) three times larger than the spinning frequency, respectively. We also numerically and experimentally develop a satellite-selective excitation technique, in which the radio frequency field is applied to the first spinning sideband of ST1 resonance. The satellite-selective 1D single pulse and 2D conventional D-HMQC experiments are demonstrated. The quadrupolar product of ²⁷Al nucleus extracted from the resulting spectra is in good agreement with the literature.

27Al-27Al double-quantum single-quantum MAS NMR: Applications to the structural characterization of microporous materials

In this paper, we review and illustrate applications, reported in the literature or used in our group, of ²⁷Al-²⁷Al double-quantum single-quantum (DQ-SQ) MAS NMR experiments for the structural characterization of Al-containing microporous solids, namely zeolites, aluminophosphates and metal-organic frameworks. Information regarding the periodic frameworks or the localization of the various aluminum species in the materials are obtained from the analysis of the two-dimensional NMR spectra, which allows getting local structural details sometimes inaccessible from other characterization technique. An application of ²⁷Al-²⁷Al of the DQ-SQ experiment for the detection of aluminum pairing in zeolite is shown.

DNP-Enhanced Ultrawideline Solid-State NMR Spectroscopy: Studies of Platinum in Metal-Organic Frameworks

Ultrawideline dynamic nuclear polarization (DNP)-enhanced (195)Pt solid-state NMR (SSNMR) spectroscopy and theoretical calculations are used to determine the coordination of atomic Pt species supported within the pores of metal-organic frameworks (MOFs). The (195)Pt SSNMR spectra, with breadths reaching 10 000 ppm, were obtained by combining DNP with broadbanded cross-polarization and CPMG acquisition. Although the DNP enhancements in static samples are lower than those typically observed under magic-angle spinning conditions, the presented measurements would be very challenging using the conventional SSNMR methods. The DNP-enhanced ultrawideline NMR spectra served to separate signals from cis- and trans-coordinated atomic Pt(2+) species supported on the UiO-66-NH2 MOF. Additionally, the data revealed a dominance of kinetic effects in the formation of Pt(2+) complexes and the thermodynamic effects in their reduction to nanoparticles. A single cis-coordinated Pt(2+) complex was confirmed in MOF-253.

Quantitative structure parameters from the NMR spectroscopy of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important characterization tools in chemistry, however, 3/4 of the NMR active nuclei are underutilized due to their quadrupolar nature. This short review centers on the development of methods that use solid-state NMR of quadrupolar nuclei for obtaining quantitative structural information. Namely, techniques using dipolar recoupling as well as the resolution afforded by double-rotation are presented for the measurement of spin–spin coupling between quadrupoles, enabling the measurement of internuclear distances and connectivities. Two-dimensional J-resolved-type experiments are then presented for the measurement of dipolar and J coupling, between spin-1/2 and quadrupolar nuclei as well as in pairs of quadrupolar nuclei. Select examples utilizing these techniques for the extraction of structural information are given. Techniques are then described that enable the fine refinement of crystalline structures using solely the electric field gradient tensor, measured using NMR, as a constraint. These approaches enable the solution of crystal structures, from polycrystalline compounds, that are of comparable quality to those solved using single-crystal diffraction.

Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules

For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R1 of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R1 vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S-I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole (14)N nuclei and mediating the QRE to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of (27)Al (S = 5/2) nuclei is also explained.

Spatial reorientation experiments for NMR of solids and partially oriented liquids

