Overtone NMR spectroscopy

A facile approach for estimating radio-frequency field strength of low-receptivity nuclei

Radio-frequency (RF) field calibration is essential in NMR spectroscopy. A common practice is to collect a nutation curve by varying the pulse length in a direct single-pulse excitation experiment or in a cross-polarization magic-angle spinning with a flip-back pulse experiment. From the null points on this curve, one can calculate the RF field strength. Nevertheless, the practical implementation is not always straightforward or can even be unrealizable, especially for low-receptivity nuclei owing to their associated low sensitivity. Several researchers used an approach that involves utilizing other nuclei with more sensitivity but nearly identical Larmor frequencies to that of the nucleus of interest. However, such an approach has not been a common practice so far. In this work, we have systematically revisited this approach using 3.2 mm rotors on different sets of nuclei covering a Larmor frequency range up to 80 MHz. The effect of solid- and solution-states on RF field strength measurements has been investigated. The detection of each set of nuclei is then carried out with a resonant circuit in the NMR probe consisting of identical coils and capacitors. Our methodology is illustrated by recording 135/137Ba NMR spectra of BaTiO3 without prior 135/137Ba RF field calibration.

Detection of remote proton-nitrogen correlations by 1H-detected 14N overtone solid-state NMR at fast MAS

Detecting proton and nitrogen correlations in solid-state nuclear magnetic resonance (NMR) is important for the structural determination of biological and chemical systems. Recent advances in proton detection-based approaches under fast magic-angle spinning have facilitated the detection of ¹H-¹⁴N correlations by solid-state NMR. However, observing remote ¹H-¹⁴N correlations by these approaches is still a challenge, especially for ¹⁴N sites having large quadrupolar couplings. To address this issue, we introduce the ¹H-¹⁴N overtone continuous wave rotational-echo saturation-pulse double-resonance (¹H-¹⁴N OT CW-RESPDOR) sequence. Unlike regular 2D correlation experiments where the indirect dimension is recorded in the time domain, the ¹H-¹⁴N OT CW-RESPDOR experiment is directly observed in the frequency domain. A set of ¹H-¹⁴N OT CW-RESPDOR filtered ¹H spectra is recorded at varying ¹⁴N OT frequencies. Thanks to the selective nature of the ¹⁴N OT pulse, the filtered ¹H spectra appear only if the ¹⁴N OT frequency hits the positions of the ¹⁴N OT central band or one of the spinning sidebands. This set of filtered ¹H spectra represents a 2D ¹H-¹⁴N OT correlation map. We have also investigated the optimizable parameters for CW-RESPDOR and figured out that these parameters are not strictly needed for our working magnetic field of 14.1 T. Hence, the experiment is easy to set up and requires almost no optimization. We have demonstrated the experimental feasibility of ¹H-¹⁴N OT CW-RESPDOR on monoclinic L-histidine and L-alanyl L-alanine. The remote ¹H-¹⁴N correlations have been efficiently detected, no matter how large the ¹⁴N quadrupolar interaction is, and agree with the crystal structures. In addition, based on the remote ¹H-¹⁴N correlations from the non-protonated ¹⁴N site of L-histidine, we can unambiguously distinguish the orthorhombic and monoclinic forms.

Low-frequency excitation of singlet-triplet transitions. Application to nuclear hyperpolarization

Coupled pairs of nuclear spin-1/2 support one singlet state and three triplet states. Transitions between the singlet state and one of the triplet states may be driven by an oscillating low-frequency magnetic field, in the presence of couplings to a third nuclear spin, and a weak bias magnetic field. The oscillating field is in the same direction as the bias field and is called a WOLF (Weak Oscillating Low Field) pulse. Application of a WOLF pulse allows for the generation of strong nuclear hyperpolarization of ¹³C nuclei, starting from the nuclear singlet polarization of a ¹H spin pair, associated with the enriched para-spin isomer of hydrogen gas. Hyperpolarization is demonstrated for two molecular systems.

