Pure Isotropic Proton NMR Spectra in Solids using Deep Learning

Abstract

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 highresolution 1 H solid-state NMR spectra with isotropic linewidths in the 50-400 Hz range.

Two‐dimensional Pure Isotropic Proton Solid State NMR

“…In the absence of any extensive experimental databases of NMR spectra, training machine learning models on synthetic datasets (of shifts or spectra) has been to shown to be an efficient way forward [18] . Here, the generation of synthetic three‐dimensional datasets used to train a LSTM neural network was based on a protocol analogous to that used previously for two‐dimensional VMAS datasets [15b] . The overall approach is illustrated schematically in Figure 1.…”

“… Spectra obtained from microcrystalline powdered samples of L‐tyrosine hydrochloride (left) and ampicillin (right). a), b) 100 kHz MAS spectra (blue) and isotropic spectra (red) inferred with the PIPNet model [15b] from a VMAS dataset of 1D spectra recorded at 36 rates between 30 and 100 kHz (reproduced from Ref. [15b]).…”

“…a), b) 100 kHz MAS spectra (blue) and isotropic spectra (red) inferred with the PIPNet model [15b] from a VMAS dataset of 1D spectra recorded at 36 rates between 30 and 100 kHz (reproduced from Ref. [15b]). c), d) Corresponding 100 kHz MAS 2D 1 H‐ 1 H DQ/SQ BABA spectra (blue) and pure isotropic 2D 1 H‐ 1 H DQ/SQ BABA spectra (red) inferred with the PIPNet2D model from a VMAS dataset of 11 and 9 2D spectra recorded at the MAS rates between 50 and 100 kHz, both after shearing to an SQ/SQ representation, for samples of L‐tyrosine hydrochloride and ampicillin, respectively, and acquired with one rotor period of DQ recoupling.…”

“…The component one‐ dimensional isotropic spectra and associated VMAS spectra were generated assuming that the dipolar couplings lead to a MAS rate dependent broadening, with a shape that is a sum of Gaussian and Lorentzian components, and that they also lead to a MAS rate dependent shift in the peak positions [12d, 15a] . We also include random parameter variations in peak positions, peak shapes, MAS dependences, phase and intensity errors, and noise, as described previously in reference [15b] but with an increased probability to generate broad isotropic peaks in order to promote diversity in the two‐dimensional isotropic lineshapes.…”

“…In this 2D dataset, the isotropic part of the interactions remains constant as a function of spinning rate, while the anisotropic parts that lead to broadening and shifts are scaled by the spinning. The isotropic part can be separated out by a suitable transform, so far shown either by parametric fitting, [15a] or more recently by a deep learning method [15b] . In the latter approach a modified convolutional LSTM neural network, dubbed PIPNet, was trained on millions of synthetic VMAS datasets to infer isotropic 1 H NMR spectra.…”