Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids

Quadrupole-Central-Transition 23Na, 39K, 87Rb NMR Studies of Alkali Metal Ions under Different Molecular Tumbling Conditions: A Simple Model to Treat Chemical Exchange Involving Quadrupolar Nuclei

We report a new NMR method for treating two-site chemical exchange involving half-integer quadrupolar nuclei in a solution. The new method was experimentally verified with extensive 23Na (I = 3/2), 39K (I = 3/2), and 87Rb (I = 3/2) NMR results from alkali metal ions (Na+, K+, and Rb+) in a solution over a wide range of molecular tumbling conditions. In the fast-motion limit, all allowed single-quantum NMR transitions for a particular quadrupolar nucleus are degenerate giving rise to one Lorentzian signal. In the slow-motion regime, although the NMR signal from quadrupolar nuclei should in principle exhibit a multi-Lorentzian line shape, only the quadrupole central transition (QCT) is often detectable in practice. In all the cases studied in this work, we found that alkali metal ions undergo fast exchange between free and bound states. Using the new theoretical method, we were able to interpret the experimental transverse relaxation data (i.e., line widths) obtained for 23Na, 39K, and 87Rb NMR signals including QCT signals over a large temperature range and extract information about ion-binding dynamics in different chemical environments. This work fills a gap in the literature where a unified approach for treating NMR transverse relaxation data for quadrupolar nuclei over the entire range of motion has been lacking. Our results suggest that the new approach is applicable in the study of alkali metal ion binding to biological macromolecules.

Multiple-quantum magic-angle spinning NMR spectra in the static limit: The I = 3/2 case

A simplified theoretical description of multiple-quantum excitation and mixing for nuclear magnetic resonance of half-integer quadrupolar nuclei is presented. The approach recasts the multiple-quantum nutation behavior in terms of reduced excitation and mixing curves through a scaling of the first-order offset frequency by the quadrupolar coupling constant. The two-dimensional correlation of the static first-order anisotropic line shape to the second-order anisotropic magic-angle-spinning (MAS) line shape is utilized to transform the three-dimensional integral over the three Euler angles into a single integral over the dimensionless first-order offset parameter. These transformations lead to a highly efficient algorithm for simulating the multiple-quantum (MQ)-MAS spectrum for arbitrary excitation and mixing radio frequency (RF) field strengths, pulse durations, and MAS rates within the static limit approximation, which is defined in terms of the rotation period, pulse duration, RF field strength, and quadrupolar coupling parameters. This algorithm enables a more accurate determination of the relative site populations and quadrupolar coupling parameters in a least-squares analysis of MQ-MAS spectra. Furthermore, this article examines practical considerations for eliminating experimental artifacts and employing affine transformations to improve least-squares analyses of MQ-MAS spectra. The optimum ratio of RF field strength to the quadrupolar coupling constant and the corresponding pulse durations that maximize sensitivity within experimental constraints are also examined.

17O NMR relaxation measurements for investigation of molecular dynamics in static solids using sodium nitrate as a model compound

17O NMR methods are emerging as a powerful tool for determination of structure and dynamics in materials and biological solids. We present experimental and theoretical frameworks for measurements of 17O NMR relaxation times in static solids focusing on the excitation of the central transition of the 17O spin 5/2 system. We employ 17O-enriched NaNO3 as a model compound, in which the nitrate oxygen atoms undergo 3-fold jumps. Rotating frame (T1ρ), transverse (T2) and longitudinal (T1) relaxation times as well as line shapes were measured for the central transition in the 280 to 195 K temperature range at 14.1 and 18.8 T field strengths. We conduct experimental and theoretical comparison between different relaxation methods and demonstrate the advantage of combining data from multiple relaxation time and line shape measurements to obtain a more accurate determination of the dynamics as compared to either of the techniques alone. The computational framework for relaxation of spin 5/2 nuclei is developed using the numerical integration of the Liouville - von Neumann equation.

Cesium Oxo-fluoro-aluminates in the CsF-Al2O3 System: Synthesis and Structural Characterization

In an experiment combining various approaches, a precise examination of a portion of the phase diagram of a CsF-Al2O3 system was carried out up to 40 mol% Al2O3. CsF-Al2O3 solidified mixtures have been investigated using high-field solid-state NMR (133Cs, 27Al, and 19F) spectroscopy and X-ray powder diffraction over a broad range of compositions with synchrotron powder diffraction and Rietveld analysis. A new cesium oxo-fluoro-aluminate, Cs2Al2O3F2, was discovered, prepared, and structurally analyzed by synchrotron diffraction analysis. In addition to Cs2Al2O3F2, we have synthesized the following pure compounds in order to aid in the interpretation of NMR spectra of the solidified samples: CsAlF4, Cs3AlF6, and CsAlO2.

