Atomic-level structural insight is central to understanding chemical function in molecular solids, with chemical-shift-driven NMR crystallography serving as a key tool for three-dimensional structure determination.¹ Conventional approaches rely on predicting chemical shifts for static candidate structures using density functional theory (DFT), which imposes significant computational constraints on system size and the number of structures considered. Moreover, these methods neglect ensemble averaging over fast (sub-nanosecond) vibrational and thermal motions, as well as nuclear quantum effects, which are particularly important for light atoms such as protons.

Ab initio path-integral molecular dynamics (PIMD) has demonstrated improved agreement between predicted and experimental chemical shifts by incorporating thermal fluctuations and quantum delocalization.² However, such approaches remain computationally prohibitive and are often limited by approximations in the potential energy surface, including incomplete treatment of exchange effects and their functional dependence.

Here, we introduce QNC-NMR,³ a machine-learning-driven framework that overcomes these limitations by combining two models: PET-MOLS, which provides an accurate machine learning interatomic potential (MLIP), and ShiftML3,⁴, which enables rapid prediction of NMR shielding. PET-MOLS facilitates PIMD simulations at a computational cost reduced by several orders of magnitude relative to ab initio methods, while maintaining accuracy through training on hybrid-functional reference data. In parallel, ShiftML3 predicts chemical shielding with near-DFT accuracy at a speed approximately two orders of magnitude faster and without system-size limitations.

This integrated approach enables ensemble-averaged chemical shifts that explicitly incorporate thermal, nuclear quantum, and exchange effects. Benchmarking on crystalline systems shows a two-fold improvement in predicting of labile proton chemical shifts. Furthermore, QNC-NMR extends accurate chemical shift prediction to large and complex systems, including amorphous pharmaceuticals, which are beyond the reach of conventional DFT and classical force-field methods.

[1] Emsley, L. Spiers Memorial Lecture: NMR Crystallography. Faraday Discuss. 2025, 255, 9–45.

[2] Dračínský, M.; Hodgkinson, P. Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics. Chemistry A European J 2014, 20 (8), 2201–2207. 3.  

[3] Kellner, M.^†; Rodriguez-Madrid, R.^†; Holmes, J. B.; Principe, V. P.; Emsley, L.; Ceriotti, M. Quantum-Corrected NMR Crystallography at Scale. arXiv 2026, arXiv:2603.06236

[4] Kellner, M.; Holmes, J. B.; Rodriguez-Madrid, R.; Viscosi, F.; Zhang, Y.; Emsley, L.; Ceriotti, M. A Deep Learning Model for Chemical Shieldings in Molecular Organic Solids Including Anisotropy. J. Phys. Chem. Lett. 2025, 16 (34), 8714–8722.