Quantum Chemical Approach to Redox Reactions Including Potential Dependence: Application to a Model for Hydrogen Evolution from Diamond

The evolution of H 2 from diamond cathodes according to the proposed mechanism H + (aq) + ⪫C−H + e - → H 2 + ⪫C • is treated with ab initio quantum mechanics. The solvated proton and diamond surface C−H bond are modeled with molecular clusters, and the electron is introduced at selected potentials by using a remote donor molecule. The reduction occurs when the electron affinity, EA, of the surface complex increases to the ionization potential, IP, of the donor as the complex traverses its reaction coordinate. When they are equal, equilibrium is assumed and electron transfer occurs. The electrochemical potential, U, is given by U = (IP/eV − 4.6) V. For the H 2 generation reaction studied, the electron transfer coincides with the transition-state structure, and the activation energy is found to decrease as the potential becomes more negative. It is shown that surface C−H bonds will re-form by H + (aq) discharge on the surface carbon radicals. The potential-dependent reduction of H + (aq) to H • is examined, too. Comparison is made with the gas-phase generation of hydrogen and surface carbon radicals. The present model employs the hydronium ion for H + (aq), methane and isobutane for surface C−H, and the self-consistent HF/STO-3G method. In general, use of an electron donor is not required. This approach should find application to many other electrochemical reactions.