Intramolecular and Environmental Contributions to Electrode Half-Reaction Entropies of M(tacn)23+/2+ (M = Fe, Co, Ni, Ru; tacn = 1,4,7-Triazacyclononane) Redox Couples

Electrode half-reaction entropies, Δ S ° rc, are measured as a function of solvent and electrolyte type and concentration for four M(tacn) 2 3+/2+ (M = Fe, Ni, Co, Ru; tacn = 1,4,7-triazacyclononane) redox couples that experience different amounts of structural change in conjunction with electron transfer. Metal dependent values of Δ S ° rc are observed for these couples and are shown to arise primarily from vibrational and electronic contributions to intramolecular entropy. Vibrational terms become important when frequencies are small and change significantly with a change in oxidation state, as occurs when an increase in number of antibonding electrons weakens metal−ligand bonds upon reduction. Entropy measurements are referenced to the Ru 3+/2+ couple, which is characterized by small inner-shell reorganization. Experimentally, mean values of Δ(Δ S ° rc ) M-Ru = 27 (7), 30 (6), and 69 (14) J mol -1 K -1 obtained from data in seven solvents are observed for M = Fe, Ni, and Co, respectively. The computed sums of vibrational (obtained using octahedral stretching frequencies of M(NH 3 ) 6 3+/2+ complexes) and electronic entropy differences equal 4, 31, and 69 J mol -1 K -1 for the same three metals relative to Ru. The unexpectedly large value of Δ(Δ S ° rc ) Fe-Ru is the result of a spin-state equilibrium in solution. Temperature-dependent magnetic susceptibility measurements yield Δ H ° = 23.8 (1.0) kJ mol -1, Δ S ° = 68.2 (2.8) J mol -1 K -1, and K SE = 0.25 (298 K) for conversion of low- to high-spin Fe(tacn) 2 2+ in D 2 O. Observation of uniform values of Δ(Δ S ° rc ) M-Ru for each couple in seven solvents indicates that, if inner- and outer-shell reorganizations are coupled during electron transfer, this fact is not reflected in the solvent dependence of Δ S ° rc . Ion-pair formation occurs between oxidized complexes and electrolyte anions. Negative and positive contributions to Δ S ° rc result as ion-paired M(tacn) 2 3+:X - is reduced to dissociated M(tacn) 2 2+ in H 2 O when X - = Cl - and ClO 4 -, respectively.