A theoretical study on anomalous temperature dependence of $pKw$ of water

$pH$⁠, with its well-known value of 7 at ambient condition, is a most basic property of water, with wide implications in chemistry and biology. The $pH$ value is determined by the tendency of autoionization of water molecules into ion pairs, $H+$ and $OH−$⁠, and is expected to vary extensively with the water condition, which determines the stability of the ion pairs. When temperature rises from the normal to the supercritical region, the $pH$ of water experimentally exhibits complex, nonmonotonic temperature dependence, that is, it first decreases from 7 and then increases rapidly. Accurate theoretical evaluation of $pH$ and microscopic understanding of this anomalous behavior have proven to be a challenging task because the hydration of these ions, especially for $OH−$⁠, is very difficult to reproduce. In the present study a molecular simulation is performed to understand this peculiar temperature dependence. The imbalance between the ion-water and the water-water molecular interaction strengths and the concomitant water density enhancement in the hydration shell, observed in the supercritical liquids, serve to put a subtle balance to produce this temperature dependence of the $pH$ value. It is found that the large charge transfers from $H+$ and $OH−$ to the surrounding water molecules take place. In these transfers, not only water molecules in the neighboring hydration shell but also those in the outer hydration shell play a significant role. The coordination number of water molecules around $OH−$ is found to be 4.5 at $300K$⁠, which decreases slowly with temperature, for example, 4 at $800K$⁠, in the present calculation.