Deep potential molecular dynamics of water self-ionization

The chemical equilibrium between self-ionized and molecular water dictates the acid-base chemistry in aqueous solutions. Despite its relevance, determining the extent of water self ionization reaction remains an outstanding problem from a theoretical perspective. The lack of computationally efficient and reactive interatomic potentials and the challenging description of the water self-ionization prevented a direct quantification of this reaction from first principles. In this work, we combined deep neural network potentials with enhanced sampling techniques to perform extensive atomistic simulations of water self-ionization at finite temperature. The free energy as a function of hydroxide and hydronium separation is computed, evidencing a finite-size dependence of the free energy curves and allowing us to evaluate the equilibrium pH of water from first principles. Our computed equilibrium pH of 7.3 ± 0.1 is close to the experimental value of 7.0. The methodology developed in this work can be readily generalized to compute acid-base equilibrium constants of other condensed phase systems.