Selective 1H-14N Distance Measurements by 14N Overtone Solid-State NMR Spectroscopy at Fast MAS

Accurate distance measurements between proton and nitrogen can provide detailed information on the structures and dynamics of various molecules. The combination of broadband phase-modulated (PM) pulse and rotational-echo saturation-pulse double-resonance (RESPDOR) sequence at fast magic-angle spinning (MAS) has enabled the measurement of multiple 1H-14N distances with high accuracy. However, complications may arise when applying this sequence to systems with multiple inequivalent 14N nuclei, especially a single 1H sitting close to multiple 14N atoms. Due to its broadband characteristics, the PM pulse saturates all 14N atoms; hence, the single 1H simultaneously experiences the RESPDOR effect from multiple 1H-14N couplings. Consequently, no reliable H-N distances are obtained. To overcome the problem, selective 14N saturation is desired, but it is difficult because 14N is an integer quadrupolar nucleus. Alternatively, 14N overtone (OT) NMR spectroscopy can be employed owing to its narrow bandwidth for selectivity. Moreover, owing to the sole presence of two energy levels (m = ± 1), the 14N OT spin dynamics behaves similarly to that of spin-1/2. This allows the interchangeability between RESPDOR and rotational-echo double-resonance (REDOR) since their principles are the same except the degree of 14N OT population transfer; saturation for the former whereas inversion for the latter. As the ideal saturation/inversion is impractical due to the slow and orientation-dependent effective nutation of 14N OT, the working condition is usually an intermediate between REDOR and RESPDOR. The degree of 14N OT population transfer can be determined from the results of protons with short distances to 14N and then can be used to obtain long-distance determination of other protons to the same 14N site. Herein, we combine the 14N OT and REDOR/RESPDOR to explore the feasibility of selective 1H-14N distance measurements. Experimental demonstrations on simple biological compounds of L-tyrosine.HCl, N-acetyl-L-alanine, and L-alanyl-L-alanine were performed at 14.1 T and MAS frequency of 62.5 kHz. The former two consist of a single 14N site, whereas the latter consists of two 14N sites. The experimental optimizations and reliable fittings by the universal curves are described. The extracted 1H-14N distances by OT-REDOR are in good agreement with those determined by PM-RESPDOR and diffraction techniques.

Evaluation of excitation schemes for indirect detection of 14N via solid-state HMQC NMR experiments

It has previously been shown that ¹⁴N NMR spectra can be reliably obtained through indirect detection via HMQC experiments. This method exploits the transfer of coherence between single-(SQ) or double-quantum (DQ) ¹⁴N coherences, and SQ coherences of a suitable spin-1/2 'spy' nucleus, e.g., ¹H. It must be noted that SQ-SQ methods require a carefully optimized setup to minimize the broadening related to the first-order quadrupole interaction (i.e., an extremely well-adjusted magic angle and a highly stable spinning speed), whereas DQ-SQ ones do not. In this work, the efficiencies of four ¹⁴N excitation schemes (DANTE, XiX, Hard Pulse (HP), and Selective Long Pulse (SLP)) are compared using J-HMQC based numerical simulations and either SQ-SQ or DQ-SQ ¹H-{¹⁴N} D-HMQC experiments on l-histidine HCl and N-acetyl-l-valine at 18.8 T and 62.5 kHz MAS. The results demonstrate that both DANTE and SLP provide a more efficient ¹⁴N excitation profile than XiX and HP. Furthermore, it is shown that the SLP scheme: (i) is efficient over a large range of quadrupole interaction, (ii) is highly robust to offset and rf-pulse length and amplitude, and (iii) is very simple to set up. These factors make SLP ideally suited to widespread, non-specialist use in solid-state NMR analyses of nitrogen-containing materials.

Quantitative analysis of 14N quadrupolar coupling using 1H detected 14N solid-state NMR

Magic-angle spinning solid-state NMR is increasingly utilized to study the naturally abundant, spin-1 nucleus 14N, providing insights into the structure and dynamics of biological and organic molecules. In particular, the characterisation of 14N sites using indirect detection has proven useful for complex molecules, where the 'spy' nucleus provides enhanced sensitivity and resolution. Here we exploit the sensitivity of proton detection, to indirectly characterise 14N sites using a moderate rf field to generate coherence between the 1H and 14N at moderate and fast-magic-angle spinning frequencies. Efficient numerical simulations have been developed that have allowed us to quantitatively analyse the resulting 14N lineshapes to determine both the size and asymmetry of the quadrupolar interaction. Exploiting only naturally occurring abundant isotopes will aid the analysis of materials with the need to resort to isotope labelling, whilst providing additional insights into the structure and dynamics that the characterisation of the quadrupolar interaction affords.

