Solvent Dynamical Effects in Electron Transfer: Comparisons of Self-Exchange Kinetics for Cobaltocenium-Cobaltocene and Related Redox Couples with Theoretical Predictions

Article abstract of DOI:10.1021/j100323a026

Rate constants, K_ex, and activation parameters for the self-exchange of cobaltocenium-cobaltocene Cp₂Co^+/0, and the decamethyl derivative Cp'₂Co^+/0, in 13 organic solvents have been evaluated by using the proton NMR line-broadening technique with the objective of probing the influence of solvent dynamics upon the electron-transfer kinetics.Together with some corresponding measurements reported earlier for ferrocenium-ferrocene Cp₂Fe^+/0, additional measurements for the decamethyl derivative, Cp'₂Fe^+/0, and with corresponding data for Cp₂Co^+/0 electrochemical exchange, these results enable a systematic comparative examination to be made of the effects of solvent dielectric relaxation on the barrier-crossing frequency for such simple outer-sphere reactions.For the facile Cp'₂Co^+/0 couple the solvent dependence of the observed frequency factors, ν_n(obsd), extracted from the k_ex values by correcting for the solvent-dependent barrier height, ΔG^*, is in approximate accordance with the relative frequency factors ν_os(calcd), predicted from the continuum model of overdamped solvent relaxation.The subunity (ca. 0.7-0.8) slope of the logarithmic ν_n(obsd) - ??_os(calcd) plot for Cp'₂C0^+/0 self-exchange is consistent with a recent theoretical prediction of the combined effect of overdamped solvent motion and reactant vibrations (ref 2g).In a given solvent, the sequence of k_ex values is Cp'₂Co^+/0 > Cp2Co^+/0 ca.Cp'₂Fe^+/0 > Cp₂Fe^+/0, with Cp₂Co^+/0 and Cp₂Fe^+/0 being about 10- and 100-folds lower, respectively, than Cp'₂Co^+/0 self-exchange.While these reactivity differences can be traced to variations in donor-acceptor orbital overlap, the solvent dependencies of k_ex for Cp₂Co^+/0 and Cp₂Fe^+/0 electron exchange nevertheless exhibit a strong influence from overdamped solvent relaxation.Marked deviations from the dielectric continuum predictions are seen, however, in several solvents.Thus the barrier-crossing frequencies in propylene carbonate, N-methylformamide, and especially methanol are substantially (4-100-fold) larger than expected from ν_os(calcd), implicating the presence of surprisingly rapid relaxation modes in these solvents.The solvent-dependent activation parameters also differ significantly from the expectations of conventional theoretical modes.