Computational Hydrogen Electrode
The computational hydrogen electrode is a way to place electrochemical surface intermediates on a free energy scale using only DFT adsorption energies, without simulating the charged electrode-electrolyte interface explicitly. Taking the standard hydrogen electrode as the potential reference, the chemical potential of a proton-electron pair at pH 0 and 1 bar H2 equals that of half an H2 molecule. The free energy of each proton-electron transfer step is then shifted by -eU at electrode potential U, with a kT ln 10 per pH unit correction for other pH values, plus zero point energy and entropy corrections. The potential at which every step becomes downhill gives a limiting potential, and its difference from the equilibrium potential gives a theoretical overpotential. The approach is used for the oxygen reduction, oxygen evolution and hydrogen evolution reactions; see also Hydrogen adsorption free energy.
Introduction of the method for oxygen reduction (2004)
Nørskov, Rossmeisl, Kitchin and coworkers introduced this six-step procedure and described it as applicable to any electrochemical reaction. Besides the hydrogen electrode reference, the bias shift and the pH correction, they include a water layer to capture hydrogen bonding to adsorbed OH, estimate that the double layer field changes O and OH adsorption energies on Pt(111) by only about 0.015 eV (so it is neglected), and take the overall O2 to water free energy from experiment to avoid the poor DFT description of gas-phase O2. Applied to Pt(111), it shows adsorbed O and OH acting as thermodynamic sinks at 1.23 V (Nørskov et al. 2004). Summary: norskov2004.