14N overtone NMR under MAS: Signal enhancement using cross-polarization methods

Polarization transfer methods are widely adopted for the purpose of correlating different nuclear species as well as to achieve signal enhancement. Polarization transfer from ¹H to the ¹⁴N overtone transition (Δm = 2) can be achieved using cross polarization methods under magic-angle spinning conditions, where spin locks of the order of several milliseconds can be obtained on common bio-solids (α-glycine and N-acetylvaline). Signal enhancement factors up to 4.4 per scan, can be achieved under favorable conditions, despite MHz-sized quadrupolar interaction. Moreover, we present a detailed theoretical treatment and accurate numerical simulations which are in excellent agreement the unusual experimental matching conditions observed for cross-polarization to ¹⁴N overtone.

A one-dimensional solid-state NMR approach for 14NH/14NH overtone correlation through 1H/1H mixing under fast MAS

Homonuclear correlations are key to structural studies using solid-state NMR. In this contribution, using 14N overtone transition (OT) as a selective excitation approach, we propose a proton-detected one-dimensional (1D) 14NOT/14NOT/1H correlation solid-state NMR method mediated through 1H/1H mixing at fast magic angle spinning to achieve NH/NH proximities in naturally abundant samples. The proposed method is time efficient by a factor of ∼7.5 in comparison to the existing fundamental 14N frequency-based three-dimensional (3D) 14N/14N/1H correlation method.

14N overtone nuclear magnetic resonance of rotating solids

By irradiating and observing at twice the 14N Larmor frequency, overtone (OT) nuclear magnetic resonance (NMR) is capable of obtaining 14NOT spectra without first-order quadrupolar broadening. Direct excitation and detection of the usually "forbidden" double-quantum transition is mediated by the perturbation from the large quadrupole interaction to the spin states quantized by the Zeeman interaction. A recent study [L. A. O'Dell and C. I. Ratcliffe, Chem. Phys. Lett. 514, 168 (2011)] has shown that 14NOT NMR under magic-angle spinning (MAS) can yield high-resolution spectra with typical second-order quadrupolar line shapes allowing the measurement of 14N chemical shift and quadrupolar coupling parameters. This article has also shown that under MAS the main 14NOT peak is shifted by twice the sample spinning frequency with respect to its static position. We present the theory of 14NOT NMR of static or rotating samples and the physical picture of the intriguing spinning-induced shift in the second case. We use perturbation theory for the case of static samples and Floquet theory for rotating samples. In both cases, the results can be described by a so-called OT parameter that scales down the 14NOT radio-frequency (rf) excitation and signal detection. This OT parameter shows that the components of the rf field, which are transverse and longitudinal with respect to the magnetic field, are both effective for 14NOTrf excitation and signal detection. In the case of MAS at angular frequency ωr , the superposition of the excitation and detection components in the OT parameter makes either the +2ωr or -2ωr term the dominant 14NOT signal, depending on the sense of sample spinning with respect to the magnetic field. This leads to an apparent 14NOT signal shifted at twice the spinning frequency. The features of 14NOT NMR spectra for both static and rotating samples are illustrated with simulations. The spinning induced shift and its dependence on the spinning direction are confirmed experimentally by reversing the spinning direction and the field of the 36 T series-connected hybrid magnet at the US National High Magnetic Field Laboratory.

DNP-enhanced solid-state NMR spectroscopy of active pharmaceutical ingredients

Solid-state NMR spectroscopy has become a valuable tool for the characterization of both pure and formulated active pharmaceutical ingredients (APIs). However, NMR generally suffers from poor sensitivity that often restricts NMR experiments to nuclei with favorable properties, concentrated samples, and acquisition of one-dimensional (1D) NMR spectra. Here, we review how dynamic nuclear polarization (DNP) can be applied to routinely enhance the sensitivity of solid-state NMR experiments by one to two orders of magnitude for both pure and formulated APIs. Sample preparation protocols for relayed DNP experiments and experiments on directly doped APIs are detailed. Numerical spin diffusion models illustrate the dependence of relayed DNP enhancements on the relaxation properties and particle size of the solids and can be used for particle size determination when the other factors are known. We then describe the advanced solid-state NMR experiments that have been enabled by DNP and how they provide unique insight into the molecular and macroscopic structure of APIs. For example, with large sensitivity gains provided by DNP, natural isotopic abundance, ¹³ C-¹³ C double-quantum single-quantum homonuclear correlation NMR spectra of pure APIs can be routinely acquired. DNP also enables solid-state NMR experiments with unreceptive quadrupolar nuclei such as ² H, ¹⁴ N, and ³⁵ Cl that are commonly found in APIs. Applications of DNP-enhanced solid-state NMR spectroscopy for the molecular level characterization of low API load formulations such as commercial tablets and amorphous solid dispersions are described. Future perspectives for DNP-enhanced solid-state NMR experiments on APIs are briefly discussed.

