Improved Phase-Modulated Homonuclear Dipolar Decoupling for Solid-State NMR Spectroscopy from Symmetry Considerations

Pure Isotropic Proton NMR Spectra in Solids using Deep Learning

The resolution of proton solid-state NMR spectra is usually limited by broadening arising from dipolar interactions between spins. Magic-angle spinning alleviates this broadening by inducing coherent averaging. However, even the highest spinning rates experimentally accessible today are not able to completely remove dipolar interactions. Here, we introduce a deep learning approach to determine pure isotropic proton spectra from a two-dimensional set of magic-angle spinning spectra acquired at different spinning rates. Applying the model to 8 organic solids yields high-resolution 1 H solid-state NMR spectra with isotropic linewidths in the 50-400 Hz range.

Theory and simulations of homonuclear three-spin systems in rotating solids

The homonuclear dipolar coupling is the internal spin interaction that contributes the most to the line shapes in magic-angle-spinning (MAS) ¹H NMR spectra of solids, and linewidths typically extend over several hundred Hertz, limiting the ¹H resolution. Understanding and reducing this contribution could provide rich structural information for organic solids. Here, we use average Hamiltonian theory to study two- and three-spin systems in the fast MAS regime. Specifically, we develop analytical expressions to third order in the case of two and three inequivalent spins (I = ½). The results show that the full third-order expression of the Hamiltonian, without secular approximations or truncation to second order, is the description that agrees the best, by far, with full numerical calculations. We determine the effect on the NMR spectrum of the different Hamiltonian terms, which are shown to produce both residual shifts and splittings in the three-spin systems. Both the shifts and splittings have a fairly complex dependence on the spinning rate with the eigenstates having a polynomial ω_r dependence. The effect on powder line shapes is also shown, and we find that the anisotropic residual shift does not have zero average so that the powder line shape is broadened and shifted from the isotropic position. This suggests that in ¹H MAS spectra, even at the fastest MAS rates attainable today, the positions observed are not exactly the isotropic shifts.

Fast remote correlation experiments for 1H homonuclear decoupling in solids

In ¹H MAS spectra, the residual homogeneous broadening under MAS is due to a combination of higher-order shifts and splittings. We have recently shown how the two-dimensional anti-z-COSY experiment can be used for the removal of the splittings. However, this requires spectra with high resolution in the indirect dimension (t₁), leading to experiment times of hours. Here, we show how anti-z-COSY can be adapted to be combined with the two-dimensional one pulse (TOP) transformation which leads to significantly reduced experimental time while retaining the line narrowing effect. The experiment is demonstrated on a powdered sample of L-histidine monohydrochloride monohydrate, where the new TAZ-COSY sequence at 100 kHz MAS, yields between a factor 1.6 and 2.3 increase in resolution compared with the equivalent one-pulse experiment, in just 20 min. The same methodology is also adapted for the acquisition of liquid state ¹H homodecoupled data, and an example is given for testosterone.

Homonuclear Decoupling in 1 H NMR of Solids by Remote Correlation

The typical linewidths of ¹H NMR spectra of powdered organic solids at 111 kHz magic‐angle spinning (MAS) are of the order of a few hundred Hz. While this is remarkable in comparison to the tens of kHz observed in spectra of static samples, it is still the key limit to the use of ¹H in solid‐state NMR, especially for complex systems. Here, we demonstrate a novel strategy to further improve the spectral resolution. We show that the anti‐z‐COSY experiment can be used to reduce the residual line broadening of ¹H NMR spectra of powdered organic solids. Results obtained with the anti‐z‐COSY sequence at 100 kHz MAS on thymol, β‐AspAla, and strychnine show an improvement in resolution of up to a factor of two compared to conventional spectra acquired at the same spinning rate.

Origin of the residual line width under frequency-switched Lee-Goldburg decoupling in MAS solid-state NMR

Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee-Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B 1 -field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B 0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.

High-resolution 1H NMR of powdered solids by homonuclear dipolar decoupling

The development of homonuclear dipolar decoupling sequences to obtain high-resolution ¹H NMR spectra from solids has recently celebrated its 50th birthday. Over the years, a series of different decoupling schemes have been developed, starting with the pioneering Lee-Goldburg and WAHUHA sequences up to the most recent generation of experimentally optimized phase-modulated schemes such as eDUMBO-1₂₂ and LG4. These schemes can all yield over an order of magnitude reduction in ¹H NMR linewidths in solids. Here we provide an overview and a broad experimental comparison of the performance of the main sequences, which has so far been absent in the literature, especially between the newest and the oldest decoupling schemes. We compare experimental results obtained using eight different decoupling schemes (LG, WHH-4, MREV-8, BR-24, FSLG/PMLG, DUMBO-1, eDUMBO-1₂₂ and LG4) on three different microcrystalline powdered samples (alanine, glycine and β-AspAla) and at three different MAS rates (3.0, 12.5 and 22.0 kHz). Finally, since these sequences can be technically demanding, we describe the experimental protocol we have used to optimize these schemes with the aim to provide simple guidelines for the optimization of CRAMPS experiments for all NMR users.

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

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

Refocused linewidths less than 10 Hz in 1H solid-state NMR

Coherence lifetimes in homonuclear dipolar decoupled ¹H solid-state NMR experiments are usually on the order of a few ms. We discover an oscillation that limits the lifetime of the coherences by recording spin-echo dephasing curves. We find that this oscillation can be removed by the application of a double spin-echo experiment, leading to coherence lifetimes of more than 45 ms in adamantane and more that 22 ms in β-AspAla, corresponding to refocused linewidths of less than 7 and 14 Hz respectively.

