Ionic atmosphere effects on the energetics of thermal and optical electron-exchange reactions: Application to ferrocenium-ferrocene self exchange

A treatment of ionic-atmosphere effects upon symmetrical electron-transfer reactions resulting from added electrolyte is outlined. Relationships are derived on the basis of the extended Debye-Huckel model for the increase in the activation free energy, ΔG_ia*, associated with reorganization of the ionic atmosphere for homogeneous-phase reactions involving a pair of spherical reactants with varying internuclear distance R. Similar relationships apply to the energetics of symmetrical optical electron transfer, since the increase in the optical transition energy, ΔE, should equal the corresponding ionic atmosphere reorganization energy, E; under the anticipated linear response conditions, E = 4ΔG_ia*. The predicted ΔG_ia* (and hence ΔE) values increase sharply with increasing R, as a consequence of the diminished “sharing” of the ionic cloud surrounding the donor and acceptor sites under these conditions. Outer-sphere electrochemical reactions, featuring a single “near-isolated” reactant, are predicted to feature substantially larger ΔG_ia* values than for homogeneous processes proceeding with the reaction partners in contact. The influence of more specific “ionic atmosphere” effects upon ΔG_ia*, especially involving reactant-electrolyte ion pairing, is also discussed. Unlike that of the nonspecific ionic atmosphere, the nuclear reorganization process associated with counterion transport between donor and acceptor sites coupled with electron transfer is nonlinear in nature, so that E ≠ 4ΔG_ia*. Some recent experimental data for electrolyte effects upon the rate constants for ferrocenium-ferrocene self exchange and related systems are examined in the light of these considerations.