On the applicability of cosine-modulated pulses for high-resolution solid-state NMR of quadrupolar nuclei with spin > 3/2

In MQMAS-based high-resolution solid-state NMR experiments of half-integer spin quadrupolar nuclei, the high radiofrequency (RF) field requirement for the MQ excitation and conversion steps with two hard-pulses is often a sensitivity limiting factor in many practical applications. Recently, the use of two cosine-modulated (cos) low-power (lp) pulses, lasting one-rotor period each, was successfully introduced for efficient MQ excitation and conversion of spin-3/2 nuclei with a reduced RF amplitude. In this study, we extend our previous investigations of spin-3/2 nuclei to systems with higher spin values and discuss the applicability of coslp-MQ excitation and conversion in MQMAS and MQ-HETCOR experiments under slow and fast spinning conditions. For the numerical simulations and experiments we used a moderate magnetic field of 14.1 T. Two spin-5/2 nuclei (⁸⁵Rb and ²⁷Al) are mainly employed with a large variety of C_Q values, but we show that the practical set up is also available for higher spin values, such as spin-9/2 with ⁹³Nb in Cs₄Nb₁₁O₃₀. We demonstrate for nuclei with spin value larger than 3/2 a preferential use of coslp-MQ acquisition for low-gamma nuclei and/or large C_Q values with a much reduced RF-field with respect to that of hard-pulses used with conventional methods.

Pushing the limit of MQMAS for low-γ quadrupolar nuclei in pharmaceutical hydrochlorides

Solid-state NMR of quadrupolar nuclei such as 35Cl has become a useful tool to characterize polymorphism in pharmaceutical hydrochlorides. The two-dimensional multiple-quantum magic-angle spinning (MQMAS) experiment can achieve isotropic resolution, and separate quadrupolar line shapes for samples with multiple sites but the pulse sequence efficiency is often low, limiting applications due to the intrinsically low NMR signals and rf field from the low gyromagnetic ratios γ. The use of cosine low-power MQMAS pulse sequences and high magnetic fields is presented to push the limit of MQMAS for insensitive low-γ quadrupolar nuclei. The improved efficiency and fields up to 35.2 T enable the acquisition of MQMAS spectra for pharmaceutical samples with multiple 35Cl sites, large quadrupolar couplings and/or in diluted dosage forms.

Practical considerations on the use of low RF-fields and cosine modulation in high-resolution NMR of I = 3/2 spin quadrupolar nuclei in solids

Despite its ease in experimental set up, the low sensitivity of MQMAS experiments is often a limiting factor in many practical applications. This is mainly due to the large radiofrequency (RF) field requirement of the two short hard-pulses often used for the optimum MQ excitation and conversion steps. Very recently, two novel MQMAS experiments have been proposed for I = 3/2 nuclei, namely lp-MQMAS and coslp-MQMAS, enabling an efficient MQ excitation/conversion with a reduced RF requirement, by utilizing two long pulses lasting one rotor period each, with or without cosine modulation. In this study, we focus on the practical considerations of these new methods and discuss their pros and cons to elucidate their appropriate use under both moderate and fast spinning conditions. Using four I = 3/2 (⁸⁷Rb, ⁷¹Ga, ³⁵Cl and ²³Na) nuclei at a moderate magnetic field (B₀ = 14.1 T), we show the superior use of these experiments, especially for samples with large C_Q values and/or low-gamma nuclei. Compared to all other existing sequences, the coslp-MQMAS method with initial WURST signal enhancement is the most robust, efficient and resolved high-resolution 2D method for spin 3/2 nuclei. Furthermore, using {²³Na}-¹H spin systems, we demonstrate the sensitivity advantage of the WURST coslp-MQ-HETCOR acquisition upon ¹H detection and fast MAS conditions.

On the use of single-frequency versus double-frequency satellite-transition pulses for MQMAS

It has been shown recently that a rotor-period long pulse applied at a frequency selective to the satellite-transitions of half-integer quadrupole nuclei can efficiently interconvert central-transition (CT) and triple-quantum (TQ) coherences for the acquisition of MQMAS spectra [I. Hung, Z. Gan, J. Magn. Reson. 324 (2021) 106913; doi: https://doi.org/10.1016/j.jmr.2021.106913]. By using a pair of such pulses and selecting opposite changes in coherence order, the anisotropic phase of the effective rf field can be refocused. Efficient multiple-quantum interconversion has led to low-power MQMAS pulse sequences capable of obtaining isotropic NMR spectra for the largest quadrupolar couplings to date. In this work, we extend the satellite-transition selective pulses from single- to double-frequency (or cosine) irradiation. By applying average Hamiltonian theory in the quadrupolar jolting frame, it is shown that the phase for TQ/CT conversion converges when the double-frequency irradiation matches the mirror-image symmetry of the satellite-transitions. The coherent conversion explains the mechanism behind the double-frequency sweep (DFS) and fast amplitude modulation (FAM) methods used for MQMAS. However, the strict matching condition limits the bandwidth of such double-frequency pulses to less than one spinning frequency. The use of a pair of identical cosine satellite-transition pulses is proposed to refocus the residual anisotropic phase spread. The refocusing leads to a more efficient MQMAS pulse sequence with a broader bandwidth suitable for large quadrupolar couplings and chemical shift ranges. Comparisons with the recently presented single-frequency lpMQMAS and other MQMAS pulse schemes show that cos-lpMQMAS is more efficient, less susceptible to fluctuations in spinning frequency, and suffers from less distortion in quadrupolar line shapes, as demonstrated with model compounds of moderate and large quadrupolar couplings, ⁸⁷RbNO₃ and β-⁷¹Ga₂O₃. In particular, the results for β-⁷¹Ga₂O₃ show an order of magnitude increase in MQMAS efficiency.

