Machine learning model for the chemistry of a solvated electron

In molecular simulations, machine-learning force fields can achieve ab initio accuracy at a lower cost but remain limited in the explicit modeling of electrons. In this work, we develop an electron-aware machine-learning force field, in which an excess electron of interest is modeled quantum mechanically, while the remaining short-range interactions and long-range Coulombic forces are machine-learned to reproduce a density functional theory calculation. We demonstrate the method on the solvated electron in bulk water and its reaction with a hydronium ion. We identify a proton transfer mechanism by which the excess proton recombines with the electron. We determine the forward reaction rates between 350 K and 450 K from first-passage survival functions, which yield an Arrhenius relationship with an activation energy of 3.2 kcal$\cdot$mol$^{-1}$, in good agreement with experiment. From an enhanced sampling simulation, we determine the equilibrium constant, and thus the reaction free energy, which is also consistent with experimental measurements.