A Bayesian approach to NMR crystal structure determination

Abstract

Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well-suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical error in the electronic structure methods. We also extend the recently-developed ShiftML machine-learning model, including the evaluation of the uncertainty of its predictions. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the of similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated 13 C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use 13 C shifts to improve the accuracy of structure determinations.

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

“…This also indicates that the force field used for the CSP procedure accurately describes the crystalline system, and supports the identification of candidate #1 as being the crystal structure. In order to elucidate the ambiguity between candidate #1 and the XRD structure, and to obtain a quantitative comparison of all candidates, a Bayesian probabilistic analysis was carried out using the approach introduced by Engel et al 31 . The two main advantages of using this method to determine the structure that best matches experiment are the quantitative determination of the confidence in the identification of the experimental structure on a continuous scale from 0 to 100%, and the combined use of NMR results for several elements, increasing the accuracy of the identification.…”

“…The predicted chemical shieldings of all snapshots extracted from the MD simulations (168,799,631 total shifts) were obtained using ShiftML version 1.2 (publicly available at https://shiftml.epfl.ch ) 29 , 31 . The conversion from predicted shieldings to isotropic shifts is described in the Supplementary Methods.…”

“…Recently a new approach to predicting chemical shifts in molecular solids was introduced 29 by training a machine-learning model on GIPAW DFT calculated chemical shifts for 3546 diverse structures from the Cambridge structural database (CSD) 30 . This model, dubbed ShiftML, can now be used to predict chemical shifts for any molecular solid (currently limited to solids comprised of C, H, N, O, S atoms) in a matter of seconds 29 , 31 , which opens up the possibility for large-scale shift computations on large structures.…”

Gaussian Process Regression for Materials and Molecules

“…This “ShiftML” model 387 achieves an accuracy comparable to the reference DFT calculations and can be combined with experimentally determined shifts to assign the crystal structure of a sample to the most compatible polymorph among a set of candidates ( Figure 40 ). In combination with model error estimation, it is also possible to establish, in a quantitative manner, the reliability of such assignment 388 and to use the ML prediction to interpret solid-state NMR experiments. 389 …”

Solid-state NMR spectroscopy

“…This has led to complete 3D structures of microcrystalline drugs and organic CO 2 capture materials 225,226 . These structures can be quantified in terms of probability and precision 227 , with average displacement parameters of 0.01 Å 2 for a recent structure of ampicillin 226 . Using fast MAS and DNP NMR spectroscopy, sensitivity is now sufficient to characterize pharmaceutical polymorphs in situ, as embedded in formulations 102,228 .…”