Polymorphs of Rb3ScF6: X-ray and Neutron Diffraction, Solid-State NMR, and Density Functional Theory Calculations Study

The crystal structures of three polymorphs of Rb₃ScF₆ have been determined through a combination of synchrotron, laboratory X-ray, and neutron powder diffraction, electron diffraction, and multinuclear high-field solid-state NMR studies. The room temperature (RT; α) and medium-temperature (β) structures are tetragonal, with space groups I4₁/a (Z = 80) and I4/m (Z = 10) and lattice parameters a = 20.2561(4) Å, c = 36.5160(0) Å and a = 14.4093(2) Å, c = 9.2015(1) Å at RT and 187 °C, respectively. The high-temperature (γ) structure is cubic space group Fm3̅m (Z = 4) with a = 9.1944(1) Å at 250 °C. The temperatures of the phase transitions were measured at 141 and 201 °C. The three α, β, and γ Rb₃ScF₆ phases are isostructural with the α, β, and δ forms of the potassium cryolite. Detailed structural characterizations were performed by density functional theory as well as NMR. In the case of the β polymorph, the dynamic rotations of the ScF₆ octahedra of both Sc crystallographic sites have been detailed.

Isotropic solid-state MQMAS NMR spectra for large quadrupolar interactions using satellite-transition selective inversion pulses and low rf fields

Multiple-quantum magic-angle spinning (MQMAS) pulse sequences are presented that are capable of obtaining isotropic NMR spectra for large quadrupolar interactions using lower rf fields. These experiments rely on rotor period long pulses applied at a large offset from the central-transition, making them selective to the satellite-transitions. Each such pulse gives rise to an anisotropic phase, which can be cancelled to obtain coherent signal evolution if a pair of pulses are applied in a symmetric manner. Thus, efficient excitation and conversion of triple-quantum coherences from and to the central-transition is achieved for MQMAS even for large quadrupolar couplings, by selective inversion of the satellite-transitions using such low-power pulses. Low-power multiple-quantum magic-angle spinning (lpMQMAS) pulse sequences are demonstrated on a model compound, RbNO₃, and also applied on β-Ga₂O₃, a sample with the largest quadrupolar interactions for which isotropic NMR spectra have been obtained to date.

Exploring the homopolar dehydrocoupling of ammonia borane by solid-state multinuclear NMR spectroscopy

Solid-state 1H-14NOT HMQC, 11B MQMAS and 1H-11B HETCOR NMR experiments are used to explore the role of homopolar B-B interaction in the thermal dehydrogenation of pure and supported ammonia borane, which is considered as one of the most promising hydrogen storage materials. This work also addresses the subtlety of the homopolar interactions in amine borane compounds, and how they differ from their heteropolar counterparts.

Perspectives of fast magic-angle spinning 87 Rb NMR of organic solids at high magnetic fields

We report solid-state ⁸⁷ Rb NMR spectra from two Rb-ionophore complexes obtained with fast magic-angle spinning (MAS) (up to 60 kHz) at 21.1 T. These Rb-ionophore complexes containing macrocycles such as benzo-15-crown-5 and cryptand [2.2.2] are typical of organic Rb salts that exhibit very large ⁸⁷ Rb quadrupole coupling constants (close to 20 MHz). We have also obtained static ⁸⁷ Rb NMR spectra for these two compounds and determined both ⁸⁷ Rb quadrupole coupling and chemical shift tensors. The experimental ⁸⁷ Rb NMR tensor parameters are compared with those obtained by quantum chemical computations. Our results demonstrate that the combination of fast MAS (60 kHz or higher) and a high magnetic field (21.1 T or higher) is sufficient to produce high-quality solid-state ⁸⁷ Rb NMR spectra for organic Rb solids at the natural abundance level. We anticipate that, with additional ⁸⁷ Rb isotope enrichment (up to 99%), the sensitivity of solid-state ⁸⁷ Rb NMR will be 400 times higher than ³⁹ K NMR, which makes the former an attractive surrogate probe for studying K⁺ ion binding in biological systems.

