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

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.

Nuclear magnetic resonance characterisation of ionic liquids and organic ionic plastic crystals: common approaches and recent advances

Ionic liquids, and their solid-state equivalents organic ionic plastic crystals, show many useful and tailorable properties that make them interesting for a wide range of applications including as electrolytes for energy storage devices. Nuclear magnetic resonance spectroscopy and related techniques offer a powerful and versatile toolkit for the characterisation of structure, interactions and dynamics in these materials. This article summarises both commonly used methods and some recent advances in this area, including solution- and solid-state methods, dynamic nuclear polarisation, imaging, diffusion and relaxation measurements, and example applications of some less commonly studied nuclei.

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.

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.

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.

Linear-scaling ab initio simulations of spin diffusion in rotating solids

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

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.

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.

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

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

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.

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.

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.

SpinDynamica: Symbolic and numerical magnetic resonance in a Mathematica environment

SpinDynamica is a set of Mathematica packages for performing numerical and symbolic analysis of a wide range of magnetic resonance experiments and phenomena. An overview of the SpinDynamica architecture and functionality is given, with some simple representative examples.

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.

Measurement of 14N quadrupole couplings in biomolecular solids using indirect-detection 14N solid-state NMR with DNP

Insights into protein structure through the determination of ¹⁴N quadrupolar interactions using magic-angle spinning dynamic nuclear polarization NMR.

Fokker-Planck formalism in magnetic resonance simulations

This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc.) are simplified significantly in Fokker-Planck space. The paper also summarises the author's experiences with writing and using the corresponding modules of the Spinach library - the methods described below have enabled a large variety of simulations previously considered too complicated for routine practical use.

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.

Solid-state NMR indirect detection of nuclei experiencing large anisotropic interactions using spinning sideband-selective pulses

Under Magic-Angle Spinning (MAS), a long radio-frequency (rf) pulse applied on resonance achieves the selective excitation of the center-band of a wide NMR spectrum. We show herein that these rf pulses can be applied on the indirect channel of Hetero-nuclear Multiple-Quantum Correlation (HMQC) sequences, which facilitate the indirect detection via spin-1/2 isotopes of nuclei exhibiting wide spectra. Numerical simulations show that this indirect excitation method is applicable to spin-1/2 nuclei experiencing a large chemical shift anisotropy, as well as to spin-1 isotopes subject to a large quadrupole interaction, such as (14)N. The performances of the long pulses are analyzed by the numerical simulations of scalar-mediated HMQC (J-HMQC) experiments indirectly detecting spin-1/2 or spin-1 nuclei, as well as by dipolar-mediated HMQC (D-HMQC) experiments achieving indirect detection of (14)N nuclei via (1)H in crystalline γ-glycine and N-acetyl-valine samples at a MAS frequency of 60kHz. We show on these solids that for the acquisition of D-HMQC spectra between (1)H and (14)N nuclei, the efficiency of selective moderate excitation with long-pulses at the (14)N Larmor frequency, ν0((14)N), is comparable to those with strong excitation pulses at ν0((14)N) or 2ν0((14)N) frequencies, given the rf field delivered by common solid-state NMR probes. Furthermore, the D-HMQC experiments also demonstrate that the use of long pulses does not produce significant spectral distortions along the (14)N dimension. In summary, the use of center-band selective weak pulses is advantageous for HMQC experiments achieving the indirect detection of wide spectra since it (i) requires a moderate rf field, (ii) can be easily optimized, (iii) displays a high robustness to CSAs, offsets, rf-field inhomogeneities, and fluctuations in MAS frequency, and (iv) is little dependent on the quadrupolar coupling constant.

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.

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.

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.

An efficient NMR method for the characterisation of 14N sites through indirect 13C detection

Nitrogen is one of the most abundant elements and plays a key role in the chemistry of biological systems. Despite its widespread distribution, the study of the naturally occurring isotope of nitrogen, (14)N (99.6%), has been relatively limited as it is a spin-1 nucleus that typically exhibits a large quadrupolar interaction. Accordingly, most studies of nitrogen sites in biomolecules have been performed on samples enriched with (15)N, limiting the application of NMR to samples which can be isotopically enriched. This precludes the analysis of naturally occurring samples and results in the loss of the wealth of structural and dynamic information that the quadrupolar interaction can provide. Recently, several experimental approaches have been developed to characterize (14)N sites through their interaction with neighboring 'spy' nuclei. Here we describe a novel version of these experiments whereby coherence between the (14)N site and the spy nucleus is mediated by the application of a moderate rf field to the (14)N. The resulting (13)C/(14)N spectra show good sensitivity on natural abundance and labeled materials; whilst the (14)N lineshapes permit the quantitative analysis of the quadrupolar interaction.