Activation energy for a model ferrous-ferric half reaction from transition path sampling

Abstract

Activation parameters for the model oxidation half reaction of the classical aqueous ferrous ion are compared for different molecular simulation techniques. In particular, activation free energies are obtained from umbrella integration and Marcus theory based thermodynamic integration, which rely on the diabatic gap as the reaction coordinate. The latter method also assumes linear response, and both methods obtain the activation entropy and the activation energy from the temperature dependence of the activation free energy. In contrast, transition path sampling does not require knowledge of the reaction coordinate and directly yields the activation energy [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Benchmark activation energies from transition path sampling agree within statistical uncertainty with activation energies obtained from standard techniques requiring knowledge of the reaction coordinate. In addition, it is found that the activation energy for this model system is significantly smaller than the activation free energy for the Marcus model, approximately half the value, implying an equally large entropy contribution.

The temperature dependence of the symmetry factor for a model Fe3+(aq)/Fe2+(aq) redox half reaction

“…Our model half reaction should reproduce this behaviour provided it is complying with the MT. All numerical studies of ferrous-ferric electron transfer agree that the symmetry factor β = 1/2 at rG 0 = 0 with the expected linear dependence on thermodynamic driving force [36,37,[39][40][41][42]. Temperature effects have been investigated as well and were also found to be consistent with the MT [16,20,21].…”

“…This small discrepancy could be due to the non-linearity introduced by the coupling in the adiabatic state (Equation (27)) as discussed in Ref. [37]. Indeed the offset (2 kJmol −1 ) is of the same magnitude as the coupling parameter γ = 3 kJ mol −1 and can therefore be regarded as a small perturbation.…”

“…A first application of this method to the ferrous/ferric half reaction can be found in Ref. [37]. These calculations will be extended to finite overpotential in the present work.…”

“…In this publication, we return therefore to previous work on this reaction [36,37] extending our numerical studies to temperature effects.…”

Removing the barrier to the calculation of activation energies

“…They applied it to a model isomerization reaction and others have employed it to determine the activation energy in other systems using transition path sampling. [10][11][12] In this paper, we extend this approach by showing that the activation energy can be obtained directly from the trajectories used to obtain the rate constant at a single temperature using other TCFs. In addition, the same tactic can be applied to calculate the activation energy within quantum mechanical TCF formulations of the reaction rate constant.…”