Sensitivity-enhanced multiple-quantum MAS NMR for half-integer spin quadrupolar nuclei using WURST-amplitude shaped pulses

Two-dimensional multiple-quantum MAS (MQMAS) NMR spectroscopy is one of the most widely used solid-state NMR techniques for resolving multiple overlapping central-transition lineshapes for half-integer spin quadrupolar nuclei. In particular when relying on nutation-driven MQ coherence transfers, this technique suffers from low sensitivity that can only be improved by increasing the rf-amplitude of the involved radio-frequency (rf) pulses, which are therefore typically operated at the rf-limit. In such situations, frequently encountered for the three-pulse z-filtered and split-t₁ shifted-echo MQMAS NMR sequences, we introduce the advantages of rf-pulses with smoothly truncated amplitude profiles, which we have termed WURST-Amplitude Shaped Pulses (WASPs). When considering the NMR spectrometer hardware, we demonstrate that WASPs feature more suitable properties in comparison to conventional rectangular pulses, enabling a substantial reduction of voltage reflections and transient effects under identical rf-conditions. By employing extensive numerical simulations and experimental validation, we further show that WASPs intrinsically possess a higher potential for nutation-based 3Q excitation involving spin-3/2 and 3Q and 5Q excitation for spin-5/2 quadrupolar nuclei, specifically when large nutation frequencies are available. The concept of smoothly truncating rf-amplitudes is also extended to Fast Amplitude Modulation (FAM) pulses, normally incorporated for rotor-driven 1Q conversion. We additionally evaluate the potential of employing WASPs with peak rf-amplitudes beyond the rf-limit for conventional rectangular rf-pulses.

Accelerating high-resolution NMR of half-integer quadrupolar nuclei in solids: SPAM-MQMAS and SPAM-STMAS

In solid-state NMR, multiple-quantum MAS (MQMAS) and satellite-transition MAS (STMAS) experiments are well-established techniques to obtain high-resolution spectra of half-integer quadrupolar nuclei. In 2004 and 2005, a soft-pulse-added-mixing (SPAM) concept was introduced by Gan and Amoureux to enhance the S/N ratio of MQMAS and STMAS experiments. Despite their robustness and simplicity, SPAM approaches have not yet been widely applied. Here, we further exploit SPAM concepts for sensitivity enhancement upon acquisition of two-dimensional MQMAS and STMAS spectra and also establish a general procedure upon implementation of SPAM-MQMAS and SPAM-STMAS NMR. Its effectiveness and ease in experimental setup are demonstrated using simulations and experiments performed on I ​= ​3/2 (²³Na, ⁸⁷Rb), 5/2 (²⁷Al, ⁸⁵Rb) and 9/2 (⁹³Nb) nuclei with a variety of quadrupolar coupling constants (C_Q). Compared to the conventional z-filter methods, sensitivity enhancements in between 2 and 4 are achievable with SPAM. We recommend to use SPAM with a ratio of 4:1 for the number of echoes and antiechoes to safely maximize the sensitivity and resolution simultaneously. In addition, a comparison of the experimental approaches is made in the context of SPAM-MQMAS and SPAM-STMAS NMR with respect to repetition delay and spinning frequency, aiming to discuss the precautions upon making a judicious choice of high-resolution NMR methods of half-integer quadrupolar nuclei.

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.

17O NMR studies of organic and biological molecules in aqueous solution and in the solid state

This review describes the latest developments in the field of ¹⁷O NMR spectroscopy of organic and biological molecules both in aqueous solution and in the solid state. In the first part of the review, a general theoretical description of the nuclear quadrupole relaxation process in isotropic liquids is presented at a mathematical level suitable for non-specialists. In addition to the first-order quadrupole interaction, the theory also includes additional relaxation mechanisms such as the second-order quadrupole interaction and its cross correlation with shielding anisotropy. This complete theoretical treatment allows one to assess the transverse relaxation rate (thus the line width) of NMR signals from half-integer quadrupolar nuclei in solution over the entire range of motion. On the basis of this theoretical framework, we discuss general features of quadrupole-central-transition (QCT) NMR, which is a particularly powerful method of studying biomolecules in the slow motion regime. Then we review recent advances in ¹⁷O QCT NMR studies of biological macromolecules in aqueous solution. The second part of the review is concerned with solid-state ¹⁷O NMR studies of organic and biological molecules. As a sequel to the previous review on the same subject [G. Wu, Prog. Nucl. Magn. Reson. Spectrosc. 52 (2008) 118-169], the current review provides a complete coverage of the literature published since 2008 in this area.

