Journal of the American Chemical Society, Vol.120, No.32, 8230-8240, 1998
Indirect determination of self-exchange electron transfer rate constants
Second-order rate constants k(ij)(obsd) measured at 25 degrees C in acetonitrile by slopped-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. Ant. Chem. Sec. 1997, 119, 5900) [three p-phenylenediamine derivatives, four ferrocene derivatives, and ten tetraalkylhydrazines] are discussed. When all 91 k(ii)(obsd) values are simultaneously fitted to Marcus's adiabatic cross rate formula k(ij)(calcd) = (k(ii)k(jj)K(ij)f(ij))(1/2), In S-ij (In K-ij)(2)/4 In(k(ii)k(jj)/Z(2)), best-fit self-exchange rate constants, k(ii)(fil), are obtained that allow remarkably accurate calculation of k(ij)(obsd); k(ij)(obsd)/k(ij)(calcd) is in the range 0.5-2.0 for all 91 reactions. The average difference without regard to sign, \Delta Delta G double dagger(ij)\, between observed cross reaction activation free energy and that calculated using the k(ii)(fit) values and equilibrium constants is 0.13 kcal/mol. The Delta G double dagger(ii)(fit) values obtained range from 2.3 kcal/mol for tetramethyltetraselenaful-valene(0/+) to 21.8 kcal/mol for tetra-n-propylhydrazine(0/+), corresponding to a factor of 2 x 10(14) in k(ii)(fit). The principal factor affecting kii(fit) for our data appears to be the internal Vertical reorganization energy (2,), but k(ii)(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 Delta G double dagger(ii)(fit) values.