Double cross polarization for the indirect detection of nitrogen-14 nuclei in magic angle spinning NMR spectroscopy

Nitrogen-14 NMR spectra at fast magic-angle spinning rates can be acquired indirectly by means of two-dimensional techniques based on double cross polarization transfer ¹H → ¹⁴N →¹H. Experimental evidence is given for polycrystalline samples of glycine, l-histidine, and the dipeptide Ala-Gly. Either one-bond or long-range correlations can be favored by choosing the length of the cross polarization contact pulses. Longer contact pulses allow the detection of unprotonated nitrogen sites. In contrast to earlier methods that exploited second-order quadrupolar/dipolar cross-terms, cross polarization operates in the manner of the method of Hartmann and Hahn, even for ¹⁴N quadrupolar couplings up to 4 MHz. Simulations explain why amorphous samples tend to give rise to featureless spectra because the ¹⁴N quadrupolar interactions may vary dramatically with the lattice environment. The experiments are straightforward to set up and are shown to be effective for different nitrogen environments and robust with respect to the rf-field strengths and to the ¹⁴N carrier frequency during cross polarization. The efficiency of indirect detection of ¹⁴N nuclei by double cross polarization is shown to be similar to that of isotopically enriched ¹³C nuclei.

Indirect detection of 10B (I = 3) overtone NMR at very fast magic angle spinning

The application of overtone nuclear magnetic resonance (OT NMR) to symmetric spin transitions of integer quadrupolar nuclei is of considerable interest since this transition is immune to the first-order quadrupolar interaction, thus resulting in narrow NMR lines. Owing to its roles in nature and its high natural abundance, ¹⁴N (I = 1) OT NMR has been explored, in which the indirect and/or direct acquisitions of ¹⁴N OT were experimentally demonstrated. However, other than ¹⁴N nucleus, no OT NMR observation of other integer quadrupolar nuclei has been reported in the literature. In this work, we extend the application of OT NMR to another integer quadrupolar nucleus, namely ¹⁰B (I = 3). However, this is not straightforward owing to the unfavorable characteristics of ¹⁰B isotope. Here, for the first time, we present the selective acquisition of ¹⁰B central (-1 ↔ +1) OT NMR via detection of ¹H nuclei on perborate monohydrate sample. Numerical calculations are in a good agreement with the experimental results. Both show that the optimal sensitivity is achieved when the carrier frequency is applied at the second OT spinning sideband, i.e. an offset of twice of the spinning frequency from the center band.

Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR

The field of dynamic nuclear polarization has undergone tremendous developments and diversification since its inception more than 6 decades ago. In this review we provide an in-depth overview of the relevant topics involved in DNP-enhanced MAS NMR spectroscopy. This includes the theoretical description of DNP mechanisms as well as of the polarization transfer pathways that can lead to a uniform or selective spreading of polarization between nuclear spins. Furthermore, we cover historical and state-of-the art aspects of dedicated instrumentation, polarizing agents, and optimization techniques for efficient MAS DNP. Finally, we present an extensive overview on applications in the fields of structural biology and materials science, which underlines that MAS DNP has moved far beyond the proof-of-concept stage and has become an important tool for research in these fields.

Composite pulses in directly and indirectly detected 14N MAS overtone spectroscopy

¹⁴N MAS overtone spectroscopy is mainly limited by narrow excitation bandwidths owing to the use of very long pulses to get stronger signals. We previously reported the use of modified 90° composite pulses for broadband excitation in ¹H-{NOTDQ14}D-HMQC experiments at ultra-fast MAS. In this work, we modified the 180° composite pulses, which are originally designed for spin 1/2 nuclei, for both indirect detection in ¹H-{NOTDQ14}D-HMQC experiment and direct detection in one-pulse experiment, and found that the modified 180° composite pulses are useful for broadband excitation. Furthermore, we found that the bandwidth can be tailored by simply adjusting the total pulse length.