High-Resolution 17O NMR Spectroscopy of Structural Water

The importance of studying site-specific interactions of structurally similar water molecules in complex systems is well known. We demonstrate the ability to resolve four distinct bound water environments within the crystal structure of lanthanum magnesium nitrate hydrate via 17O solid state nuclear magnetic resonance (NMR) spectroscopy. Using high-resolution multidimensional experiments at high magnetic fields (18.8-35.2 T), each individual water environment was resolved. The quadrupole coupling constants and asymmetry parameters of the 17O of each water were determined to be between 6.6 and 7.1 MHz, 0.83 and 0.90, respectively. The resolution of the four unique, yet similar, structural waters within a hydrated crystal via 17O NMR spectroscopy demonstrates the ability to decipher the unique electronic environment of structural water within a single hydrated crystal structure.

Investigating FAM-N pulses for signal enhancement in MQMAS NMR of quadrupolar nuclei

Although a popular choice for obtaining high-resolution solid-state NMR spectra of quadrupolar nuclei, the inherently low sensitivity of the multiple-quantum magic-angle spinning (MQMAS) experiment has limited its application for nuclei with low receptivity or when the available sample volume is limited. A number of methods have been introduced in the literature to attempt to address this problem. Recently, we have introduced an alternative, automated approach, based on numerical simulations, for generating amplitude-modulated pulses (termed FAM-N pulses) to enhance the efficiency of the triple- to single-quantum conversion step within MQMAS. This results in efficient pulses that can be used without experimental reoptimisation, ensuring that this method is particularly suitable for challenging nuclei and systems. In this work, we investigate the applicability of FAM-N pulses to a wider variety of systems, and their robustness under more challenging experimental conditions. These include experiments performed under fast MAS, nuclei with higher spin quantum numbers, samples with multiple distinct sites, low-γ nuclei and nuclei subject to large quadrupolar interactions.

Adiabatic sweep cross-polarization magic-angle-spinning NMR of half-integer quadrupolar spins

The use of frequency-swept radiofrequency (rf) pulses for enhancing signals in the magic-angle spinning (MAS) spectra of half-integer quadrupolar nuclides was explored. The broadband adiabatic inversion cross-polarization magic-angle spinning (BRAIN-CPMAS) method, involving an adiabatic inversion pulse on the S-channel and a simultaneous rectangular spin-lock pulse on the I-channel (¹H), was applied to I(1/2)→S(3/2) systems. Optimal BRAIN-CPMAS matching conditions were found to involve low rf pulse strengths for both the I- and S-spin channels. At these low and easily attainable rf field strengths, level-crossing events among the energy levels |3/2〉,|1/2〉,|-1/2〉,|-3/2〉 that are known to complicate the CPMAS of quadrupolar nuclei, are mostly avoided. Zero- and double-quantum polarization transfer modes, akin to those we have observed for I(1/2)→S(1/2) polarization transfers, were evidenced by these analyses even in the presence of the quadrupolar interaction. ¹H-²³Na and ¹H-¹¹B BRAIN-CPMAS conditions were experimentally explored on model compounds by optimizing the width of the adiabatic sweep, as well as the rf pulse powers of the ¹H and ²³Na/¹¹B channels, for different MAS rates. The experimental data obtained on model compounds containing spin-3/2 nuclides, matched well predictions from numerical simulations and from an average Hamiltonian theory model. Extensions to half-integer spin nuclides with higher spins and potential applications of this BRAIN-CPMAS approach are discussed.

A novel pulse scheme for multiple quantum excitation, SFAM to enhance the sensitivity of MQMAS experiments

The basic MQMAS sequence consists of two hard pulses, one excites the equilibrium population to MQ (Multiple Quantum) coherence, and the other converts back to detectable coherence after some evolution time t1 (Medek et al., 1995). Unfortunately the MQ excitation and conversion processes are very inefficient due to the nonlinear nature of MQ processes. MQ conversion (converting MQ back to detectable coherence) efficiency can significantly be enhanced with DFS (Double Frequency Sweep) or FAM (Fast Amplitude Modulation) type pulses instead of rectangular pulse irradiation (Goldbourt and Madhu, 2002). In contrary to conversion, it is more challenging to enhance MQ excitation in MQMAS experiments, since most methods result in distorted lineshapes (Goldbourt and Madhu, 2002; Lim and Grey, 1998). In the present work MQ excitation of single crystals was studied, and the understanding of the process led to a principle, which was extended to the excitation of powder samples as well. The resulting method was implemented into the MQMAS sequence to enhance MQ excitation of powder samples under MAS condition. The new sequence called SFAM (Shifted Fast Amplitude Modulation) can provide high enhancements at low RF powers (ϵ>4 at νrf=40 kHz) compared to rectangular pulses. Although simulated lineshapes of SFAM predict only minor deviations from ideal lineshapes, experimentally obtained lineshapes along the anisotropic dimension show rather strong distortions. SFAM is relatively simple to optimize, and shows robustness with respect to the miscalibration or inhomogeneity of the RF power as well as to other parameters of the pulse scheme. A good agreement was found between numerically and experimentally optimized parameters.