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.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

Enhancing the resolution of 1H and 13C solid-state NMR spectra by reduction of anisotropic bulk magnetic susceptibility broadening

We demonstrate that natural isotopic abundance 2D heteronuclear correlation (HETCOR) solid-state NMR spectra can be used to significantly reduce or eliminate the broadening of ¹H and ¹³C solid-state NMR spectra of organic solids due to anisotropic bulk magnetic susceptibility (ABMS). ABMS often manifests in solids with aromatic groups, such as active pharmaceutical ingredients (APIs), and inhomogeneously broadens the NMR peaks of all nuclei in the sample. Inhomogeneous peaks with full widths at half maximum (FWHM) of ∼1 ppm typically result from ABMS broadening and the low spectral resolution impedes the analysis of solid-state NMR spectra. ABMS broadening of solid-state NMR spectra has previously been eliminated using 2D multiple-quantum correlation experiments, or by performing NMR experiments on diluted materials or single crystals. However, these experiments are often infeasible due to their poor sensitivity and/or provide limited gains in resolution. 2D ¹H-¹³C HETCOR experiments have previously been applied to reduce susceptibility broadening in paramagnetic solids and we show that this strategy can significantly reduce ABMS broadening in diamagnetic organic solids. Comparisons of 1D solid-state NMR spectra and ¹H and ¹³C solid-state NMR spectra obtained from 2D ¹H-¹³C HETCOR NMR spectra show that the HETCOR spectrum directly increases resolution by a factor of 1.5 to 8. The direct gain in resolution is determined by the ratio of the inhomogeneous ¹³C/¹H linewidth to the homogeneous ¹H linewidth, with the former depending on the magnitude of the ABMS broadening and the strength of the applied field and the latter on the efficiency of homonuclear decoupling. The direct gains in resolution obtained using the 2D HETCOR experiments are better than that obtained by dilution. For solids with long proton longitudinal relaxation times, dynamic nuclear polarization (DNP) was applied to enhance sensitivity and enable the acquisition of 2D ¹H-¹³C HETCOR NMR spectra. 2D ¹H-¹³C HETCOR experiments were applied to resolve and partially assign the NMR signals of the form I and form II polymorphs of aspirin in a sample containing both forms. These findings have important implications for ultra-high field NMR experiments, optimization of decoupling schemes and assessment of the fundamental limits on the resolution of solid-state NMR spectra.

Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook

It has been slightly more than fifty years since the first homonuclear spin decoupling scheme, Lee-Goldburg decoupling, was proposed for removing homonuclear dipolar interactions in solid-state nuclear magnetic resonance. A family of such schemes has made observation of high-resolution NMR spectra of abundant spins possible in various applications in solid state. This review outlines the strategies used in this field and the future prospects of homonuclear spin decoupling in solid-state NMR.

High resolution triple resonance micro magic angle spinning NMR spectroscopy of nanoliter sample volumes

To be able to study mass-limited samples and small single crystals, a triple resonance micro-magic angle spinning (μMAS) probehead for the application of high-resolution solid-state NMR of nanoliter samples was developed. Due to its excellent rf performance this allows us to explore the limits of proton NMR resolution in strongly coupled solids. Using homonuclear decoupling we obtain unprecedented (1)H linewidths for a single crystal of glycine (Δν(CH2) = 0.14 ppm) at high field (20 T) in a directly detected spectrum. The triple channel design allowed the recording of high-resolution μMAS (13)C-(15)N correlations of [U-(13)C-(15)N] arginine HCl and shows that the superior (1)H resolution opens the way for high-sensitivity inverse detection of heteronuclei even at moderate spinning speeds and rf-fields. Efficient decoupling leads to long coherence times which can be exploited in many correlation experiments.

Minimizing the effects of RF inhomogeneity and phase transients allows resolution of two peaks in the (1)H CRAMPS NMR spectrum of adamantane

One of the limiting factors to achieving highly resolved (1)H NMR spectra with (1)H homonuclear decoupling sequences is imperfections in the applied radiofrequency (RF) pulses, most notably phase transients and RF inhomogeneity. Through a series of simulations and solid-state NMR experiments, it is demonstrated that the combined effects of phase transients and RF inhomogeneity can be minimized by a combination of (i) restricting the sample to small volume of the rotor, (ii) by employing a super-cycled version of the DUMBO decoupling sequence, and (iii) by carefully adjusting the probe tuning such that the asymmetric component of phase transients is minimized. Under these optimal conditions, it was possible to clearly resolve two signals in the (1)H CRAMPS NMR spectrum of adamantane arising from the CH and CH2 protons in the molecule. It is proposed that adamantane could be a very useful setup sample for (1)H CRAMPS NMR as the two peaks are only resolved when the effects of RF inhomogeneity and phase transients are minimized.

High-resolution NMR of hydrogen in organic solids by DNP enhanced natural abundance deuterium spectroscopy

We demonstrate that high field (9.4 T) dynamic nuclear polarization (DNP) at cryogenic (∼100 K) sample temperatures enables the rapid acquisition of natural abundance (1)H-(2)H cross-polarization magic angle spinning (CPMAS) solid-state NMR spectra of organic solids. Spectra were obtained by impregnating substrates with a solution of the stable DNP polarizing agent TEKPol in tetrachloroethane. Tetrachloroethane is a non-solvent for the solids, and the unmodified substrates are then polarized through spin diffusion. High quality natural abundance (2)H CPMAS spectra of histidine hydrochloride monohydrate, glycylglycine and theophylline were acquired in less than 2h, providing direct access to hydrogen chemical shifts and quadrupolar couplings. The spectral resolution of the (2)H solid-state NMR spectra is comparable to that of (1)H spectra obtained with state of the art homonuclear decoupling techniques.