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.

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 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.

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.