Structural study by solid-state (71)Ga NMR of thin film transistor precursors

Solid-state (71)Ga NMR was used to investigate the structures of several heterometallic Group 13 hydroxo-aquo clusters, [Ga13-xInx (μ3-OH)6(μ2-OH)18(H2O)24](NO3)15 which are envisioned for thin film transistors. The characterization of these clusters in the solid state provides additional information in understanding the synthesis, structure and speciation of these precursors for high-quality, ultrasmooth thin films. Yet important structural information regarding these clusters - including the exact composition, isomeric structure, and coordination environments - were unknown prior to this precise NMR spectroscopy study. These molecular species, termed "Ga13-xInx", contain three types of six-coordinate metal sites, with bridging OH(-) groups and H2O as capping ligands, and we report results on Ga7In6, Ga8In5, Ga10In3, Ga11In2, Ga12In1, and Ga13. Utilizing two magnetic fields (13.9 T and 21.1 T), the solid-state NMR spectra were interpreted in conjunction with computational modeling (using CASTEP) and simulation of spectral lineshapes (using Dmfit). The metal sites are best represented as distorted octahedra, and they exhibit a range of quadrupolar couplings and asymmetry parameters, which can be addressed using longitudinal strain analysis. Until now, there has been speculation about the sites for transmetallation within the synthetic cluster community. Here, we show that Ga NMR is a powerful technique to monitor the transmetallation of In for Ga in the Ga13-xInx clusters, specifically substituting in the "outer ring" sites, and not the "core" or "middle ring".

Structural Insights into Bound Water in Crystalline Amino Acids: Experimental and Theoretical (17)O NMR

We demonstrate here that the (17)O NMR properties of bound water in a series of amino acids and dipeptides can be determined with a combination of nonspinning and magic-angle spinning experiments using a range of magnetic field strengths from 9.4 to 21.1 T. Furthermore, we propose a (17)O chemical shift fingerprint region for bound water molecules in biological solids that is well outside the previously determined ranges for carbonyl, carboxylic, and hydroxyl oxygens, thereby offering the ability to resolve multiple (17)O environments using rapid one-dimensional NMR techniques. Finally, we compare our experimental data against quantum chemical calculations using GIPAW and hybrid-DFT, finding intriguing discrepancies between the electric field gradients calculated from structures determined by X-ray and neutron diffraction.

A 3D experiment that provides isotropic homonuclear correlations of half-integer quadrupolar nuclei

Two 3D experiments, capable of producing enhanced resolution two-spin double-quantum (DQ) homonuclear correlations for half-integer quadrupolar nuclei, are described. The first uses a split-t1 MQMAS sequence followed by a sandwiched oR(3) symmetry-based dipolar recoupling sequence to directly excite DQ coherences. In this case an isotropic single-quantum (SQ) coherence starts the homonuclear DQ excitation. In the second experiment a single strong pulse is used to create triple quantum (TQ) coherence followed by a further single pulse conversion to zero-order before a non-sandwiched oR(3) DQ sequence. The first experiment is demonstrated using (87)Rb in RbNO3, with three Rb sites in a ∼5ppm range, and the second to (11)B in caesium triborate, CsB3O5, with two three-coordinated sites separated by ∼2ppm and one four-coordinated boron site. In both cases, all sites are clearly resolved and their connections observed. The second experiment has higher sensitivity and a good signal to noise is obtained in a reasonable time despite the long T1 relaxation time of (11)B in this material.

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.

Understanding multi-quantum NMR through secular approximation

With the development of technology and improved understanding of nuclear spin-spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between "Secular-Approximation" (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.

The combined effect of quadrupolar and dipolar interactions on the excitation and evolution of triple quantum coherences in ⁷Li solid state magic angle spinning NMR

Magic-angle spinning triple-quantum NMR spectra of lithium-7 provide enhanced spectral dispersion for the inherent low chemical shift range of this nucleus, while maintaining linewidths, which are free of any quadrupolar broadening to first order. Since the quadrupolar interaction of (7)Li is very small, in the order of the radio frequency nutation frequencies and only moderately larger than the spinning rates, such spectra are also only marginally affected by the second order quadrupolar interaction under large magnetic fields. In the current study we demonstrate that the existence of two and more proximate (7)Li spins, as encountered in many materials, affects both excitation and evolution of triple-quantum coherences due to the combined effect of quadrupolar and homonuclear dipolar interactions. We show that the generation of (7)Li triple-quantum coherences using two π/2 pulses separated by one-half rotor period is superior in such cases to a single pulse excitation since the excitation time is shorter; thus the maximum signal is only marginally affected by the homonuclear dipolar couplings. When the quadrupolar-dipolar cross terms dominate the spectra, single- and triple-quantum lineshapes are very similar and therefore a true gain in dispersion is maintained in the latter spectrum. The effects of quadrupolar-dipolar cross terms are experimentally demonstrated by comparing a natural abundance and a (6)Li-diluted samples of lithium acetate, resulting in the possibility of efficient excitation of triple quantum coherences over longer periods of time, and in longer life times of triple-quantum coherences.