Practical considerations for the acquisition of ultra-wideline 14N NMR spectra

Several considerations for the acquisition, processing, and analysis of high quality ultra-wideline (UW) ¹⁴N solid-state NMR (SSNMR) powder patterns under static conditions are discussed. It is shown that the ¹⁴N quadrupolar parameters may be determined accurately using the frequencies of only two discontinuities in ¹⁴N NMR powder patterns that are dominated by the first-order quadrupolar interaction, thereby eliminating the need for the acquisition of the entire pattern and concomitantly reducing experimental time. A framework for utilizing the WURST-CPMG pulse sequence to improve the efficiency of UW ¹⁴N SSNMR experiments is explored in two parts: (i) a systematic investigation of the design and parameterization of the WURST pulse is presented, and (ii) the development of the practical aspects of CPMG refocusing for the acquisition of UW ¹⁴N SSNMR powder patterns is discussed, with a focus on maximizing both signal-to-noise and resolution, and minimizing spectral distortions. Finally, a strategy is demonstrated that allows for the measurement of the ¹⁴N quadrupolar parameters for any nitrogen moiety whose quadrupolar coupling constant falls within the range 0.8≤|C_Q|≤1.5MHz, by acquiring only two ¹⁴N NMR sub-spectra at strategically located transmitter frequencies; these results are compared to full powder patterns which are acquired using frequency-stepped methods. The methodologies and practical considerations outlined herein are not only useful for the rapid acquisition of UW ¹⁴N NMR spectra, but may also be modified and applied for UW NMR of a plethora of quadrupolar and spin-1/2 nuclides.

Optimisation of excitation schemes for 14N overtone MAS NMR using numerically exact simulations

Numerically exact simulations of the ¹⁴N overtone (¹⁴N^OT) MAS NMR experiment are used to investigate the effects of the applied magnetic field strength as well as three types of excitation pulse. The results show that both the resolution and sensitivity of ¹⁴N^OT MAS NMR increase linearly with the applied static magnetic field strength. Standard RF excitation pulses are compared with frequency-swept WURST pulses as well as several composite pulses. WURST pulses are demonstrated to provide the largest bandwidths, while the direction of the frequency sweep is shown to be important when these pulses are used for the direct observation of ¹⁴N^OT signals. A composite pulse is shown to provide the most efficient excitation overall, but only when applied on resonance. WURST excitation pulses are therefore the best option when studying a sample with unknown ¹⁴N NMR parameters.

Broad-band excitation in indirectly detected (14)N overtone spectroscopy with composite pulses

We show here that composite pulses allow broad-band excitation of nitrogen-14 overtone frequencies in proton detected D-HMQC experiments (referred to (1)H-{NOTDQ14} D-HMQC). Experimental verifications have been performed on glycine, L-histidine and N-acetyl-valine (NAV) samples. Composite pulses enable symmetric excitations of (14)N sites with large shift differences. Therefore, this approach is promising for recording high resolution (1)H-{NOTDQ14} D-HMQC spectra of most amino-acids, pharmaceutical samples and peptides.

(14)N overtone NMR under MAS: signal enhancement using symmetry-based sequences and novel simulation strategies

Overtone ¹⁴N NMR spectroscopy is a promising route for the direct detection of ¹⁴N signals with good spectral resolution.

Overtone ¹⁴N NMR spectroscopy is a promising route for the direct detection of ¹⁴N signals with good spectral resolution. Its application is currently limited, however, by the absence of efficient polarization techniques for overtone signal enhancement and the lack of efficient numerical simulation techniques to aid in both the development of new methods and the analysis and interpretation of experimental data. In this paper we report a novel method for the transfer of polarization from ¹H to the ¹⁴N overtone using symmetry-based R-sequences that overcome many of the limitations of adiabatic approaches that have worked successfully on static samples. Refinement of these sequences and the analysis of the resulting spectra have been facilitated through the development of an efficient simulation strategy for ¹⁴N overtone NMR spectroscopy of spinning samples, using effective Hamiltonians on top of Floquet and Fokker–Planck equations.

Natural abundance 14N and 15N solid-state NMR of pharmaceuticals and their polymorphs

¹⁴N and ¹⁵N solid-state NMR at natural abundance are used in tandem for the investigation of pharmaceuticals and their polymorphs.

