Machine Learning for NMR Observables Sensitive to Nuclear Quantum Effects

Nuclear quantum effects (NQEs) are essential for an accurate description of systems containing light elements. Their omission in classical simulations can lead to significant deviations between theoretical predictions and experimental measurements, particularly for nuclear magnetic resonance (NMR) observables that are highly sensitive to quantum nuclear motion. Although NQEs can be treated rigorously by using ab initio path-integral molecular dynamics (AI-PIMD), the substantial computational cost associated with these simulations continues to limit their applicability to large systems and long timescales. To address this limitation, we developed a machine learning-driven PIMD (MLPIMD) workflow for the accurate and efficient prediction of NMR observables, in which NQEs at finite temperature are explicitly included. As a demonstration, we investigate the experimentally measured isotropic chemical shifts, δ iso , of the 3 He monomer ( 3 He@C 70 6- ) and dimer ( 3 He 2 @C 70 6- ) endohedral fullerene hexaanions. The resulting predictions show excellent agreement with the experiment and reveal a pronounced influence of NQEs on the 3 He chemical shifts in both systems. In particular, NQEs are found to play a key role in determining the chemical-shift difference between the monomer and dimer species. The methodology introduced here is broadly applicable and provides a general framework for investigating NMR observables sensitive to NQEs in complex molecular systems.