Motional reorientation experiments are extensions of Magic Angle Spinning (MAS) where the rotor axis is changed in order to average out, reintroduce, or scale anisotropic interactions (e.g. dipolar couplings, quadrupolar interactions or chemical shift anisotropies). This review focuses on Variable Angle Spinning (VAS), Switched Angle Spinning (SAS), and Dynamic Angle Spinning (DAS), all of which involve spinning at two or more different angles sequentially, either in successive experiments or during a multidimensional experiment. In all of these experiments, anisotropic terms in the Hamiltonian are scaled by changing the orientation of the spinning sample relative to the static magnetic field. These experiments vary in experimental complexity and instrumentation requirements. In VAS, many one-dimensional spectra are collected as a function of spinning angle. In SAS, dipolar couplings and/or chemical shift anisotropies are reintroduced by switching the sample between two different angles, often 0° or 90° and the magic angle, yielding a two-dimensional isotropic-anisotropic correlation spectrum. Dynamic Angle Spinning (DAS) is a related experiment that is used to simultaneously average out the first- and second-order quadrupolar interactions, which cannot be accomplished by spinning at any unique rotor angle in physical space. Although motional reorientation experiments generally require specialized instrumentation and data analysis schemes, some are accessible with only minor modification of standard MAS probes. In this review, the mechanics of each type of experiment are described, with representative examples. Current and historical probe and coil designs are discussed from the standpoint of how each one accomplishes the particular objectives of the experiment(s) it was designed to perform. Finally, applications to inorganic materials and liquid crystals, which present very different experimental challenges, are discussed. The review concludes with perspectives on how motional reorientation experiments can be applied to current problems in chemistry, molecular biology, and materials science, given the many advances in high-field NMR magnets, fast spinning, and sample preparation realized in recent years.

Solid-State (63)Cu, (65)Cu, and (31)P NMR Spectroscopy of Photoluminescent Copper(I) Triazole Phosphine Complexes

The results of a solid-state (63/65)Cu and (31)P NMR investigation of several copper(I) complexes with functionalized 3-(2'-pyridyl)-1,2,4-triazole and phosphine ligands that have shown potential in the preparation of photoluminescent devices are reported. For each complex studied, distinct NMR parameters, with moderate (63)Cu nuclear quadrupolar coupling constant (CQ) values ranging from -17.2 to -23.7 MHz, are attributed to subtle variations in the distorted four-coordinate environments about the copper nuclei. The spans of the copper chemical shift (CS) tensors, δ11-δ33, for the mono- and bisphosphine complexes are also similar, ranging from 1000 to 1150 ppm, but that for a complex with a strained bidentate phosphine ligand is only 650 ppm. The effects of residual dipolar and indirect spin-spin coupling arising from the (63/65)Cu- (31)P spin pairs, observed in the solid-state (31)P NMR spectra of these complexes, yield information about the orientations of the copper electric field gradient (EFG) tensors relative to the Cu-P bond. Variable-temperature (31)P NMR measurements for [Cu(bptzH)(dppe)]ClO4 (bptzH = 5-tert-butyl-3-(2'-pyridyl)-1,2,4-triazole; dppe = 1,2-bis(diphenylphosphino)ethane), undertaken to investigate the cause of the broad unresolved spectra observed at room temperature, demonstrate that the broadening arises from partial self-decoupling of the (63/65)Cu nuclei, a consequence of rapid quadrupolar relaxation. Ab initio calculations of copper EFG and CS tensors were performed to probe relationships between NMR parameters and molecular structure. The analysis demonstrated that CQ((63/65)Cu) is negative for all complexes studied here and that the largest components of the EFG tensors are generally coincident with δ11.

PRESTO polarization transfer to quadrupolar nuclei: implications for dynamic nuclear polarization

We show both experimentally and numerically that in experiments involving transfer of magnetization from ¹H to the quadrupolar nuclei under MAS, the PRESTO technique consistently outperforms the traditionally used CP method, affording more quantitative intensities, improved lineshapes, better sensitivity, and easier optimization.

New methods and applications in solid-state NMR spectroscopy of quadrupolar nuclei

Solid-state nuclear magnetic resonance (NMR) spectroscopy has long been established as offering unique atomic-scale and element-specific insight into the structure, disorder, and dynamics of materials. NMR spectra of quadrupolar nuclei (I > (1)/2) are often perceived as being challenging to acquire and to interpret because of the presence of anisotropic broadening arising from the interaction of the electric field gradient and the nuclear electric quadrupole moment, which broadens the spectral lines, often over several megahertz. Despite the vast amount of information contained in the spectral line shapes, the problems with sensitivity and resolution have, until very recently, limited the application of NMR spectroscopy of quadrupolar nuclei in the solid state. In this Perspective, we provide a brief overview of the quadrupolar interaction, describe some of the basic experimental approaches used for acquiring high-resolution NMR spectra, and discuss the information that these spectra can provide. We then describe some interesting recent examples to showcase some of the more exciting and challenging new applications of NMR spectra of quadrupolar nuclei in the fields of energy materials, microporous materials, Earth sciences, and biomaterials. Finally, we consider the possible directions that this highly informative technique may take in the future.

