Prediction of Electron-Transfer Reactivities from Contemporary Theory: Unified Comparisons for Electrochemical and Homogeneous Reactions

Suitable theoretical formalisms are outlined for examining and predicting rate parameters for outer-sphere electron transfer in heterogeneous and homogeneous environments on a unified basis. They are utilized to calculate rate constants and activation parameters for 1 1 electrochemical and 45 homogeneous self-exchange and cross reactions involving transition-metal aquo, ammine, ethylenediamine, and polypyridine redox couples from the appropriate structural and thermodynamic data. Comparison between the calculated and experimental work-corrected rate constants, k,,, and k,,, respectively, indicates that almost uniformly kdd 5 k , the latter values being typically ca. 10-103-fold smaller. These rate discrepancies are reflected chiefly in the activation entropies, although partly compensated by differences between the experimental and calculated activation enthalpies. Although the values of kmld/k, depend somewhat upon the reaction environment as determined by the nature of the coordinated ligands and the metal surface, they are approximately independent of the magnitude of k , or the driving force. Taken together, these findings suggest tht the major origin of the discrepancies between kcaid and k,, is associated with changes in local solvent structure when forming the precursor state. Nonadiabaticity may contribute importantly by necessitating that the reacting centers be in very close proximity. Reactions at "hydrophilic" metal surfaces, such as lead and gallium, that are known to strongly adsorb water molecules yield remarkably similar theory-experiment disparities to those seen with cationic coreactants in homogeneous solution. The markedly closer agreement obtained for some reactions at mercury is attributed to the relatively mild perturbation exerted by this metal surface upon the local solvent structure.