Dynamic Nuclear Polarization of Oxygen-17

Oxygen-17 detected DNP NMR of a water/glycerol glass enabled an 80-fold enhancement of signal intensities at 82 K, using the biradical TOTAPOL. The >6,000-fold savings in acquisition time enables (17)O-(1)H distance measurements and heteronuclear correlation experiments. These experiments are the initial demonstration of the feasibility of DNP NMR on quadrupolar (17)O.

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

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

Two-dimensional MAS NMR correlation protocols involving double-quantum filtering of quadrupolar spin-pairs

Three two-dimensional (2D) NMR homonuclear correlation techniques invoking double-quantum (2Q) filtration of the central transitions of half-integer spins are evaluated numerically and experimentally. They correlate directly detected single-quantum (1Q) coherences in the t(2) domain with either of 1Q, two-spin 2Q or single-spin multiple-quantum coherence-evolutions in the indirect (t(1)) dimension. We employ experimental (23)Na and (27)Al NMR on sodium sulfite and the natural mineral sillimanite (SiAl(2)O(5)), in conjunction with simulated 2D spectra from pairs of dipolar-recoupled spins-3/2 and 5/2 at different external magnetic fields, to compare the correlation strategies from the viewpoints of 2D spectral resolution, signal sensitivity, implementational aspects and their relative merits for establishing internuclear proximities and quadrupolar tensor orientations.

Improving sensitivity and resolution of MQMAS spectra: a 45Sc-NMR case study of scandium sulphate pentahydrate

To efficiently obtain multiple-quantum magic-angle spinning (MQMAS) spectra of the nuclide 45Sc (I=7/2), we have combined several previously suggested techniques to enhance the signal-to-noise ratio and to improve spectral resolution for the test sample, scandium sulphate pentahydrate (ScSPH). Whereas the 45Sc-3QMAS spectrum of ScSPH does not offer sufficient resolution to clearly distinguish between the 3 scandium sites present in the crystal structure, these sites are well-resolved in the 5QMAS spectrum. The loss of sensitivity incurred by using MQMAS with 5Q coherence order is partly compensated for by using fast-amplitude modulated (FAM) sequences to improve the efficiency of both 5Q coherence excitation and conversion. Also, heteronuclear decoupling is employed to minimise dephasing of the 45Sc signal during the 5Q evolution period due to dipolar couplings with the water protons in the ScSPH sample. Application of multi-pulse decoupling schemes such as TPPM and SPINAL results in improved sensitivity and resolution in the F(1) (isotropic) dimension of the 5QMAS spectrum, the best results being achieved with the recently suggested SW(f)-TPPM sequence. By numerical fitting of the 45Sc-NMR spectra of ScSPH from 3QMAS, 5QMAS and single-quantum MAS at magnetic fields B(0)=9.4 T and 17.6 T, the isotropic chemical shift delta(iso), the quadrupolar coupling constant chi, and the asymmetry parameter eta were obtained. Averaging over all experiments, the NMR parameters determined for the 3 scandium sites, designated (a), (b) and (c) are: delta(iso)(a)=-15.5+/-0.5 ppm, chi(a)=5.60+/-0.10 MHz, eta(a)=0.06+/-0.05; delta(iso)(b)=-12.9+/-0.5 ppm, chi(b)=4.50+/-0.10 MHz, eta(b)=1.00+/-0.00; and delta(iso)(c)=-4.7+/-0.2 ppm, chi(c)=4.55+/-0.05 MHz, eta(c)=0.50+/-0.02. The NMR scandium species were assigned to the independent crystallographic sites by evaluating their experimental response to proton decoupling, and by density functional theory (DFT) calculations using the PAW and GIPAW approaches, in the following way: Sc(1) to (c), Sc(2) to (a), and Sc(3) to (b). The need to compute NMR parameters using an energy-optimised crystal structure is once again demonstrated.

Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.

