Hydration Free Energies of Alkali Metal and Halide Ions from Data-Driven Many-Body Potentials

Single-ion hydration free energies stringently test molecular models for aqueous ions, but quantitative comparison is complicated by the interplay of short-range ion-water interactions, long-range electrostatics, many-body polarization, and nuclear quantum effects (NQE). Here, we compute hydration free energies for alkali-metal cations (Li⁺-Cs⁺) and halide anions (F^--I^-) using MB-nrg ion potentials in MB-pol water. Free energies are evaluated with a staged alchemical cycle in which ion-water interactions are introduced sequentially (charge, polarization, and explicit 2-body and 3-body terms), enabling stable sampling of each contribution. To perform robust charging transformations within the MBX electrostatics framework, we implement a soft-core Coulomb scaling and evaluate free-energy changes using finite-difference thermodynamic integration. Model fidelity is assessed primarily by comparison to experimental within-series reference differences, ΔΔG_hyd, which reduce sensitivity to single-ion reference conventions. Across both ion families, MB-nrg/MB-pol reproduces the expected monotonic weakening of hydration with increasing ionic size, yielding RMSE values of 2.12 and 3.39 kcal/mol for the alkali-metal and halide ΔΔG_hyd series, respectively. Including NQE produces only small shifts in ΔG_hyd 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.