Quantum mechanical theory and a local reaction center model were applied to study electron transfer reactions in different systems. It was revealed that potential-dependent activation energies can be related to experimentally measured Tafel plot by an Arrhenius-like equation. This approach should be very helpful in future determinations of reaction pathways in the electrochemical environment.
The local reaction center model for the Heyrovsky reaction during hydrogen evolution on platinum is:
Pt−H⋯H+(OH2)(OH2)2 + e−(U) → Pt⋯H−H⋯OH2(OH2)2
The calculated reversible potential with the adjustment of Pt−H bond strength, was 0.04 V, in good agreement with experiment. At the reversible potential the activation energy was calculated to be 0.076 eV, compared to the experimental value 0.12 eV.
The calculated potential-dependent activation energies were substituted into an Arrhenius-like equation:
ik = |ioxk − iredk | = A(U)|exp(−Eoxa(U)/RT) − exp(−Ereda(U)/RT)|
The predicted Tafel plot using this equation fitted the experimental one for Pt(100) electrodes, giving a strong support for Volmer-Heyrovsky mechanism with Heyrovsky step being rate limiting.
Two redox reactions were studied on platinum electrode in basic solutions: the formation of underpotential deposited hydrogen by forming a Pt−H bond,
Pt⋯H2O + e−(U) → Pt−H + OH−(aq)
and the electro-oxidation of water, forming a Pt−OH bond.
Pt−OH2 + OH−(aq) → Pt−OH + H2O + e−(U)
Both the linear correlation model and the double layer model yield satisfactory onset potentials for forming Pt−H and Pt−OH bonds in base.
For the first electron transfer step in the oxygen reduction reaction,
Pt2O2 + H+(aq) + e−(U) → Pt2OOH
we found that it is necessary to calculate both reduction and oxidation activation energies. When the transition states for reduction and oxidation were in significant disagreement, the structure averaging technique was found to work, making it possible to iteratively find better converged transition states.
In the absence of defects, conducting diamond is a poor electrocatalyst for hydrogen evolution relative to platinum. This is expected since it is more difficult to break a surface C−H bond than a surface Pt−H bond. Consequently, the activation energies for the Heyrovsky reaction,
C* −H⋯H+(OH2)(OH2)2 + e−(U) → C*⋯H−H⋯OH2(OH2)2
are higher for all potentials. The observed catalytic reactivity for hydrogen evolution on boron-doped diamond electrodes was attributed to the formation of weakly adsorbed hydrogen atoms that was made possible by the subsurface substitutional boron atoms.