Nuclear Quantum Effects and the Grotthuss Mechanism Dictate the pH of Liquid Water

Water's ability to autoionize into hydronium (H₃O⁺) and hydroxide (OH^-) ions dictates the acidity or basicity of aqueous solutions, influencing the reaction pathways of many chemical and biochemical processes. In this study, we determine the molecular mechanism of the autoionization process by leveraging both the computational efficiency of a deep neural network potential trained on highly accurate data calculated within density-corrected density functional theory and the ability of enhanced sampling techniques to ensure a comprehensive exploration of the underlying multidimensional free-energy landscape. By properly accounting for nuclear quantum effects, our simulations provide an accurate estimate of the autoionization constant of liquid water (pK_w = 13.71 ± 0.16), offering a realistic molecular-level picture of the autoionization process and emphasizing its quantum-mechanical nature. Importantly, our simulations highlight the central role played by the Grotthuss mechanism in stabilizing solvent-separated ion pair configurations, revealing its profound impact on acid-base equilibria in aqueous environments.