Indirect determination of self-exchange electron transfer rate constants

Abstract

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.