For the Ru(III/II) couple in [(bpy)2ClOs(4,4'-bpy)Ru(NH3)5]3+ (bpy = 2,2'-bipyridine; 4,4'-bpy = 4,4'-bipyridine), E( 1/2 ) varies linearly with the donor number (DN) of the solvent with a slope of -26 ± 3 mV/DN unit ranging from nitromethane to dimethyl sulfoxide. For the Os(III/II) couple, the variation is -3 ± 1 mV/DN unit. Plots of ΔE( 1/2 ) = E( 1/2 )(2)-E( 1/2 )(1) vs DN (E( 1/2 ) is the half wave potential for the first or second wave by cyclic voltammetry) undergo a change in slope at DN~14 where there is a change in oxidation states in the mixed-valence form from Os(III)-Ru(II) to Os(II)-Ru(III). By extrapolation of these data, ΔG° for the mixed-valence equilibrium, [(bpy)2ClOs(III)(4,4'-bpy)Ru(II)(NH3)5]4+ ⇆ [(bpy)2CIOs(II)(4,4'-bpy)Ru(III)(NH3)5]4+, varies from ±5.8 kcal/mol in nitromethane to -7.5 kcal/mol in dimethyl sulfoxide. It differs from ΔE( 1/2 ) by up to ~20% even though it has sometimes been assumed in the literature that ΔE(1/2) = -ΔG°. For [(bpy)2ClOs(pz)Ru(NH3)5]3+ (pz = pyrazine) both Os(III/II) and Ru(III/II) couples are significantly solvent dependent for solvents of DN <24. In these solvents oxidation states in the mixed-valence form are Os(III)-Ru(II). The slopes of E(1/2) vs DN plots are -21 ± 4 mV/DN unit (Ru(III/II)) and -8 ± 4 mV/DN unit (Os(III/II)). At DN > 24 the oxidation states switch to Os(II)-Ru(III) and the solvent dependence reverts to being largely in Ru(III/II). There is evidence in the electrochemical data, in comparisons between [(bpy)2ClOs(pz)Ru(NH3)5]3+ and [(bpy)2ClOs(4,4'-bpy)Ru(NH3)5]3+ for significant through-bridge electronic coupling in [(bpy)2ClOs(III)(pz)Ru(II)(NH3)5]4+, but not in [(bpy)2ClOs(II)(pz)Ru(III)(NH3)5]4+. The difference in behavior is caused by extensive H-bonding to the solvent at -Ru(III)(NH3)53+ in [(bpy)2ClOs(II)(pz)Ru(III)(NH3)5]4+. This mixes solvent character into dπ(Ru(III)) which decreases electronic coupling across the bridge.
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