Electron Transfer of Hydrated Transition-Metal Ions and the Electronic State of Co 3+ (aq).

Electron transfer (ET) is broadly described by Marcus-type theories and plays a central role in many materials and catalytic systems and in biomolecules such as cytochromes. Classic ET processes are the self-exchange reactions between hydrated transition-metal ions such as Fe2+ (aq) + Fe3+ (aq) → Fe3+ (aq) + Fe2+ (aq). A well-known anomaly of Marcus theory is Co2+ /Co3+ exchange, which proceeds ∼105 times faster than predicted. Co3+ (aq) is a complex and reactive system widely thought to feature low-spin Co3+ . We studied the self-exchange process systematically for Cr2+ /Cr3+ , V2+ /V3+ , Fe2+ /Fe3+ , and Co2+ /Co3+ using six distinct density functionals. We identify directly the ∼105 anomaly of Co2+ /Co3+ from the electronic reorganization energies without the use of empirical cross-relations. Furthermore, when Co3+ is modeled as high-spin, the anomaly disappears, bringing all four processes on a linear trend within the uncertainty of the experiments and theory. We studied both the acid-independent [Co(H2 O)6 ]3+ species that dominates at low pH and the acid-dependent [Co(OH)(H2 O)5 ]2+ species that becomes important at higher pH and used two distinct explicit second-sphere hydration models and models of perchlorate anion association. The high-spin state with weaker Co-O bonds is stabilized by vibrational energy and entropy by ∼11 and ∼12 kJ mol-1 , correcting the gap estimates from absorption spectroscopy. High-spin Co3+ (aq) explains the full experimental data series of the M(aq) systems. Low-spin Co3+ and high-spin Co2+ involve changes in the eg occupation upon ET with associated M-O bond changes and increased reorganization energy. In contrast, with high-spin Co3+ (aq), the redox-active electrons shuffle between t2g orbitals to minimize structural changes, producing a relative rate in excellent agreement with the experiments. This eg occupation effect explains most of the experimental differences in the rate constants, with the remaining part explained by second-sphere hydration and anion effects. Our results consistently suggest that some high-spin Co3+ (aq) is active during the experiments.