Self-Consistent Theory for Predicting Reaction Mechanisms and Potentials in Acid and Base: H(ads) and OH(ads) Deposition on the Pt(111) Electrode
Authors: Zhao Meng , Anderson Alfred B. 
Published: February 2020

It has recently been shown that the reversible potentials, U
rev, for electron transfer reactions such as reduction of H+(aq) to form under potential deposited H(ads) and oxidation of an OH bond of H2O(ads) in acid electrolyte can be predicted accurately by modeling reactants and products with a comprehensive theory for the electrochemical interface.1,2 Predictions are based on calculated Gibbs energies for the reactant and product during a reaction being equal at the reversible potential. The reversible potential is identified as the potential at the crossing point for reaction and product Gibbs energies plotted as functions of electrode potential. Using two-dimensional density functional band theory, the electrode potential is changed by adding charge, q, to the translational cell: U(q) = [-4.454 - Ef(q)]V/eV, where 4.454 eV is the calculated thermodynamic work function of the standard hydrogen electrode and E
f is the Fermi energy. Solutions at pH = 0 are modeled by a hydrated hydronium ion, H9O4
+, immersed in dielectric continuum containing 1 M cations and anions whose distribution is calculated with a modified Poisson-Boltzmann theory. Because the theory is fully self-consistent, specifying hydronium as the cation in the electrolyte for pH = 0 automatically gives the electrode potential by the above equation for whatever adsorbate and surface charge are present. For pH = 14 base, a hydrated hydroxyl anion, OH-(H2O)3, is used, and again the electrode surface potential is found self-consistently by the above equation.
A significant measure of the accuracy of our theory is the predicted autoionization energy of water. Using the hydrated hydronium ion and hydroxyl ion models, we calculate the autoionization energy for water in bulk solution to be 0.845 eV at 298 K, corresponding to Kw = 0.52 x 10-14, in good agreement with experiment. The autoionization energy also is the difference between the reaction energy for water oxidation to OH(aq) + H+ + e- and the reaction energy for OH-(aq) oxidation to OH(aq) + e-. When these two reactions place the OH on the electrode surface as OH(ads), the difference in reaction energies is still 0.845 eV, but the difference in reversible potentials between acid and base is no longer the solution value 0.845 V. This is because the reversible potentials are influenced by the adsorption energies of OH, which depend on surface conditions. The figure shows predictions of reversible potentials on the standard hydrogen electrode (SHE) scale for the reduced system consisting of 2/3 monolayer (ML) H2O(ads) being oxidized to 1/6 ML OH(ads) + 1/2 ML H2O(ads) in acid and OH-(aq) being oxidized to OH(ads) in base, for which the difference is 0.74 V(SHE). Converting to the reversible hydrogen electrode (RHE) scale, the potentials become 0.64 V(RHE) in acid and 0.75 V(RHE) in base. The shift to higher potential for base shows clearly in the measured onset potentials for OH(ads) formation in acid and base.3

This presentation will introduce the theory and outline several applications to forming OH(ads) and H(ads) on Pt(111) electrodes in acid and base. The theory opens the door for finding mechanisms for electrocatalytic reactions in strong base.
References
1. Anderson, A. B. Insights Into Electrocatalysis. Phys. Chem. Chem. Phys.
2012, 14, 1330-1338.
2. Asiri, H. A.; Anderson, A. B. Using Gibbs Energies to Calculate the Pt(111) Hupd Cyclic Voltammogram. J. Phys. Chem. C
2013, 117, 17509-17513.
3. Gomez-Marin, A. M.; Rizo, R.; Feliu, J. M. Some Reflections on the Understanding of the Oxygen Reduction Reaction at Pt(111). Beilstein J. Nanotechnol.
2013, 4, 956-976.

Figure 1