The Grotthuss Mechanism of Aqueous Proton Diffusion is Non-Markovian*

The structure and dynamics of aqueous protons play fundamental roles in many areas of chemistry, biology, and physics. There is a general consensus that the proton achieves its anomalously large diffusion (up to 7 times larger than similarly sized cations) through a structural exchange process, referred to as the Grotthuss mechanism, whereby protons are passed from one molecule to the next. While there has been a multitude of computational studies focused on unraveling the intricacies of proton transport, they have been biased by the assumptions made about the proton dynamics due to the lack of a robust determination of the proton diffusion coefficient from first-principles. Through extensive ab initio molecular dynamics simulations, we provide a thorough statistical determination of the proton diffusion coefficient. These simulations demonstrate that the standard assumption of Markovian dynamics for the Grotthuss mechanism is too simplistic. Proton transitions are correlated and result in the timescale of the Grotthuss mechanism being substantially shorter than was previously thought, no matter the structure that the aqueous proton adopts.