NMR spectrum prediction for dynamic molecules by machine learning: A case study of trefoil knot molecule

Nuclear magnetic resonance (NMR) spectroscopy is one of the indispensable techniques in chemistry because it enables us to obtain accurate information on the chemical, electronic, and dynamic properties of molecules. Computational simulation of the NMR spectra requires time-consuming density functional theory (DFT) calculations for an ensemble of molecular conformations. For large flexible molecules, it is considered too high-cost since it requires time-averaging of the instantaneous chemical shifts of each nuclear spin across the conformational space of molecules for NMR timescales. Here, we present a Gaussian process/deep kernel learning-based machine learning (ML) method for enabling us to predict, average in time, and analyze the instantaneous chemical shifts of conformations in the molecular dynamics trajectory. We demonstrate the use of the method by computing the averaged 1H and 13C chemical shifts of each nuclear spin of a trefoil knot molecule consisting of 24 para-connected benzene rings (240 atoms). By training ML model with the chemical shift data obtained from DFT calculations, we predicted chemical shifts for each conformation during dynamics. We were able to observe the merging of the time-averaged chemical shifts of each nuclear spin in a singlet 1H NMR peak and two 13C NMR peaks for the knot molecule, in agreement with experimental measurements. The unique feature of the presented method is the use of the learned low-dimensional deep kernel representation of local spin environments for comparing and analyzing the local chemical environment histories of spins during dynamics. It allowed us to identify two groups of protons in the knot molecule, which implies that the observed singlet 1H NMR peak could be composed of the contributions from protons with two distinct local chemical environments.