Field-Driven Proton Transport in Water Revealed by Machine Learning Molecular Dynamics

Excess-proton transport in water arises from the coupling of proton transfer (PT), hydrogen-bond rearrangement, and solvent polarization. While equilibrium Grotthuss diffusion has been widely studied, its response under strong electric fields remains difficult to resolve because simulations must capture both chemical reactivity and induced polarization over long time scales. Here, we have developed a reactive and polarizable machine-learning interatomic potential for molecular dynamics simulations of the hydrated excess proton in water. A fine-tuned PiNet2 model provides an accurate zero-field reference for structure and diffusion, while an AD(OS)-based finite-field coupling enables non-equilibrium simulations under an applied electric field. In the linear-response regime, below 0.04 V/Å, the proton mobility obtained from drift velocity agrees closely with the equilibrium diffusion coefficient. The proton drift velocity remains nearly linear with field strength up to 0.15 V/Å, a field strength at which the ionic mobility of a constrained hydronium ion decreases. Our simulations revealed a distinct field-response of protonated water, whose hydrogen-bond network largely preserves its structural fluctuations and mobility without a comparable dielectric-saturation signature. Furthermore, free-energy analysis shows that strong fields stabilize the hydronium species with four-fold H-bond coordination.