Fast Method for Calculating Spatially Resolved Heterogeneous Electron-Transfer Kinetics and Its Application to Graphene with Defects

Establishing the relationship between the electrochemical activity of a surface and its chemical structure is extremely important for the development of new functional materials for electrochemical energy conversion systems. Here, we present a fast method, which combines a theoretical model and density functional theory calculations, for the prediction of nonadiabatic electron-transfer kinetics at nanoscale surfaces with spatial resolution. We propose two approaches for the calculation of electronic coupling, which characterizes the interaction strength between electronic states of a redox-active molecule and surface electronic states and depends on the position of the molecule above the surface. The first one is based on the linear approximation between the electronic coupling and overlap integral and takes into account the molecular wave function explicitly. The second one uses Tersoff-Hamann and Chen approximations that are based on the model assumption about the molecular orbital structure and allow ultrafast electron-transfer kinetic calculations only from the surface wave function. The proposed method was applied for the electron-transfer kinetic investigation of graphene with defects. We have shown that defects can act as electrocatalytic sites, selectively increasing the electrontransfer rate in a different range of standard redox potentials depending on the defect type.