Comparison of various NMR methods for the indirect detection of nitrogen-14 nuclei via protons in solids

We present an experimental comparison of several through-space Hetero-nuclear Multiple-Quantum Correlation experiments, which allow the indirect observation of homo-nuclear single- (SQ) or double-quantum (DQ) (14)N coherences via spy (1)H nuclei. These (1)H-{(14)N} D-HMQC sequences differ not only by the order of (14)N coherences evolving during the indirect evolution, t1, but also by the radio-frequency (rf) scheme used to excite and reconvert these coherences under Magic-Angle Spinning (MAS). Here, the SQ coherences are created by the application of center-band frequency-selective pulses, i.e. long and low-power rectangular pulses at the (14)N Larmor frequency, ν0((14)N), whereas the DQ coherences are excited and reconverted using rf irradiation either at ν0((14)N) or at the (14)N overtone frequency, 2ν0((14)N). The overtone excitation is achieved either by constant frequency rectangular pulses or by frequency-swept pulses, specifically Wide-band, Uniform-Rate, and Smooth-Truncation (WURST) pulse shapes. The present article compares the performances of four different (1)H-{(14)N} D-HMQC sequences, including those with (14)N rectangular pulses at ν0((14)N) for the indirect detection of homo-nuclear (i) (14)N SQ or (ii) DQ coherences, as well as their overtone variants using (iii) rectangular or (iv) WURST pulses. The compared properties include: (i) the sensitivity, (ii) the spectral resolution in the (14)N dimension, (iii) the rf requirements (power and pulse length), as well as the robustness to (iv) rf offset and (v) MAS frequency instabilities. Such experimental comparisons are carried out for γ-glycine and l-histidine.HCl monohydrate, which contain (14)N sites subject to moderate quadrupole interactions. We demonstrate that the optimum choice of the (1)H-{(14)N} D-HMQC method depends on the experimental goal. When the sensitivity and/or the robustness to offset are the major concerns, the D-HMQC sequence allowing the indirect detection of (14)N SQ coherences should be employed. Conversely, when the highest resolution and/or adjusted indirect spectral width are needed, overtone experiments are the method of choice. The overtone scheme using WURST pulses results in broader excitation bandwidths than that using rectangular pulses, at the expense of reduced sensitivity. Numerically exact simulations also show that the sensitivity of the overtone (1)H-{(14)N} D-HMQC experiment increases for larger quadrupole interactions.

(14)N overtone transition in double rotation solid-state NMR

Solid-state NMR transitions involving outer energy levels of the spin-1 (14)N nucleus are immune, to first order in perturbation theory, to the broadening caused by the nuclear quadrupole interaction. The corresponding overtone spectra, when acquired in conjunction with magic-angle sample spinning, result in lines, which are just a few kHz wide, permitting the direct detection of nitrogen compounds without the need for labeling. Despite the success of this technique, "overtone" resonances are still broadened due to indirect, second order effects arising from the large quadrupolar interaction. Here we demonstrate that another order of magnitude in spectral resolution may be gained by using double rotation. This brings the width of the (14)N solid-state NMR lines much closer to the region commonly associated with high-resolution solid-state NMR spectroscopy of (15)N and demonstrates the improvements in resolution that may be possible through the development of pulsed methodologies to suppress these second order effects.

Efficient polarization transfer between spin-1/2 and ¹⁴N nuclei in solid-state MAS NMR spectroscopy

Polarization transfer between spin-1/2 nuclei and quadrupolar spin-1 nuclei such as (14)N in solid-state NMR is severely challenged by the typical presence of large quadrupole coupling interactions. This has effectively prevented the use of the abundant (14)N spin as a probe to structural information and its use as an element in multi-dimensional solid-state NMR correlation experiments for assignment and structural characterization. In turn, this has been a contributing factor to the extensive use of isotope labeling in biological solid-state NMR, where (14)N is replaced with (15)N. The alternative strategy of using the abundant (14)N spins calls for methods enabling efficient polarization transfer between (14)N and its binding partners. This work demonstrates that the recently introduced (RESPIRATION)CP transfer method can be optimized to achieve efficient (1)H ↔(14)N polarization transfer under magic angle spinning conditions. The method is demonstrated numerically and experimentally on powder samples of NH4NO3 and L-alanine.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average. The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix-the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape. We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental (139)La spectra of La2O3.

