Theoretical calculation of activation energies for Pt + H+ (aq) + e-(U) ↔ Pt-H: Activation energy-based symmetry factors in the Marcus normal and inverted regions

Abstract

The low coverage reversible potential for underpotential deposition of hydrogen on platinum in acid electrolyte is calculated quantum mechanically with two approaches, (i) one using the calculated reaction energy for the overall reaction and an added constant and (ii) the other based on a model of the electrochemical interface. The former yields 0.40 V and the latter 0.48 V, both close to the observed value of ∼0.40 V. Electrode-potential-dependent activation energies are calculated using the interface model for the reduction of the hydronium ion to form the Pt-H bond and for the reverse oxidation reaction over the -0.3 to 3.0 V range. To make this possible, the model explicitly excludes the hydrogen evolution reaction at the cathodic end and water oxidation at the anodic end of the potential range. Cathodic and anodic symmetry factors are determined from the slopes of the activation energy curves, which are used as models for the corresponding activation free energy curves. They are extended into the Marcus-inverted regions for oxidation and reduction. The symmetry factors add to 1.0 in the normal region and in the inverted regions and are not linear functions of the electrode potential.