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

Slow electron transfer reactions involving tetraisopropylhydrazine

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Indirect determination of self-exchange electron transfer rate constants

Second-order rate constants kij(obsd) measured at 25 °C in acetonitrile by stopped-flow spectrophotometry for forty-four electron transfer (ET) reactions among fourteen 0/+1 couples [three aromatic compounds (tetrathiafulvalene, tetramethyltetraselenafulvalene, and 9,10-dimethyl-9,10-dihydrophenazine), four 2,3-disubstituted 2,3-diazabicyclo[2.2.2]octane derivatives, six acyclic hydrazines, and the bridgehead diamine 1,5-diazabicyclo[3.3.3]undecane] and seventeen compounds and forty-seven reactions from a previous study (J. Am. Chem. Soc. 1997, 119, 5900) [three p-phenylenediamine derivatives, four ferrocene derivatives, and ten tetraalkylhydrazines] are discussed. When all 91 kij(obsd) values are simultaneously fitted to Marcus's adiabatic cross rate formula kij(calcd) = (kiikjjKijfij)1/2, ln fij = (ln Kij)2/4 ln(kiikjj/Z2), best-fit self-exchange rate constants, kii(fit), are obtained that allow remarkably accurate calculation of kij(obsd); kij(obsd)/kij(calcd) is in the range 0.5−2.0 for all 91 reactions. The average difference without regard to sign, |ΔΔGij|, between observed cross reaction activation free energy and that calculated using the kii(fit) values and equilibrium constants is 0.13 kcal/mol. The ΔGii(fit) values obtained range from 2.3 kcal/mol for tetramethyltetraselenafulvalene0/+ to 21.8 kcal/mol for tetra-n-propylhydrazine0/+, corresponding to a factor of 2 × 1014 in kii(fit). The principal factor affecting kii(fit) for our data appears to be the internal vertical reorganization energy (λv), but kii(fit) values also incorportate the effects of changes in the electronic matrix coupling element (V). Significantly smaller V values for ferrocenes and for hydrazines with alkyl groups larger than methyl than for aromatics and tetramethylhydrazine are implied by the observed ΔGii(fit) values