Proton Tunneling in the Hydrogen-Evolution Reaction

Abstract

The quantum-mechanical theory of tunneling was applied to the proton-discharge step of the hydrogen-evolution reaction. An unsymmetric Eckart barrier with allowance for zero-point energies was employed. The quantum-mechanical rate iq was calculated by integration with a digital computer for a large number of combinations of barrier width, barrier heights, heats of reaction, and temperatures over a large potential range for protium, deuterium, and tritium. From these results the quantum-mechanical transmission coefficient τ and the quantum-mechanical correction Γ to the separation factor, Tafel slopes, and activation energies were calculated. By comparison to observed values of SH,T, and SH,T as a function of temperature and potential the most probable barrier parameters were obtained. These values were tested by comparison of calculated and observed activation energy, Tafel slopes, SH,D as a function of potential, and the rate of protium evolution at high cathodic overpotentials as a function of temperature. The degree of proton tunneling was found to be significant being 69% at a cathodic overpotential of 1 V for Hg in acid solution.