Symmetry pathways in solid-state NMR

Simulating multipulse NMR spectra of polycrystalline solids in the frequency domain

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated.

Multipurpose Broadband NMR Inversion Sequences

Solution-state 2D correlation experiments increase signal-to-noise, provide improved resolution, and inform about molecular connectivity. NMR experiments are compromised when the nuclei have broad chemical shift ranges that exceed the bandwidth of the experiment. Spectra acquired under these conditions are unphasable and artifact-prone, and peaks may disappear from the spectrum altogether. Existing remedies provide usable spectra only in specific experimental contexts. Here, we introduce a general broadband strategy that leads to a library of high performing NMR experiments. We achieve arbitrary and independent evolution of NMR interactions by only changing delays in our pulse block, letting the block replace inversion elements in any NMR experiment. The experiments improve the experimental bandwidth for both nuclei by an order of magnitude over conventional sequences, covering chemical shift ranges of most molecules, even at ultrahigh field. This library enables robust spectroscopy of molecules such as perfluorinated oils (¹⁹F{¹³C}) and fluorophosphorous compounds in battery electrolytes (¹⁹F{³¹P}).

Machine Learning Full NMR Chemical Shift Tensors of Silicon Oxides with Equivariant Graph Neural Networks

The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Recently, machine learning has been applied to NMR in the prediction of isotropic chemical shifts from a structure. Current machine learning models, however, often ignore the full chemical shift tensor for the easier-to-predict isotropic chemical shift, effectively ignoring a multitude of structural information available in the NMR chemical shift tensor. Here we use an equivariant graph neural network (GNN) to predict full ²⁹Si chemical shift tensors in silicate materials. The equivariant GNN model predicts full tensors to a mean absolute error of 1.05 ppm and is able to accurately determine the magnitude, anisotropy, and tensor orientation in a diverse set of silicon oxide local structures. When compared with other models, the equivariant GNN model outperforms the state-of-the-art machine learning models by 53%. The equivariant GNN model also outperforms historic analytical models by 57% for isotropic chemical shift and 91% for anisotropy. The software is available as a simple-to-use open-source repository, allowing similar models to be created and trained with ease.

Half-integer-spin quadrupolar nuclei in magic-angle spinning paramagnetic NMR: The case of NaMnO2

A combination of solid-state NMR methods for the extraction of ²³Na shift and quadrupolar parameters in the as-synthesized, structurally complex NaMnO₂ Na-ion cathode material, under magic-angle spinning (MAS) is presented. We show that the integration of the Magic-Angle Turning experiment with Rotor-Assisted Population transfer (RAPT) can be used both to identify shifts and to extract a range of magnitudes for their quadrupolar couplings. We also demonstrate the applicability of the two-dimensional one pulse (TOP) based double-sheared Satellite Transition Magic-Angle Spinning (TOP-STMAS) showing how it can yield a spectrum with separated shift and second-order quadrupolar anisotropies, which in turn can be used to analyze a quadrupolar lineshape free of anisotropic bulk magnetic susceptibility (ABMS) induced shift dispersion and determine both isotropic shift and quadrupolar products. Combining all these experiments, the shift and quadrupolar parameters for all observed Na environments were extracted and yielded excellent agreement with the density functional theory (DFT) based models that were reported in previous literature. We expect these methods to open the door for new possibilities for solid-state NMR to probe half-integer quadrupolar nuclei in paramagnetic materials and other systems exhibiting large shift dispersion.

Silicon-29 echo train coherence lifetimes and geminal 2J-couplings in network modified silicate glasses

The natural abundance ²⁹Si echo-train coherence lifetimes in network-modified silicate glasses were examined under static and magic-angle spinning (MAS) conditions. The nuclear magnetic properties of modifier cations were found to play a major role in determining ²⁹Si coherence lifetimes, leading to differences as large as three orders of magnitude. In compositions with abundant NMR active nuclei, such as alkali silicates, the ²⁹Si coherence lifetimes are dominated by coherent dephasing due to residual heteronuclear dipolar couplings, whereas in compositions dilute in NMR active nuclei, such as alkaline earth silicates, the ²⁹Si coherence lifetimes are dominated by incoherent dephasing due to paramagnetic impurities. Expressing the inverse of the coherence lifetime as a residual full width at half maximum (FWHM), we found that increasing rates of both MAS and a π-pulse train are effective in removing the residual ²⁹Si heteronuclear broadenings, with a near-linear relationship between FWHM and MAS rotor period and π-pulse spacing. Based on these results, we conclude that accurate ²⁹Si J coupling measurements will be the most challenging in lithium silicate glasses due to strong homonuclear dipolar couplings among ⁷Li nuclei, requiring MAS speeds up to 100 kHz, and be the least challenging in the alkaline earth silicate glasses. At a modest MAS speed of 14kHz, distributions of geminal J couplings across Si-O-Si linkages were measured in alkali and alkaline earth silicate glasses giving mean values of 4.2Hz and 5.1Hz in 0.4 CaO·0.6 SiO₂ and 0.33 Ba₂O·0.67 SiO₂ glasses, respectively, and 5.2Hz and 5.3Hz in 0.33 Na₂O·0.67 SiO₂ and 0.33 K₂O·0.67 SiO₂ glasses, respectively. We also observe greater variance in the J distributions of alkaline earth silicate glasses consistent with greater structural disorder due to increased modifier cation potential, i.e., the charge-to-radius ratio, Z/r of the cation.

