Estimation of self-exchange electron transfer rate constants for organic compounds from stopped-flow studies

Second-order rate constants k12(obsd) measured at 25 °C in acetonitrile by stopped-flow for 47 electron transfer (ET) reactions among ten tetraalkylhydrazines, four ferrocene derivatives, and three p-phenylenediamine derivatives are discussed. Marcus's adiabatic cross rate formula k12(calcd) = (k11 k22 k12 f12)1/2, ln f12 = (ln K12)2/4 ln(k11k22/Z2) works well to correlate these data. When all k12(obsd) values are simultaneously fitted to this relationship, best-fit self-exchange rate constants, kii(fit), are obtained that allow remarkably accurate calculation of k12(obsd); k12(obsd)/k12‘(calcd) is in the range of 0.55−1.94 for all 47 reactions. The average ΔΔGij between observed activation free energy and that calculated using kii(fit) is 0.13 kcal/mol. Simulations using Jortner vibronic coupling theory to calculate k12 using parameters which produce the wide range of kii values observed predict that Marcus's formula should be followed even when V is as low as 0.1 kcal/mol, in the weakly nonadiabatic region. Tetracyclohexylhydrazine has a higher kii than tetraisopropylhydrazine by a factor of ca. 10. Replacing the dimethylamino groups of tetramethyl-p-phenylenediamine by 9-azabicyclo[3.3.1]nonyl groups has little effect on kii, demonstrating that conformations which have high intermolecular aromatic ring overlap are not necessary for large ET rate constants. Replacing a γ CH2 group of a 9-azabicyclo[3.3.1]nonyl group by a carbonyl group lowers kii by a factor of 17 for the doubly substituted hydrazine and by considerably less for the doubly substituted p-phenylenediamine