Simulating quadrupolar NMR dynamics in solid electrolyte Li₁₀GeP₂S₁₂

Quadrupolar solid-state (SS) nuclear magnetic resonance (NMR) spectroscopy is an excellent tool to trace lithium (Li) ion diffusion in solid electrolytes due to its sensitivity to dynamics over timescales from nanoseconds to seconds. However, the structural and dynamical complexity of battery materials limits the unambiguous interpretation of experimental data. Fast ionic motion can partially average experimentally observable quantities, leaving the underlying distribution of electric field gradients (EFGs) experimentally inaccessible and thus the measured data hard to interpret. In contrast, atomic simulation approaches, while providing the structure-observable relationship, are often constrained to idealized models. Established methods such as density functional theory (DFT) remain computationally expensive for realistic time and length scales. Here, we show how experimental complexity in the fast-ion conductor Li₁₀GeP₂S₁₂ (LGPS) can be approached via a machine-learning (ML) assisted workflow. ML acceleration enables microsecond-scale molecular dynamics (MD) simulations and efficient predictions of EFG tensors via a tensorial model. By time averaging the EFG tensors from the MD trajectory, we compute the temperature dependence of ⁷Li NMR quadrupolar observables subject to motional narrowing. Our prediction of the quadrupolar coupling of 24 kHz for tetragonal LGPS is in excellent agreement with the experimental value of 23 kHz. Furthermore, we emulate a spin-alignment echo (SAE) experiment in silico and apply the inverse Laplace transform (ILT) to extract correlation times for ionic motion of Li in different LGPS crystal structures. Finally, we assess whether SAE can differentiate inter-grain versus intra-grain ion dynamics via the orientational dependence of the EFG tensor.