Dynamic nuclear polarisation enhanced14N overtone MAS NMR spectroscopy

Dynamic nuclear polarisation has been used to obtain solid-state¹⁴N overtone NMR spectra with signal enhancement levels of over two orders of magnitude, including natural abundance C–N and H–N correlation spectra.

The WURST kind of pulses in solid-state NMR

WURST pulses (wideband, uniform rate, smooth truncation) were first introduced two decades ago by Kupče and Freeman as a means of achieving broadband adiabatic inversion of magnetisation for solution-state (13)C decoupling at high magnetic field strengths. In more recent years these pulses have found use in an increasingly diverse range of applications in solid-state NMR. This article reviews a number of recent developments that take advantage of WURST pulses, including broadband excitation, refocusing and cross polarisation for the acquisition of ultra-wideline powder patterns, signal enhancement for half-integer and integer spin quadrupolar nuclei, spectral editing, direct and indirectly observed (14)N overtone MAS, and symmetry-based homonuclear recoupling. Simple mathematical descriptions of WURST pulses and some brief theory behind their operation in the adiabatic and non-adiabatic regimes are provided, and various practical considerations for their use are also discussed.

14N overtone NMR spectra under magic angle spinning: experiments and numerically exact simulations

It was recently shown that high resolution (14)N overtone NMR spectra can be obtained directly under magic angle spinning (MAS) conditions [L. A. O'Dell and C. I. Ratcliffe, Chem. Phys. Lett. 514, 168 (2011)]. Preliminary experimental results showed narrowed powder pattern widths, a frequency shift that is dependent on the MAS rate, and an apparent absence of spinning sidebands, observations which appeared to be inconsistent with previous theoretical treatments. Herein, we reproduce these effects using numerically exact simulations that take into account the full nuclear spin Hamiltonian. Under sample spinning, the (14)N overtone signal is split into five (0, ±1, ±2) overtone sidebands separated by the spinning frequency. For a powder sample spinning at the magic angle, the +2ω(r) sideband is dominant while the others show significantly lower signal intensities. The resultant MAS powder patterns show characteristic quadrupolar lineshapes from which the (14)N quadrupolar parameters and isotropic chemical shift can be determined. Spinning the sample at other angles is shown to alter both the shapes and relative intensities of the five overtone sidebands, with MAS providing the benefit of averaging dipolar couplings and shielding anisotropy. To demonstrate the advantages of this experimental approach, we present the (14)N overtone MAS spectrum obtained from L-histidine, in which powder patterns from all three nitrogen sites are clearly resolved.

Proton-nitrogen-14 overtone two-dimensional correlation NMR spectroscopy of solid-sample at very fast magic angle sample spinning

(1)H-(14)N overtone (OT) heteronuclear multiple quantum coherence (HMQC) experiment at very fast magic angle spinning (MAS) is reported. The (14)N OT coherence is excited and reconverted by (14)N OT pulses at twice the (14)N Larmor frequency. The OT coherence is free from the first order quadrupolar broadening. MAS further removes the broadening due to chemical shift anisotropy (CSA). With a small 0.75 mm MAS rotor and coil system, very fast MAS up to 90 kHz and very strong rf field are achieved, enhancing the sensitivity of indirect (14)N OT observation via protons. In comparison with (1)H-(14)N double-quantum HMQC, an enhancement factor of 1.8 is obtained for glycine with the (14)N OT irradiation. The bandwidth in the (14)N OT dimension is limited due to long (14)N OT pulses.

QUEST-QUadrupolar Exact SofTware: a fast graphical program for the exact simulation of NMR and NQR spectra for quadrupolar nuclei

We present a new program for the exact simulation of solid-state NMR spectra of quadrupolar nuclei in stationary powdered samples which employs diagonalization of the combined Zeeman-quadrupolar Hamiltonian. The program, which we call QUEST (QUadrupolar Exact SofTware), can simulate NMR spectra over the full regime of Larmor and quadrupolar frequency ratios, which encompasses scenarios ranging from high-field NMR to nuclear quadrupole resonance (NQR, where the Larmor frequency is zero) and does not make use of approximations when treating the quadrupolar interaction. With the use of the fast powder averaging scheme of Alderman, Solum, and Grant, exact NMR spectral simulations are only marginally slower than the second-order perturbation theory counterpart. The program, which uses a graphical user interface, also incorporates chemical shift anisotropy and non-coincident chemical shift and quadrupolar tensor frames. The program is validated against newly-acquired experimental data through several examples including: the low-field (79/81)Br NMR spectra of CaBr(2), the (14)N overtone NMR spectrum of glycine, the (187)Re NQR spectra of Re(2)(CO)(10), and lastly the (127)I overtone NQR spectrum of SrI(2), which, to the best of our knowledge, represents the first direct acquisition of an overtone NQR spectrum for a powdered sample.

