Determining the Partial Molar Volume of the Hydrated Electron from First-Principles Simulated Solution Volumes

The microscopic solvation structure of the hydrated electron remains difficult to characterize directly despite extensive experimental and theoretical efforts. The partial molar volume,V¯e-, provides an indirect thermodynamic probe, but quantitative agreement with experiment is challenging due to the strong dependence on the theoretical model. Here, we present a first-principles approach, accelerated by machine learning potentials, for determining V¯e- from volume differences among charge-neutral H2O, HCl, NaCl, and Na-eaq- reference systems. Rather than relying on direct NPT sampling, we determine the equilibrium volumes from pressure-density relations obtained through NVT simulations. Their system size dependence is described using a physically motivated density-volume relation, from which V¯e- is extracted by extrapolation to infinite dilution. The resulting V¯e- is 26 ± 7 cm3 mol-1 on the absolute single ion scale, statistically consistent with the experimental estimate of 26 ± 6 cm3 mol-1. This agreement demonstrates that the present framework can connect microscopic solvation structure with experimentally accessible thermodynamic properties and offers a transferable approach for other aqueous systems.