Comparisons of Measured Rate Constants with Spectroscopically Determined Electron-Transfer Parameters^†

This work involves comparison of rate constants measured for an intervalence (IV) compound with electron-transfer parameters derived from its optical absorption spectrum. The temperature-dependent rate constants for the radical cation having 3-tert-butyl-2,3-diazabicyclo[2.2.2]oct-2-yl (hydrazine) charge-bearing units attached para to a tetramethylbenzene bridge (1⁺) were previously measured. In this study, resonance Raman is used to calculate the magnitudes of the distortions of normal modes of vibration caused by excitation into the intervalence absorption band. These data produce a vibrational reorganization energy λ_v^sym of 9250 cm^-1, and averaged single-mode ω_v for use in the Golden Rule equation of 697 cm^-1. Zhu−Nakamura theory has been used to calculate preexponential factors for analysis of the previously measured variable temperature optical spectra using quartic-enhanced intervalence bands to extract the total reorganization energy and the intramolecular electron-transfer rate constants for intramolecular electron transfer using electron spin resonance. In contrast to using the Golden Rule equation, separation of λ into solvent and vibrational components is not significant for these data. The Zhu−Nakamura theory calculations produce ln(k/T) versus 1/T slopes that are consistent with the experimental data for electronic couplings that are somewhat larger than the values obtained from the optical spectra using Hush's method.