NMR spectroscopy of coin cell batteries with metal casings

Battery cells with metal casings are commonly considered incompatible with nuclear magnetic resonance (NMR) spectroscopy because the oscillating radio-frequency magnetic fields (“rf fields”) responsible for excitation and detection of NMR active nuclei do not penetrate metals. Here, we show that rf fields can still efficiently penetrate nonmetallic layers of coin cells with metal casings provided “B₁ damming” configurations are avoided. With this understanding, we demonstrate noninvasive high-field in situ ⁷Li and ¹⁹F NMR of coin cells with metal casings using a traditional external NMR coil. This includes the first NMR measurements of an unmodified commercial off-the-shelf rechargeable battery in operando, from which we detect, resolve, and separate ⁷Li NMR signals from elemental Li, anodic β-LiAl, and cathodic Li_xMnO₂ compounds. Real-time changes of β-LiAl lithium diffusion rates and variable β-LiAl ⁷Li NMR Knight shifts are observed and tied to electrochemically driven changes of the β-LiAl defect structure.

Separation of quadrupolar and paramagnetic shift interactions in high-resolution nuclear magnetic resonance of spinning powders

Separation and correlation of the shift anisotropy and the first-order quadrupolar interaction of spin I = 1 nuclei under magic-angle spinning (MAS) are achieved by the phase-adjusted spinning sideband (PASS) nuclear magnetic resonance (NMR) experiment. Compared to methods for static samples, this approach has the benefit of higher sensitivity and resolution. Moreover, the PASS experiment has the advantage over previous MAS sequences in the ability to completely separate the shift anisotropy and first-order quadrupolar interactions. However, the main drawback of the pulse sequence is the lower excitation bandwidth. The sequence is comprehensively evaluated using theoretical calculations and numerical simulations and applied experimentally to the ²H NMR of a range of paramagnetic systems: deuterated nickel(II) acetate tetrahydrate, deuterated copper(II) chloride dihydrate, and two forms of deuterated oxyhydride ion conductor BaTiO_3-xH_y. Our results show that despite the issue with broadband excitation, the extracted shift and quadrupolar interaction tensors and the Euler angles relating the two tensors match well with the NMR parameters obtained with static NMR methods. Therefore, the new application of the PASS experiment is an excellent addition to the arsenal of NMR experiments for ²H and potentially ¹⁴N in paramagnetic solids.

A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation

For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the paramagnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J.Magn.Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to predict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation.

Separated quadrupole and shift interactions of 2H NMR spectra in paramagnetic solids by asymmetric pulse sequences

Separated pure-quadrupole (PQ) and -shift (PS) spectra of ²H nuclear magnetic resonance (NMR) of paramagnetic solids are obtained and correlated by simple pulse sequences that can acquire the full magnetization under ideal conditions. Two-dimensional NMR signals obtained using an asymmetric π-pulse-inserted quadrupole-echo (APIQE) sequence yielded separated spectra through the skew operation of an affine transform (AT) before a Fourier transform. Modified APIQE sequences that acquire whole echo signals were fabricated, and separated PQ and PS spectra were obtained by applying a combination of AT, such as rotation and skew operations, to the signal data. These methods were demonstrated for diamagnetic Zn(CD₃CO₂)₂⋅2H₂O and paramagnetic Nd(CD₃CO₂)₃⋅1.5H₂O. Further, the dynamics of the D₂O molecule and [Co(D₂O)₆]²⁺ ion in paramagnetic CoSiF₆⋅6D₂O was analyzed based on the temperature dependence of the separated spectra.

