but lowers these RMSE values to 1.61 and 2.31 kcal/mol, respectively, which are consistent with very small NQE-induced changes in ion-water structure. Ion-water radial distribution functions show that electrostatics rapidly establishes the first hydration shell, while the explicit many-body corrections relax short-range overstructuring toward the fully interacting reference distribution and NQE slightly broadens and reduces first-shell structuring. Overall, these results establish a practical foundation for predictive hydration free-energy calculations with data-driven many-body potentials in bulk water, and motivate extensions to interfacial hydration and nanoconfined aqueous environments.
Saha et al. (2026) studied this question.