Residual dipolar coupling between quadrupolar nuclei under magic-angle spinning and double-rotation conditions

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.

Broadband excitation and indirect detection of nitrogen-14 in rotating solids using Delays Alternating with Nutation (DANTE)

A train of short rotor-synchronized pulses in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE) applied to nitrogen-14 nuclei (I=1) in samples spinning at the magic angle at high frequencies (typically νrot=62.5 kHz so that τrot=16 μs) allows one to achieve uniform excitation of a great number of spinning sidebands that arise from large first-order quadrupole interactions, as occur for aromatic nitrogen-14 nuclei in histidine. With routine rf amplitudes ω1(14N)/(2π)=60 kHz and very short pulses of a typical duration 0.5<τp<2 μs, efficient excitation can be achieved with 13 rotor-synchronized pulses in 13 τrot=208 μs. Alternatively, with 'overtone' DANTE sequences using 2, 4, or 8 pulses per rotor period one can achieve efficient broadband excitation in fewer rotor periods, typically 2-4 τrot. These principles can be combined with the indirect detection of 14N nuclei via spy nuclei with S=½ such as 1H or 13C in the manner of Dipolar Heteronuclear Multiple-Quantum Correlation (D-HMQC).

Exact calculation of the response of a quadrupolar nucleus to radio frequency irradiation

The effect of a pulse in NMR is usually considered as a rotation of the frame of reference of the spin system. For spins-1/2, this concept is an important and very useful tool. The assumption behind this concept is that while the radio frequency irradiation is on, this term dominates all other interactions. Although this is usually true for spins-1/2, typical interactions for a quadrupolar nucleus can be very large and the assumption is no longer valid. The full solution is complex, but two extreme cases are already solved. If the quadrupole interaction is very small, then the assumption is valid and the pulse does act like a rotation of the frame of reference. At the other extreme, if the interaction is large and the spin, I, is half-integral, then the central transition remains relatively narrow and can be treated as a fictitious spin-1/2. The pulse then acts as a rotation, but with a scaling factor of I + 1/2. This paper treats the general case, where no approximations are made. The effects can be observed in a nutation experiment, in which the observed signal is plotted as a function of pulse width, in a simple one-pulse experiment. If the pulse acts as a rotation, then the nutation plot will be a sine wave, but otherwise it will be a sum of sinusoids. This is true even for a single-crystal sample with a single quadrupolar coupling. If the sample is a powder, then the nutation plot will be a sum of many sinusoids, since the quadrupole coupling will vary with the powder average. This paper sketches out the theory of these effects based on a full and exact description of a quadrupolar system and illustrates it with some nutation spectra of 23Na in a powdered sample of sodium nitrate.

High-resolution 14N-edited 1H-13C correlation NMR experiment to study biological solids

It was recently shown that nuclear magnetic resonance (NMR) spectra of nitrogen-14 (spin I=1) can be obtained by indirect detection via spin S=1/2 nuclei in powders spinning at the magic angle. An increased number of solid-state NMR methods are now available to tailor sequences for specific purposes, e.g., hetero-nuclear dipolar recoupling or homo-nuclear dipolar decoupling schemes. Here, we combine the latest recoupling and decoupling techniques to obtain high-resolution (1)H-(13)C through-space correlation spectra, where only the correlation peaks of those carbons close to nitrogen nuclei are observed. The experiment is demonstrated on a (13)C enriched l-histidine. HCl x H(2)O powder sample.

3D 1H-13C-14N correlation solid-state NMR spectrum

Nitrogen-14 (spin I=1) has always been a nucleus difficult to observe in solid-state NMR and until recently its observation was restricted to one-dimensional (1D) spectra. We present here the first 3D 1H-13C-14N NMR correlation spectrum. This spectrum was acquired on a test sample L-histidine.HCl.H2O using a recently developed technique, which consists in indirectly observing 14N nuclei via dipolar recoupling with an HMQC-type experiment.