Low-power synchronous helical pulse sequences for large anisotropic interactions in MAS NMR: Double-quantum excitation of 14N

We develop a theoretical framework for a class of pulse sequences in the nuclear magnetic resonance (NMR) of rotating solids, which are applicable to nuclear spins with anisotropic interactions substantially larger than the spinning frequency, under conditions where the radiofrequency amplitude is smaller than or comparable to the spinning frequency. The treatment is based on average Hamiltonian theory and allows us to derive pulse sequences with well-defined relationships between the pulse parameters and spinning frequency for exciting specific coherences without the need for any detailed calculations. This framework is applied to the excitation of double-quantum spectra of ¹⁴N and is used both to evaluate the existing low-power pulse schemes and to predict the new ones, which we present here. It is shown that these sequences can be designed to be γ-encoded and therefore allow the acquisition of sideband-free spectra. It is also shown how these new double-quantum excitation sequences are incorporated into heteronuclear correlation NMR, such as ¹H-¹⁴N dipolar double-quantum heteronuclear multiple-quantum correlation spectroscopy. The new experiments are evaluated both with numerical simulations and experiments on glycine and N-acetylvaline, which represent cases with "moderate" and "large" quadrupolar interactions, respectively. The analyzed pulse sequences perform well for the case of a "moderate" quadrupolar interaction, however poorly with a "large" quadrupolar interaction, for which future work on pulse sequence development is necessary.

Separation of quadrupolar and paramagnetic shift interactions with TOP-STMAS/MQMAS in solid-state lighting phosphors

A new approach for processing satellite-transition magic-angle spinning (STMAS) and multiple-quantum magic-angle spinning (MQMAS) data, based on the two-dimensional one-pulse (TOP) method, which separates the second-rank quadrupolar anisotropy and paramagnetic shift interactions via a double shearing transformation, is described. This method is particularly relevant in paramagnetic systems, where substantial inhomogeneous broadening may broaden the lineshapes. Furthermore, it possesses an advantage over the conventional processing of MQMAS and STMAS spectra because it overcomes the limitation on the spectral width in the indirect dimension imposed by rotor synchronization of the sampling interval. This method was applied experimentally to the 27 Al solid-state nuclear magnetic resonance of a series of yttrium aluminum garnets (YAGs) doped with different lanthanide ions, from which the quadrupolar parameters of paramagnetically shifted and bulk unshifted sites were extracted. These parameters were then compared with density functional theory calculations, which permitted a better understanding of the local structure of Ln substituent ions in the YAG lattice.

Statistical learning of NMR tensors from 2D isotropic/anisotropic correlation nuclear magnetic resonance spectra

Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state nuclear magnetic resonance (NMR) spectrum containing multiple overlapping anisotropic subspectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the truncated singular value decomposition and the smooth least absolute shrinkage and selection operator based regularization methods, which (a) stabilize the solution and (b) promote sparsity and smoothness in the solution. We also propose an unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this article, we provide the details of the linear-inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic and experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.

Enabling Natural Abundance 17O Solid-State NMR by Direct Polarization from Paramagnetic Metal Ions

Dynamic nuclear polarization (DNP) significantly enhances the sensitivity of nuclear magnetic resonance (NMR), increasing its applications and the quality of NMR spectroscopy as a characterization tool for materials. Efficient spin diffusion among the nuclear spins is considered to be essential for spreading the hyperpolarization throughout the sample, enabling large DNP enhancements. This scenario mostly limits the polarization enhancement of low-sensitivity nuclei in inorganic materials to the surface sites when the polarization source is an exogenous radical. In metal-ion-based DNP, the polarization agents are distributed in the bulk sample and act as a source of both relaxation and polarization enhancement. We have found that as long as the polarization agent is the main source of relaxation, the enhancement does not depend on the distance between the nucleus and dopant. As a consequence, the requirement of efficient spin diffusion is lifted, and the entire sample can be directly polarized. We exploit this finding to measure high-quality NMR spectra of ¹⁷O in the electrode material Li₄Ti₅O₁₂ doped with Fe(III) despite its low abundance and long relaxation time.

Quantification of Uncoupled Spin Domains in Spin-Abundant Disordered Solids

Materials often contain minor heterogeneous phases that are difficult to characterize yet nonetheless significantly influence important properties. Here we describe a solid-state NMR strategy for quantifying minor heterogenous sample regions containing dilute, essentially uncoupled nuclei in materials where the remaining nuclei experience heteronuclear dipolar couplings. NMR signals from the coupled nuclei are dephased while NMR signals from the uncoupled nuclei can be amplified by one or two orders of magnitude using Carr-Meiboom-Purcell-Gill (CPMG) acquisition. The signal amplification by CPMG can be estimated allowing the concentration of the uncoupled spin regions to be determined even when direct observation of the uncoupled spin NMR signal in a single pulse experiment would require an impractically long duration of signal averaging. We use this method to quantify residual graphitic carbon using 13C CPMG NMR in poly(carbon monofluoride) samples synthesized by direct fluorination of carbon from various sources. Our detection limit for graphitic carbon in these materials is better than 0.05 mol%. The accuracy of the method is discussed and comparisons to other methods are drawn.

