Explaining Kinetic Trends of Inner-Sphere Transition Metal Ion Redox Reactions at Electrodes

Heterogeneous inner-sphere metal-ion charge transfer (CT) reactions are important in a variety of applications relevant to catalysis. Predicting the kinetics of inner-sphere CT reactions using simple descriptors would enable the design of improved electrocatalysts for these applications. Here report that the average energy of the d electrons (i.e., d-band center) of a transition metal electrode rationalizes the kinetic trends of inner-sphere CT of transition metal ions. Using surface-enhanced Raman spectroscopy (SERS) combined with DFT calculations, we study anion adsorption on metal surfaces and identify the anion-bridged CT intermediate on an Au electrode for V²⁺/V³⁺, an important redox reaction for flow batteries, showing that it is inner-sphere. We also show that the kinetic parameters correlate with the energy of an adsorbed vanadium intermediate on Au, Ag, Cu, Bi, W, Rh, Fe, Cr, and Ta electrodes. We demonstrate that the energy of the adsorbed vanadium intermediate linearly correlates with the d-band center, such that the d-band center serves as a simple descriptor for the V²⁺/V³⁺ kinetics. We extract kinetic data from the literature for four other inner-sphere CT reactions of transition metal ions involving Cr, Fe, and Co-based complexes to show that the d-band center also linearly correlates with kinetic trends for these systems. The d-band center of the electrode is a general descriptor for heterogeneous inner-sphere CT because it correlates with the adsorption strength of the metal ion intermediate. The d-band center descriptor is analogous to the d-electron configuration of metal ions serving as a descriptor for homogeneous inner-sphere CT because the d-electron configuration controls bond strengths of intermediate metal ion complexes.