Predicting the Ionic Product of Water

We present a first-principles calculation and mechanistic characterization of the ion product of liquid water (K _W ), based on Quantum Cluster Equilibrium (QCE) theory with a variety of ab initio and density functional methods. The QCE method is based on T-dependent Boltzmann weighting of different-sized clusters and consequently enables the observation of thermodynamically less favored and therefore low populated species such as hydronium and hydroxide ions in water. We find that common quantum chemical methods achieve semi-quantitative accuracy in predicting K _W and its T-dependence. Dominant ion-pair water clusters of the QCE equilibrium distribution are found to exhibit stable 2-coordinate buttress-type motifs, all with maximally Grotthus-ordered H-bond patterns that successfully prevent recombination of hydronium and hydroxide ions at 3-coordinate bridgehead sites. We employ standard quantum chemistry techniques to describe kinetic and mechanistic aspects of ion-pair formation, and we obtain NBO-based bonding indices to characterize other electronic, structural, spectroscopic, and reactive properties of cluster-mediated ionic dissociation.