Calculation of solvent free energies for heterogeneous electron transfer at the water–metal interface: Classical versus quantum behavior

Abstract

A computer simulation method is developed for the study of the adiabatic heterogeneous electron transfer reactions between an ion in solution and a metal electrode. The particular system studied is the Fe2+/Fe3+ electron transfer reaction with a Pt(111) electrode. The adiabatic classical free energy curve for the reaction is computed using umbrella sampling and molecular dynamics generated by the adiabatic solution to an Anderson–Newns-like Hamiltonian. Reactive flux calculations are then performed to determine the effect of transition state recrossings on the classical adiabatic rate constant. These effects are not found to be large (κ∼0.6). The water solvent model is next quantized using Feynman path integral techniques and the quantum adiabatic free energy curve for electronic transfer is calculated. The latter calculation shows that the solvent activation free energy barrier and thermodynamic driving force for the electron transfer process can be significantly affected by the water quantization. These results suggest that classical models for water may not be adequate, or at least need to be modified, for the accurate computer simulation of many heterogeneous electron transfer reactions.