Quantum tunneling on water. II. Quantitative rate formalism of barrierless electron transfer and application to oxidation reactions.

In contrast to its presumably inert bulk counterpart, the air-water interface of microdroplets exhibits surprising redox reactivity, enabling both oxidation and reduction of a wide range of substrates. We have recently proposed a theoretical model of interfacial quantum tunneling to rationalize microdroplet redox chemistry. By generalizing Marcus' theory of concerted electron transfer to heterogeneous interfacial water environments, this model is able to qualitatively explain the counterintuitive thermodynamics and kinetics of redox chemistry observed on the air-water interface. Following the general framework developed in Part I, this study quantitatively analyzes the solvation distribution Pθ of OH- donors from a statistical mechanics perspective and further derives a closed-form rate expression for barrierless electron transfer. The resulting compact formalism highlights a distinct interfacial pathway to reach donor-acceptor energy degeneracy and mathematically shows how interfacial water can facilitate and gate electron tunneling, complementing the classical Marcus picture of solvent reorganization. Fundamentally, translational symmetry is broken at the air-water interface, unlocking a new degree of freedom of solvation coordinates that are otherwise inaccessible in the bulk. For practical estimates, a phenomenological exponential model for Pθ is proposed and evaluated with the input of interfacial water structure. When applied to the spontaneous formation of H2O2 in water microdroplets with molecular O2 and O3 as electron acceptors, this formalism yields reasonable agreement with experimental measurements, which, to the best of our knowledge, marks the first attempt to predict on-water redox reaction kinetics from first principles. Hence, both the physical underpinning and practical utility of our model are firmly supported. The newly developed rate formalism is expected to facilitate quantitative modeling and calculation of redox chemistry on water.