Revealing the mechanism of the water autoprotolysis on the basis of Marcus theory and TD-DFT methodology

Abstract

The rate constants for the autoprotolysis (kA) and corresponding ions recombination (kR) reaction of water and related protic liquids are computed considering both processes as reversible, sequential two-step reactions according to a breaking mechanism, which is supported both experimentally and computationally. The first step, according to the Marcus Theory (MT), consists of an horizontal single electron transfer (SET) occurring in the most stable water dimer, the reaction initial state (IS), to produce the transition state (TS). The second step is a hydrogen atom transfer (HAT), taking place consecutively at the said TS, leading to the reaction final state (FS) after relaxation. The optimized structure of the endergonic FS was calculated by means of the Time Dependent Density Functional Theory (TD-DFT). The determination of the free energy of activation for the autoprotolysis and for the corresponding ions recombination (∆GA≠ and ∆GR≠, respectively) was carried out following the outer-sphere adiabatic MT. The generality of both the proposed mechanism and used computational method is supported by the accurate calculation (MAPE ca. 13%) of the autoprotolysis constants (pKA) of water and five protic liquids (small alcohols and ammonia), covering a range of ca. 15 pKA units. Alternative feasible water mechanisms such as the Single Proton Transfer (SPT) mechanism, based on the non-concerted proton transfer between two water molecules, and the Concerted SET and Hydrogen Atom Transfer (CSETHAT) mechanism were also considered. Nonetheless, all these alternative mechanisms were discarded due to their computed slower autoprotolysis kinetics.