Tracking Li atoms in real-time with ultra-fast NMR simulations

We present for the first time a multiscale machine learning approach to jointly simulate atomic structure and dynamics with the corresponding solid state Nuclear Magnetic Resonance (ssNMR) observables. We study the use-case of spin-alignment echo (SAE) NMR for exploring Li-ion diffusion within the solid state electrolyte material Li₃PS₄ (LPS) by calculating quadrupolar frequencies of ⁷Li. SAE NMR probes long-range dynamics down to microsecond-timescale hopping processes. Therefore only a few machine learning force field schemes are able to capture the time- and length scales required for accurate comparison with experimental results. By using a new class of machine learning interatomic potentials, known as ultra-fast potentials (UFPs), we are able to efficiently access timescales beyond the microsecond regime. In tandem, we have developed a machine learning model for predicting the full ⁷Li electric field gradient (EFG) tensors in LPS. By combining the long timescale trajectories from the UFP with our model for ⁷Li EFG tensors, we are able to extract the autocorrelation function (ACF) for ⁷Li quadrupolar frequencies during Li diffusion. We extract the decay constants from the ACF for both crystalline β-LPS and amorphous LPS, and find that the predicted Li hopping rates are on the same order of magnitude as those predicted from the Li dynamics. This demonstrates the potential for machine learning to finally make predictions on experimentally relevant timescales and temperatures, and opens a new avenue of NMR crystallography: using machine learning dynamical NMR simulations for accessing polycrystalline and glass ceramic materials.