Improvements in Resolution of ¹H NMR of solids.

Magic angle spinning (MAS) in 1H NMR has allowed progress from featureless spectra in static samples to linewidths of a few hundreds of Hertz for powdered solids at the fastest spinning rates available today (100-150 kHz). While this is a remarkable improvement, this level of resolution is still limiting to the widespread use of 1H NMR for complex systems. This review will discuss two recent alternative strategies that have significantly improved 1H resolution, when combined with fast MAS. The first is based on anti-z-COSY, a 2D experiment originally used for J decoupling in liquids, which removes residual broadening due to splittings caused by imperfect coherent averaging of MAS. The second strategy is to obtain pure isotropic proton (PIP) spectra in solids, by parametrically mapping any residual broadening due to imperfect averaging into a second dimension of a multidimensional correlation spectrum.

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.

Two-dimensional Pure Isotropic Proton Solid State NMR.

One key bottleneck of solid-state NMR spectroscopy is that 1 H NMR spectra of organic solids are often very broad due to the presence of a strong network of dipolar couplings. We have recently suggested a new approach to tackle this problem. More specifically, we parametrically mapped errors leading to residual dipolar broadening into a second dimension and removed them in a correlation experiment. In this way pure isotropic proton (PIP) spectra were obtained that contain only isotropic shifts and provide the highest 1 H NMR resolution available today in rigid solids. Here, using a deep-learning method, we extend the PIP approach to a second dimension, and for samples of L-tyrosine hydrochloride and ampicillin we obtain high resolution 1 H-1 H double-quantum/single-quantum dipolar correlation and spin-diffusion spectra with significantly higher resolution than the corresponding spectra at 100 kHz MAS, allowing the identification of previously overlapped isotropic correlation peaks.

Pure Isotropic Proton Solid State NMR.

Resolution in proton solid state magic angle sample spinning (MAS) NMR is limited by the intrinsically imperfect nature of coherent averaging induced by either MAS or multiple pulse sequence methods. Here, we suggest that instead of optimizing and perfecting a coherent averaging scheme, we could approach the problem by parametrically mapping the error terms due to imperfect averaging in a k-space representation, in such a way that they can be removed in a multidimensional correlation leaving only the desired pure isotropic signal. We illustrate the approach here by determining pure isotropic 1H spectra from a series of MAS spectra acquired at different spinning rates. For six different organic solids, the approach is shown to produce pure isotropic 1H spectra that are significantly narrower than the MAS spectrum acquired at the fastest possible rate, with linewidths down to as little as 48 Hz. On average, we observe a 7-fold increase in resolution, and up to a factor of 20, as compared with spectra acquired at 100 kHz MAS. The approach is directly applicable to a range of solids, and we anticipate that the same underlying principle for removing errors introduced here can be applied to other problems in NMR spectroscopy.

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 ωr 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.

Homonuclear Decoupling in 1 H†NMR of Solids by Remote Correlation.

The typical linewidths of 1 H 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 1 H 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 1 H NMR spectra of powdered organic solids. Results obtained with the anti-z-COSY sequence at 100 kHz MAS on thymol, ß-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.

Barriers to resolution in 1H NMR of rotating solids.

The role of 1H solid-state NMR in structure elucidation of solids is becoming more preponderant, particularly as faster magic-angle spinning rates (MAS) become available which improve 1H detected assignment strategies. However, current 1H spectral resolution is still relatively poor, with linewidths of typically a few hundred Hz, even at the fastest rates available today. Here we detail and assess the factors limiting proton linewidths and line shapes in MAS experiments with five different samples, exemplifying the different sources of broadening that affect the residual linewidth. We disentangle the different contributions through one- and two-dimensional experiments: by using dilution to identify the contribution of ABMS; by using extensive deuteration to identify the dipolar contributions; and by using variable MAS rates to determine the ratio between homogeneous and inhomogeneous components. We find that the overall widths and the nature of the different contributions to the linewidths can vary very considerably. While we find that faster spinning always yields narrower lines and longer coherence lifetimes, we also find that for some resonances the dipolar contribution is no longer dominant at 100 kHz MAS. When the inhomogeneous sources of broadening, such as ABMS and chemical shift disorder, are dominant, two-dimensional 1H-1H correlation experiments yield better resolution for assignment. Particularly the extraction of the antidiagonal of a 2D peak will remove any correlated inhomogeneous broadening, giving substantially narrower 1H linewidths.

Bayesian probabilistic assignment of chemical shifts in organic solids.

A prerequisite for NMR studies of organic materials is assigning each experimental chemical shift to a set of geometrically equivalent nuclei. Obtaining the assignment experimentally can be challenging and typically requires time-consuming multidimensional correlation experiments. An alternative solution for determining the assignment involves statistical analysis of experimental chemical shift databases, but no such database exists for molecular solids. Here, by combining the Cambridge Structural Database with a machine learning model of chemical shifts, we construct a statistical basis for probabilistic chemical shift assignment of organic crystals by calculating shifts for more than 200,000 compounds, enabling the probabilistic assignment of organic crystals directly from their two-dimensional chemical structure. The approach is demonstrated with the 13C and 1H assignment of 11 molecular solids with experimental shifts and benchmarked on 100 crystals using predicted shifts. The correct assignment was found among the two most probable assignments in more than 80% of cases.

Structure determination of an amorphous drug through large-scale NMR predictions.

Knowledge of the structure of amorphous solids can direct, for example, the optimization of pharmaceutical formulations, but atomic-level structure determination in amorphous molecular solids has so far not been possible. Solid-state nuclear magnetic resonance (NMR) is among the most popular methods to characterize amorphous materials, and molecular dynamics (MD) simulations can help describe the structure of disordered materials. However, directly relating MD to NMR experiments in molecular solids has been out of reach until now because of the large size of these simulations. Here, using a machine learning model of chemical shifts, we determine the atomic-level structure of the hydrated amorphous drug AZD5718 by combining dynamic nuclear polarization-enhanced solid-state NMR experiments with predicted chemical shifts for MD simulations of large systems. From these amorphous structures we then identify H-bonding motifs and relate them to local intermolecular complex formation energies.

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.