Boron–boron J coupling constants are unique probes of electronic structure: a solid-state NMR and molecular orbital study

J couplings measured between ¹¹B spin pairs in solid diboron compounds provide insight into electronic structure and crystallographic symmetry.

23Na magic-angle spinning and double-rotation NMR study of solid forms of sodium valproate

Sodium valproate is a pharmaceutical with applications in the treatment of epilepsy, bipolar disorder, and other ailments. Sodium valproate can exist in many hydrated and acid-stabilized forms in the solid state, and it can be difficult to obtain precise structural information about many of these. Here, we present a 13C and 23Na solid-state NMR study of several forms of sodium valproate, only one of which has been previously structurally characterized by single-crystal X-ray diffraction. 23Na magic-angle spinning (MAS), double-rotation (DOR), and multiple-quantum magic-angle spinning (MQMAS) NMR spectra are shown to provide useful information on the number of molecules in the asymmetric unit, the local coordination geometry of the sodium cations, and the presence of amorphous phases. Two previously identified forms are shown to be highly similar, or identical, according to the 23Na NMR data. The utility of carrying out both DOR and MQMAS NMR experiments to identify all crystallographically unique sites is demonstrated. 13C cross-polarization MAS NMR spectra also provide complementary information on the number of molecules in the asymmetric unit and the crystallinity of the sample.

Dynamic nuclear polarization of 17O: direct polarization

Dynamic nuclear polarization of (17)O was studied using four different polarizing agents: the biradical TOTAPOL and the monoradicals trityl and SA-BDPA, as well as a mixture of the latter two. Field profiles, DNP mechanisms, and enhancements were measured to better understand and optimize directly polarizing this low-gamma quadrupolar nucleus using both mono- and biradical polarizing agents. Enhancements were recorded at <88 K and were >100 using the trityl (OX063) radical and <10 with the other polarizing agents. The >10,000-fold savings in acquisition time enabled a series of biologically relevant small molecules to be studied with small sample sizes and the measurement of various quadrupolar parameters. The results are discussed with comparison to room temperature studies and GIPAW quantum chemical calculations. These experimental results illustrate the strength of high field DNP and the importance of radical selection for studying low-gamma nuclei.

Broadband excitation in solid-state NMR using interleaved DANTE pulse trains with N pulses per rotor period

We analyze the direct excitation of wide one-dimensional spectra of nuclei with spin I=1/2 or 1 in rotating solids submitted to pulse trains in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE), either with one short rotor-synchronized pulse of duration τp in each of K rotor periods (D1(K)) or with N interleaved equally spaced pulses τp in each rotor period, globally also extending over K rotor periods (D(N)(K)). The excitation profile of D(N)(K) scheme is a comb of rf-spikelets with Nν(R)=N/T(R) spacing from the carrier frequency, and a width of each spikelet inversely proportional to the length, KT(R), of D(N)(K) scheme. Since the individual pulse lengths, τp, are typically of a few hundreds of ns, D(N)(K) scheme can readily excite spinning sidebands families covering several MHz, provided the rf carrier frequency is close enough to the resonance frequency of one the spinning sidebands. If the difference of isotropic chemical shifts between distinct chemical sites is less than about 1.35/(KT(R)), D(N)(K) scheme can excite the spinning sidebands families of several sites. For nuclei with I=1/2, if the homogeneous and inhomogeneous decays of coherences during the DANTE sequence are neglected, the K pulses of a D1(K) train have a linearly cumulative effect, so that the total nutation angle is θ(tot)=K2πν1τp, where ν1 is the rf-field amplitude. This allows obtaining nearly ideal 90° pulses for excitation or 180° rotations for inversion and refocusing across wide MAS spectra comprising many spinning sidebands. If one uses interleaved DANTE trains D(N)(K) with N>1, only spinning sidebands separated by intervals of Nν(R) with respect to the carrier frequency are observed as if the effective spinning speed was Nν(R). The other sidebands have vanishing intensities because of the cancellation of the N contributions with opposite signs. However, the intensities of the remaining sidebands obey the same rules as in spectra obtained with νR. With increasing N, the intensities of the non-vanishing sidebands increase, but the total intensity integrated over all sidebands decreases. Furthermore, the NK pulses in a D(N)(K) train do not have a simple cumulative effect and the optimal cumulated flip angle for optimal excitation, θ(tot)(opt)=NK2πν1τp, exceeds 90°. Such D(N)(K) pulse trains allow achieving efficient broadband excitation, but they are not recommended for broadband inversion or refocusing as they cannot provide proper 180° rotations. Since D(N)(K) pulse trains with N>1 are shorter than basic D1(K) sequences, they are useful for broadband excitation in samples with rapid homogeneous or inhomogeneous decay. For nuclei with I=1 (e.g., for (14)N), the response to basic D1(K) pulse train is moreover affected by inhomogeneous decay due to 2nd-order quadrupole interactions, since these are not of rank 2 and therefore cannot be eliminated by spinning about the magic angle. For large quadrupole interactions, the signal decay produced by second-order quadrupole interaction can be minimized by (i) reducing the length of D(N)(K) pulse trains using N>1, (ii) fast spinning, (iii) large rf-field, and (iv) using high magnetic fields to reduce the 2nd-order quadrupole interaction.

