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.