Artefact-free broadband 2D NMR for separation of quadrupolar and paramagnetic shift interactions

Two new two-dimensional, broadband, solid-state NMR experiments for separating and correlating the quadrupolar and shift interactions of spin I=1 nuclei in paramagnetic systems are proposed. The new pulse sequences incorporate the short, high-power adiabatic pulses (SHAPs) into the shifting d-echo experiment of Walder et al. [J. Chem. Phys., 142, 014201 (2015)], in two different ways, giving double and quadruple adiabatic shifting d-echo sequences. These new experiments have the advantage over previous methods of both suppressing spectral artefacts due to pulse imperfections, and exhibiting a broader excitation bandwidth. Both experiments are analysed with theoretical calculations and simulations, and are applied experimentally to the ²H NMR of deuterated CuCl₂ ⋅2H₂O, and two deuterated samples of the ion conductor oxyhydride BaTiO_3-xH_y prepared using two different methods. For the CuCl₂ ⋅2H₂O sample, both new methods obtain very high-quality spectra from which the parameters describing the shift and quadrupolar interaction tensors, and their relative orientation, were extracted. The two BaTiO_3-xH_y samples exhibited different local hydride environments with different tensor parameters. The ²H spectra of these oxyhydrides exhibit inhomogeneous broadening of the ²H shifts, and so whilst the quadrupolar interaction parameters were easily extracted, the measurement of the shift parameters was more complex. However, effective shift parameters were extracted, which combine the effects of both the paramagnetic shift tensor and the inhomogeneous broadening.

Line narrowing in 1H NMR of powdered organic solids with TOP-CT-MAS experiments at ultra-fast MAS

The residual broadening observed in ¹H spectra of rigid organic solids at natural abundance under 111 kHz magic angle spinning (MAS) is typically a few hundred Hertz. Here we show that refocusable and non-refocusable interactions contribute roughly equally to this residual at high-fields (21.14 T), and suggest that the removal of the non-refocusable part will produce significant increase in spectral resolution. To this end, we demonstrate an experiment for the indirect acquisition of constant-time experiments at ultra-fast MAS (CT-MAS) which verifies this hypothesis. The combination of this experiment with the two-dimensional one pulse (TOP) transformation reduces the experimental time to a fraction of the original cost while retaining the narrowing effects. Results obtained with TOP-CT-MAS at 111 kHz MAS on a sample of β-AspAla yield up to 30% higher resolution spectra than the equivalent one-pulse experiment, in less than 10 min.

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.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Hydrogen motional disorder in crystalline iron group chloride dihydrates

The principal components and the relative orientation of the ²H paramagnetic shift and quadrupolar coupling tensors have been measured for the MCl₂·2D₂O family of compounds, M = Mn, Fe, Co, Ni, and Cu, using the two-dimensional shifting-d echo nuclear magnetic resonance experiment in order to determine (1) the degree of unpaired electron delocalization and (2) the number and location of crystallographically distinct hydrogen sites around oxygen and their fractional occupancies. Expressions for the molecular susceptibility of 3d ion systems, where the spin-orbit coupling is a weak perturbation onto the crystal field, are derived using the generalized Van Vleck equation and used to predict molecular susceptibilities. These predicted molecular susceptibilities are combined with various point dipole source configurations modeling unpaired electron delocalization to predict ²H paramagnetic shift tensors at potential deuterium sites. The instantaneous deuterium quadrupolar coupling and shift tensors are then combined with parameterized motional models, developed for trigonally (M = Mn, Fe, Co, and Cu) and pyramidally (M = Ni) coordinated D₂O ligands, to obtain the best fit of the experimental 2D spectra. Dipole sources placed onto metal nuclei with a small degree of delocalization onto the chlorine ligands yield good agreement with the experiment for M = Mn, Fe, Co, and Ni, while good agreement for CuCl₂·2D₂O is obtained with additional delocalization onto the oxygen. Our analysis of the salts with trigonally coordinated water ligands (M = Mn, Fe, Co, and Cu) confirms the presence of bisector flipping and the conclusions from neutron scattering measurements that hydrogen bonding to chlorine on two adjacent chains leads to the water molecule in the [M(D₂O)₂Cl₄] cluster being nearly coplanar with O-M-Cl involving the shortest metal-chlorine bonds of the cluster. In the case of NiCl₂·2D₂O, the experimental parameters were found to be consistent with a motional model where the D₂O ligands are pyramidally coordinated to the metal and undergo bisector flipping while the water ligand additionally hops between two orientations related by a 120° rotation about the Ni-O bond axis. The position of the three crystallographically distinct hydrogen sites in the unit cell was determined along with fractional occupancies. This restricted water ligand motion is likely due to van der Waals interactions and is concerted with the motion of neighboring ligands.