Application of shaped adiabatic pulses to MQMAS NMR spectroscopy of spin 3/2 nuclei

Competition between nutation (r.f. driven) and adiabatic (rotor-driven) multi-quantum coherence transfer mechanisms in spin 3/2 systems results in diminished performance of rotation induced adiabatic coherence transfer (RIACT) in isotropic multiple-quantum magic-angle spinning (MQMAS) experiments for small e(2)qQ/h (<2 MHz) and high radio-frequency powers. We present a simple shaped RIACT pulse consisting of a truncated sine wave (spanning 0-0.8pi) that corrects the sensitivity losses, phase twist and relative intensity errors that can arise in MQMAS spectra utilizing constant-amplitude RIACT pulses. The shaped RIACT pulse may enhance the study of metals in biomolecules where quadrupole couplings of S=3/2 nuclei such as (23)Na tend to be small.

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in solid-state NMR of spin-7/2 nuclei

We here investigate the sensitivity enhancement of central-transition NMR spectra of quadrupolar nuclei with spin-7/2 in the solid state, generated by fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM). Considerable intensity is gained for the central-transition resonance of single-quantum spectra by means of spin population transfer from the satellite transitions, both under static and magic-angle-spinning (MAS) conditions. It is also shown that incorporation of a SW-FAM train into the excitation part of a 7QMAS sequence improves the efficiency of 7Q coherence generation, resulting in improved signal-to-noise ratio. The application of FAM-type pulse trains may thus facilitate faster spectra acquisition of spin-7/2 systems.

Measurement of through-space connectivities between spin-1/2 and quadrupolar nuclei in solid-state NMR: the TEDOR-MQMAS method

We present the transferred echo double-resonance multiple-quantum MAS (TEDOR-MQMAS) method that allows to analyze under high resolution the through-bond connectivities between spin-1/2 and quadrupolar nuclei. This method avoids some of the limitations related to the spin-lock of half-integer quadrupolar nuclei under MAS. However, the losses observed during the TEDOR transfer are related to the T'(2) constants, and they may thus be more important than those observed during the CP-MAS transfer, which are related to T(1rho) > T'(2).

Use of SPAM and FAM pulses in high-resolution MAS NMR spectroscopy of quadrupolar nuclei

The merits of SPAM and FAM pulses for enhancing the conversion of triple- to single-quantum coherences in the two-dimensional MQMAS experiment are compared using (87)Rb (spin I=3/2) and (27)Al (I=5/2) NMR of crystalline and amorphous materials. Although SPAM pulses are more easily optimized, our experiments and simulations suggest that FAM pulses yield greater signal intensity in all cases. In conclusion, we argue that, as originally suggested, SPAM and FAM pulses are best implemented in phase-modulated whole-echo MQMAS experiments and that the use of SPAM pulses to record separate echo and antiecho data sets, which are then combined, generally yields lower signal-to-noise ratios.

Spin-locking and recoupling of homonuclear dipolar interaction between spin-3/2 nuclei under magic-angle sample spinning

Numerical simulations and experiments were used to examine the possibility of employing strong spin-lock fields for recoupling of homonuclear dipolar interactions between spin-3/2 quadrupolar nuclei and to compare it to the rotary-resonance recoupling at weak spin-lock fields. It was shown that strong spin-lock pulses under MAS conditions can lead to recoupling, provided that the electric-field gradient principal axes systems of the coupled nuclei are aligned and that their quadrupolar coupling constants are approximately the same. The phenomenon is based on the fact that strong spin-lock pulses induce adiabatic transfer of magnetization between the central-transition coherence and the triple-quantum coherence with equal periodicity as is the periodicity of the time-dependent dipolar coupling. Because of the synchronous variation of the state of the spin system and of the dipolar interaction, the effect of the latter on the central-transition coherence and on the triple-quantum coherence is not averaged out by sample rotation. The approach is, however, very sensitive to the relative orientation of the electric-field gradient principal axes systems and therefore less robust than the approach based on weak spin-lock pulses that satisfy rotary-resonance condition.

Cross polarization from spins I=1∕2 to spins S=1 in nuclear magnetic resonance with magic angle sample spinning

Spin locking of the nuclear magnetization of a spin with S=1 such as deuterium in the presence of a radio-frequency field under magic angle spinning (MAS) is described in terms of adiabatic modulations of the energy levels. In a brief initial period, part of the initial density operator nutates about the Hamiltonian and is dephased. The remaining spin-locked state undergoes persistent oscillatory transfer processes between various coherences with a periodicity given by the rotation of the sample. While all crystallites in the powder undergo such periodic transfer processes, the phases of the oscillations depend on the angle gamma of the crystallites. The angle gamma is the azimuthal angle defining the orientation of the unique axis of the quadrupolar interaction tensor in a rotor-fixed frame. The theory is extended to describe cross-polarization between spins S=1 and I=12 under MAS. There are four distinct Hartmann-Hahn matching conditions that correspond to four zero-quantum matching conditions, all of which are shifted and broadened compared to their spin S=12 counterparts. These matching conditions are further split into a family of sideband conditions separated by the spinning frequency. The theory allows the calculation of both shifts and broadening factors of the matching conditions, as verified by simulations and experiments.