First-principles NMR of oxide glasses boosted by machine learning

Solid-state NMR has established itself as a cutting-edge spectroscopy for elucidating the structure of oxide glasses thanks to several decades of methodological and instrumental progress. First-principles calculations of NMR properties combined with molecular-dynamics (MD) simulations provides a powerful complementary approach for the interpretation of NMR data, although they still suffer from limitations in terms of size, time and high consumption of computational resources. We address this challenge by developing a machine-learning framework to boost predictive modelling of NMR spectra. We use kernel ridge regression techniques (least-squares support vector regression and linear ridge regression) combined with smooth overlap of atomic position (SOAP) atom-centered descriptors to efficiently predict NMR interactions: the isotropic magnetic shielding and the electric field gradient (EFG) tensor. As illustrated in this work, this approach enables the simulation of magic-angle spinning (MAS) and multiple-quantum magic-angle spinning (MQMAS) NMR spectra of very large models (more than 10 000 atoms) and an efficient averaging of NMR properties over MD trajectories of nanoseconds for incorporating finite-temperature effects, at the computational cost of classical MD simulations. We illustrate these advances for sodium silicate glasses (SiO₂-Na₂O). NMR parameters (isotropic chemical shift and electric field gradient) could be predicted with an accuracy of 1 to 2% in terms of the total span of the NMR parameter values. To include vibrational effects, an approach is proposed of scaling the EFG tensor in NMR simulations with a factor obtained from the time auto-correlation functions computed on MD trajectories.