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields. Since RF fields are limited by hardware, they seldom dominate the other interactions of these nuclei and so the spectra show unusual dependence on the pulse width used. The theory is tested with (23)Na NMR nutation spectra of a single crystal of sodium nitrate, in which the RF is comparable with the quadrupole coupling and is not necessarily on resonance with any of the transitions. Both the intensity and phase of all three transitions are followed as a function of flip angle. This provides a more rigorous trial than a powder sample where many of the details are averaged out. The formalism is based on a symbolic approach which encompasses all the published results, yet is easily implemented numerically, since no explicit spin operators or their commutators are needed. The classic perturbation results are also easily derived. There are no restrictions or assumptions on the spin of the nucleus or the relative sizes of the interactions, so the results are completely general, going beyond the standard first-order treatments in the literature.

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.

Investigation of the Effect of Finite Pulse Errors on BABA Pulse Sequence Using Floquet-Magnus Expansion Approach

This paper presents the study of finite pulse widths for the BABA pulse sequence using the Floquet-Magnus expansion (FME) approach. In the FME scheme, the first order F1 is identical to its counterparts in average Hamiltonian theory (AHT) and Floquet theory (FT). However, the timing part in the FME approach is introduced via the Λ1 (t) function not present in other schemes. This function provides an easy way for evaluating the spin evolution during "the time in between" through the Magnus expansion of the operator connected to the timing part of the evolution. The evaluation of Λ1 (t) is useful especially for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provides a natural choice of Λ1 (0) is ignored. This work uses the Λ1 (t) function to compare the efficiency of the BABA pulse sequence with δ - pulses and the BABA pulse sequence with finite pulses. Calculations of Λ1 (t) and F1 are presented.

Solid-State NMR Spectroscopy of Metal–Organic Framework Compounds (MOFs)

Nuclear Magnetic Resonance (NMR) spectroscopy is a well-established method for the investigation of various types of porous materials. During the past decade, metal–organic frameworks have attracted increasing research interest. Solid-state NMR spectroscopy has rapidly evolved into an important tool for the study of the structure, dynamics and flexibility of these materials, as well as for the characterization of host–guest interactions with adsorbed species such as xenon, carbon dioxide, water, and many others. The present review introduces and highlights recent developments in this rapidly growing field.

Solid-state NMR techniques for the structural determination of amyloid fibrils

This review discusses the solid-state NMR techniques developed for the study of amyloid fibrils. Literature up to the end of 2010 has been surveyed and the materials are organized according to five categories, viz. homonuclear dipolar recoupling and polarization transfer via J-coupling, heteronuclear dipolar recoupling, correlation spectroscopy, recoupling of chemical shift anisotropy, and tensor correlation. Our emphasis is on the NMR techniques and their practical aspects. The biological implications of the results obtained for amyloid fibrils are only briefly discussed. Our main objective is to showcase the power of NMR in the study of biological unoriented solids.