Low-power broadband solid-state MAS NMR of 14N

We propose two broadband pulse schemes for ¹⁴N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of ¹⁴N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum ¹⁴N correlation spectroscopy, and ¹H-¹⁴N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH₄)₂C₂O₄) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.

Correlating geminal 2JSi–O–Si couplings to structure in framework silicates

The dependence of a ²⁹Si geminal J coupling across the inter-tetrahedral linkage on local structure was examined using first-principles DFT calculations.

17O MAS NMR Correlation Spectroscopy at High Magnetic Fields

The structure of two protected amino acids, FMOC-l-leucine and FMOC-l-valine, and a dipeptide, N-acetyl-l-valyl-l-leucine (N-Ac-VL), were studied via one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy. Utilizing ¹⁷O magic-angle spinning (MAS) NMR at multiple magnetic fields (17.6-35.2 T/750-1500 MHz for ¹H) the ¹⁷O quadrupolar and chemical shift parameters were determined for the two oxygen sites of each FMOC-protected amino acids and the three distinct oxygen environments of the dipeptide. The one- and two-dimensional, ¹⁷O, ¹⁵N-¹⁷O, ¹³C-¹⁷O, and ¹H-¹⁷O double-resonance correlation experiments performed on the uniformly ¹³C,¹⁵N and 70% ¹⁷O-labeled dipeptide prove the attainability of ¹⁷O as a probe for structure studies of biological systems. ¹⁵N-¹⁷O and ¹³C-¹⁷O distances were measured via one-dimensional REAPDOR and ZF-TEDOR experimental buildup curves and determined to be within 15% of previously reported distances, thus demonstrating the use of ¹⁷O NMR to quantitate interatomic distances in a fully labeled dipeptide. Through-space hydrogen bonding of N-Ac-VL was investigated by a two-dimensional ¹H-detected ¹⁷O R³-R-INEPT experiment, furthering the importance of ¹⁷O for studies of structure in biomolecular solids.

(17)O NMR Investigation of Water Structure and Dynamics

The structure and dynamics of the bound water in barium chlorate monohydrate were studied with (17)O nuclear magnetic resonance (NMR) spectroscopy in samples that are stationary and spinning at the magic-angle in magnetic fields ranging from 14.1 to 21.1 T. (17)O NMR parameters of the water were determined, and the effects of torsional oscillations of the water molecule on the (17)O quadrupolar coupling constant (CQ) were delineated with variable temperature MAS NMR. With decreasing temperature and reduction of the librational motion, we observe an increase in the experimentally measured CQ explaining the discrepancy between experiments and predictions from density functional theory. In addition, at low temperatures and in the absence of (1)H decoupling, we observe a well-resolved (1)H-(17)O dipole splitting in the spectra, which provides information on the structure of the H2O molecule. The splitting arises because of the homogeneous nature of the coupling between the two (1)H-(17)O dipoles and the (1)H-(1)H dipole.

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.

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.

Sideband separation experiments in NMR with phase incremented echo train acquisition

A general approach for enhancing sensitivity of nuclear magnetic resonance sideband separation experiments, such as Two-Dimensional One Pulse (TOP), Magic-Angle Turning (MAT), and Phase Adjust Spinning Sidebands (PASS) experiments, with phase incremented echo-train acquisition (PIETA) is described. This approach is applicable whenever strong inhomogeneous broadenings dominate the unmodulated frequency resonances, such as in non-crystalline solids or in samples with large residual frequency anisotropy. PIETA provides significant sensitivity enhancements while also eliminating spectral artifacts would normally be present with Carr-Purcell-Meiboom-Gill acquisition. Additionally, an intuitive approach is presented for designing and processing echo train acquisition magnetic resonance experiments on rotating samples. Affine transformations are used to relate the two-dimensional signals acquired in TOP, MAT, and PASS experiments to a common coordinate system. Depending on sequence design and acquisition conditions two significant artifacts can arise from truncated acquisition time and discontinuous damping in the T2 decay. Here we show that the former artifact can always be eliminated through selection of a suitable affine transformation, and give the conditions in which the latter can be minimized or removed entirely.

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.