Molecular dynamics investigation of ferrous-ferric electron transfer in a hydrolyzing aqueous solution: calculation of the pH dependence of the diabatic transfer barrier and the potential of mean force.

We present a molecular model for ferrous-ferric electron transfer in an aqueous solution that accounts for electronic polarizability and exhibits spontaneous cation hydrolysis. An extended Lagrangian technique is introduced for carrying out calculations of electron-transfer barriers in polarizable systems. The model predicts that the diabatic barrier to electron transfer increases with increasing pH, due to stabilization of the Fe3+ by fluctuations in the number of hydroxide ions in its first coordination sphere, in much the same way as the barrier would increase with increasing dielectric constant in the Marcus theory. We have also calculated the effect of pH on the potential of mean force between two hydrolyzing ions in aqueous solution. As expected, increasing pH reduces the potential of mean force between the ferrous and ferric ions in the model system. The magnitudes of the predicted increase in diabatic transfer barrier and the predicted decrease in the potential of mean force nearly cancel each other at the canonical transfer distance of 0.55 nm. Even though hydrolysis is allowed in our calculations, the distribution of reorganization energies has only one maximum and is Gaussian to an excellent approximation, giving a harmonic free energy surface in the reorganization energy F(DeltaE) with a single minimum. There is thus a surprising amount of overlap in electron-transfer reorganization energies for Fe(2+)-Fe(H2O)6(3+), Fe(2+)-Fe(OH)(H2O)5(2+), and Fe(2+)-Fe(OH)2(H2O)+ couples, indicating that fluctuations in hydrolysis state can be viewed on a continuum with other solvent contributions to the reorganization energy. There appears to be little justification for thinking of the transfer rate as arising from the contributions of different hydrolysis states. Electronic structure calculations indicate that Fe(H2O)6(2+)-Fe(OH)n(H2O)(6-n)(3-n)+ complexes interacting through H3O2- bridges do not have large electronic couplings.