Computational methods for intramolecular electron transfer in a ferrous–ferric iron complex

Abstract

The limitations of common theoretical and molecular computational approaches for predicting electron transfer quantities were assessed, using an archetypal bridged ferrous–ferric electron transfer system in aqueous solution. The basis set effect on the magnitude of the electronic coupling matrix element computed using the quasi-diabatic method was carefully examined, and it was found that the error related to a poor basis set could exceed the thermal energy at room temperature. A range of approaches to determining the external (solvent) reorganization energy were also investigated. Significant improvements from the Marcus continuum model can be obtained by including dipolar Born–Kirkwood–Onsager correction. In this regard, we also found that Klamt’s Conductor-Like Screening Model (COSMO) yields estimations of the external reorganization energy similar to those obtained with explicit solvent molecular dynamics simulations if the fast-frequency modes are neglected, which makes it an attractive alternative to laborious umbrella sampling simulations. By using the COSMO model, we also confirm that a decrease in curvature of the potential energy surface is a manifestation of the dielectric saturation observed in the first solvation layer. The linearity of solvent response to the charge redistribution was assessed by analyzing the energy gap autocorrelation function as well as the solvent density and dipole moment fluctuations. Molecular dynamics was also used to evaluate the sign and magnitude of the solvent reorganization entropy and to determine its effect on the predicted electron transfer rate. Finally, we present a simple way of estimating the vibration frequency along the reaction coordinate, which also enables prediction of the mass-dependent isotopic signature of electron transfer reactions.