Energy relationships in optical and thermal electron transfer. Temperature dependence of an intervalence transfer absorption band

The temperature dependence of the intervalence transfer (IT) band for the transition [(bpy)₂ClRu^II(pz)Ru^III(NH₃) ₅]⁴⁺ → [(bpy)₂ClRu^III(pz)Ru^II(NH₃) ₅]⁴⁺ (pz = pyrazine; bpy = 2,2′-bipyridine) has been studied in CH₃OD and in a nitrile solvent mixture. The temperature dependences of E_1/2 for the component Ru^III/II couples in this complex were also studied by cyclic voltammetry. The temperature dependence of the absorption band, which was quite large, (∂E_op/∂T) = -10 cm^-1 K^-1 in CH₃OD, μ = 0.035 M, was found to be the same, within experimental error, as the temperature dependence of the difference between the E_1/2 values for the Ru^III/II couples. This agreement provides experimental evidence that the absorption band energy includes the free energy change between the initial and final states and not just the change in enthalpy or internal energy. This is consistent with a model proposed by Marcus and Sutin for electron-transfer based on free energy surfaces despite the inability of the dielectric continuum model to account for the solvent-dependent behavior of this dimer. A quantum mechanical model is also found to predict that the absorption band energy should be temperature dependent because the band energy depends upon the free energy change. This model is based on potential energy surfaces and harmonic oscillator wave functions but includes differences in frequencies and reorganizational energies between the initial and final states, which is the crucial feature for the definition of an entropic change. Complications appear in the relationships that exist between optical and thermal electron transfer, and they are presented and discussed.