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

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

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

Effective Hamiltonian and spin dynamics in fast MAS TRAPDOR-HMQC experiments involving spin-3/2 quadrupolar nuclei

We present a theoretical and numerical description of the spin dynamics associated with TRAPDOR-HMQC (T-HMQC) experiment for a ¹H (I) - ³⁵Cl (S) spin system under fast magic angle spinning (MAS). Towards this an exact effective Hamiltonian describing the system is numerically evaluated with matrix logarithm approach. The different magnitudes of the heteronuclear and pure S terms in the effective Hamiltonian allow us to suggest a truncation approximation, which is shown to be in excellent agreement with the exact time evolution. Limitations of this approximation, especially at the rotary resonance condition, are discussed. The truncated effective Hamiltonian is further employed to monitor the buildup of various coherences during TRAPDOR irradiation. We observe and explain a functional resemblance between the magnitude of different terms in the truncated effective Hamiltonian and the amplitudes of various coherences during TRAPDOR irradiation, as function of crystallite orientation. Subsequently, the dependence of the sign (phase) of the T-HMQC signal on the coherence type generated is investigated numerically and analytically. We examine the continuous creation and evolution of various coherences at arbitrary times, i.e., at and between avoided level crossings. Behavior between consecutive crossings is described analytically and reveals 'quadrature' evolution of pairs of coherences and coherence interconversions. The adiabatic, sudden, and intermediate regimes for T-HMQC experiments are discussed within the approach established by A. J. Vega. Equations as well as numerical simulations suggest the existence of a driving coherence which builds up between consecutive crossings and then gets distributed at crossings among other coherences. In the intermediate regime, redistribution of the driving coherence to other coherences is almost uniform such that coherences involving S-spin double-quantum terms may be efficiently produced.

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.

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.

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.

Sensitivity enhanced (14)N/(14)N correlations to probe inter-beta-sheet interactions using fast magic angle spinning solid-state NMR in biological solids

(14)N/(14)N correlations are vital for structural studies of solid samples, especially those in which (15)N isotopic enrichment is challenging, time-consuming and expensive. Although (14)N nuclei have high isotopic abundance (99.6%), there are inherent difficulties in observing (14)N/(14)N correlations due to limited resolution and sensitivity related to: (i) low (14)N gyromagnetic ratio (γ), (ii) large (14)N quadrupolar couplings, (iii) integer (14)N spin quantum number (I = 1), and (iv) very weak (14)N-(14)N dipolar couplings. Previously, we demonstrated a proton-detected 3D (14)N/(14)N/(1)H correlation experiment at fast magic angle spinning (MAS) on l-histidine·HCl·H2O utilizing a through-bond (J) and residual dipolar-splitting (RDS) based heteronuclear multiple quantum correlation (J-HMQC) sequence mediated through (1)H/(1)H radio-frequency driven recoupling (RFDR). As an extension of our previous work, in this study we show the utility of dipolar-based HMQC (D-HMQC) in combination with (1)H/(1)H RFDR mixing to obtain sensitivity enhanced (14)N/(14)N correlations in more complex biological solids such as a glycyl-l-alanine (Gly-l-Ala) dipeptide, and parallel (P) and antiparallel (AP) β-strand alanine tripeptides (P-(Ala)3 and AP-(Ala)3, respectively). These systems highlight the mandatory necessity of 3D (14)N/(14)N/(1)H measurements to get (14)N/(14)N correlations when the amide proton resonances are overlapped. Moreover, the application of long selective (14)N pulses, instead of short hard ones, is shown to improve the sensitivity. Globally, we demonstrate that replacing J-scalar with dipolar interaction and hard- with selective-(14)N pulses allows gaining a factor of ca. 360 in experimental time. On the basis of intermolecular NH/NH distances and (14)N quadrupolar tensor orientations, (14)N/(14)N correlations are effectively utilized to make a clear distinction between the parallel and antiparallel arrangements of the β-strands in (Ala)3 through the observation of inter-β-sheet correlations.

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.

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.

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.