Delocalized radical cations having two nitrogen-centered charge bearing units bridged by π systems may be considered Class III intervalence compounds. The transition energy of the longest wavelength band may therefore be equated with the E op of Hush theory, which is twice the electronic interaction matrix element V. The optically estimated value of V (V op = E op/2) drops significantly (6.0 kcal/mol) when the methyl groups of tetramethyl-p-phenylenediamine radical cation (1 + , V op = 23.3 kcal/mol) are replaced by phenyl groups in the tetraphenyl compound (3 + ) and detectably (0.6 kcal/mol) when they are replaced by bicyclic alkyl groups in bis(9-azabicyclo[3.3.1]non-9-yl)-p-phenylenediamine (4 + ). The V op values observed for n bonds connecting the nitrogens follow the relationship V = V 0 exp(−β n (n−1)/2) rather well for dinitrogen (n = 3), p-phenylene (n = 5), and biphenylene (n = 9) bridges with β n ∼ 0.3. AM1-NCG calculations are fairly successful at predicting changes in E op for these compounds and 1,5-dimethyl-1,5-dihydrophenazine radical cation (8 + ) but fail totally for methylviologen radical cation (10 + ). AM1 calculations predict [Me2N(CHCH) y NMe2]+ to localize at y = 6 and [Me2N(C⋮C) y NMe2]+ at y = 5, and in both cases calculated V drops below calculated λ/2, as expected. V values for nitrogen-centered and transition metal-centered intervalence compounds are compared. Significantly larger V values for the nitrogen-centered examples cause charge delocalization to occur for larger π systems than for transition metal-centered examples.

Second-order rate constants k 12 (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 k 12 (calcd) ) (k 11 k 22 k 12 f 12 ) 1/2 , ln f 12 ) (ln K 12 ) 2 /4 ln(k 11 k 22 /Z 2 ) works well to correlate these data. When all k 12 (obsd) values are simultaneously fitted to this relationship, best-fit self-exchange rate constants, k ii (fit), are obtained that allow remarkably accurate calculation of k 12 (obsd); k 12 (obsd)/k 12 ′(calcd) is in the range of 0.55-1.94 for all 47 reactions. The average ∆∆G ij q between observed activation free energy and that calculated using k ii (fit) is 0.13 kcal/mol. Simulations using Jortner vibronic coupling theory to calculate k 12 using parameters which produce the wide range of k ii 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 k ii 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 k ii , demonstrating that conformations which have high intermolecular aromatic ring overlap are not necessary for large ET rate constants. Replacing a γ CH 2 group of a 9-azabicyclo[3.3.1]nonyl group by a carbonyl group lowers k ii by a factor of 17 for the doubly substituted hydrazine and by considerably less for the doubly substituted p-phenylenediamine.

Rate constants (k ij ) measured by stopped flow are reported for 50 additional intermolecular electron transfer reactions between 0 and 1+ oxidation states of various compounds, enlarging our data set to 141 reactions between 45 couples in acetonitrile containing 0.1 M tetrabutylammonium perchlorate at 25°C. Hydrazines with both saturated and unsaturated substituents, ferrocene derivatives, and heteroatom-substituted aromatic compounds are included in the couples studied. Least-squares fit of all the reactions to simple Marcus cross-reaction theory provides an internally consistent set of best fit intrinsic barriers ∆G ‡ ii (fit) (for selfelectron transfer of each couple) covering a range of over 19 kcal/mol (rate constant range 2 × 10 14 ) that predicts the k ij rather accurately. All reactions have ratios of calculated to observed k ij in the range 0.3-3.3 and 95% fall in the range 0.5-2.0. These results require that the preexponential factor for a cross reaction is close to the geometric mean of those for the self-reactions, which is not expected. Changes in internal reorganization energy (λ v ) have major effects on ∆G ‡ ii (fit), and changes in electronic overlap (H ab ) have easily detectable ones, but the reactions studied are clearly not strongly nonadiabatic, even though in many cases the only electronic overlap at the transition state is between nonbonded alkyl groups. It is argued that these reactions occur in the "elbow region" between nonadiabatic and adiabatic electron transfer. IntroductionOuter-sphere single electron transfer (ET) reactions between a neutral species i 0 , and a radical cation, j + , eq 1, are the simplest cases for calculation of rate constants. Marcus introduced the

Second-order rate constants k ij (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 k ij (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, ln f ij = (ln K ij )2/4 ln(k ii k jj /Z 2), best-fit self-exchange rate constants, k ii (fit), 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, |ΔΔG ⧧ 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 ΔG ⧧ ii (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 k ii (fit). The principal factor affecting k ii (fit) for our data appears to be the internal vertical reorganization energy (λv), 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 ΔG ⧧ ii (fit) values.