INDIRECT DETERMINATION OF SELF-EXCHANGE ELECTRON-TRANSFER RATE CONSTANTS

Second-order rate constants k(ij)(obsd) measured at 25 degrees C in ac etonitrile by slopped-flow spectrophotometry for forty-four electron t ransfer (ET) reactions among fourteen 0/+1 couples [three aromatic com pounds (tetrathiafulvalene, tetramethyltetraselenafulvalene, and 9,10- dimethyl-9,10-dihydrophenazine), four 2,3-disubstituted 2,3-diazabicyc lo[2.2.2]octane derivatives, six acyclic hydrazines, and the bridgehea d diamine 1,5-diazabicyclo [3.3.3]undecane] and seventeen compounds an d forty-seven reactions from a previous study (J. Ant. Chem. Sec. 1997 , 119, 5900) [three p-phenylenediamine derivatives, four ferrocene der ivatives, and ten tetraalkylhydrazines] are discussed. When all 91 k(i i)(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 D elta G double dagger(ij)\, between observed cross reaction activation free energy and that calculated using the k(ii)(fit) values and equili brium constants is 0.13 kcal/mol. The Delta G double dagger(ii)(fit) v alues obtained range from 2.3 kcal/mol for tetramethyltetraselenaful-v alene(0/+) to 21.8 kcal/mol for tetra-n-propylhydrazine(0/+), correspo nding to a factor of 2 x 10(14) in k(ii)(fit). The principal factor af fecting kii(fit) for our data appears to be the internal Vertical reor ganization energy (2,), but k(ii)(fit) values also incorportate the ef fects of changes in the electronic matrix coupling element (V). Signif icantly 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.