Sixty-five electron-transfer reactions including 27 new 0, +1 couples have been added to our data set of cross-reactions between 0 and +1 couples, bringing it to 206 reactions involving 72 couples that have been studied by stopped-flow kinetics in acetonitrile containing supporting electrolyte at 25 degrees C, formal potentials determined by cyclic voltammetry, and analyzed using Marcus cross-rate theory. Perhaps surprisingly, a least-squares analysis demonstrates that intrinsic rate constants exist that predict the cross-rate constants to within a factor of 2 of the observed ones for 93% of the reactions studied, and only three of the reactions have a cross-rate constant that lies outside of the factor of 3, that corresponds to a factor of 10 uncertainty in the rate constant for an unknown couple. Many triarylamines, which have very high intrinsic reactivity, are included among the newly studied couples. The enthalpy contribution to the Marcus reorganization energy, lambda'v, has been calculated for 46 of the couples studied, at the (U)B3LYP/6-31+G (or for the larger and lower barrier compounds, at the less time-consuming (U)B3LYP/6-31G) level. In combination with a modified Levich and Dogodnadze treatment that assumes that the rate constant is proportional to (KeHab2/lambda1/2) exp[-DeltaG/RT], this allows estimation of the electronic coupling (Hab) at the transition state for intermolecular electron transfer, (more properly H'ab, the product of the square root of the encounter complex formation constant times Hab) for these couples. Although the principal factor affecting intermolecular electron-transfer rate constants is clearly lambda, H'ab effects are easily detectable, and the dynamic range in our estimates of them is over a factor of 600.

Collisional deactivation of highly vibrationally excited azulene in the electronic ground state was investigated using infrared fluorescence detection. Azulene (S0, E) was prepared with E≂17 500 cm−1 and E≂30 600 cm−1 by laser excitation at 600 and 337 nm, respectively. Advantage was taken of the fast internal conversion rate to S0 azulene from S1(600 nm) and S2(337 nm) electronic states. The collider gases investigated are He, Ne, Ar, Kr, Xe, H2, D2, N2, CO, O2, CO2, H2O, NH3, CH4, SF6, n-C4H10, and unexcited azulene. The results are expressed in terms of 〈ΔE(E)〉, the average energy transferred per collision, which can depend on the vibrational excitation energy E of the azulene. Using previously obtained knowledge of the dependence of infrared fluorescence intensity on E [M. J. Rossi and J. R. Barker, Chem. Phys. Lett. 85, 21 (1982)], two methods were used to obtain 〈ΔE(E)〉 values from the fluorescence decay curves: (1) an approximate method that considered only the average energy, and (2) solution of the full collisional master equation. Both methods gave 〈ΔE(E)〉 values that depend strongly on E. The limited experimental information on the identity of the energy-transfer processes operative in the deactivation of azulene is discussed. Additional experimental results on vibration-to-vibration energy transfer from azulene to CO2 are presented, which indicate that the emission at 4.3 μm observed previously [J. R. Barker, M. J. Rossi, and J. R. Pladziewicz, Chem. Phys. Lett. 90, 99 (1982)] originates not only from CO2(001), but from other states with one quantum of excitation in ν3. The experimental results are discussed in terms of models for energy transfer, which have appeared in the literature. It is concluded that only a superficial understanding exists and theory has lagged far behind experiments on energy transfer.

The self-exchange electron-transfer (ET) rate constant k 22 for 1,2,3,4,5-pentamethylferrocene was determined by NMR line broadening to be 8.5(±0.8) × 106 M-1 s-1 (25 °C, CD3CN/0.09 M Et4NBF4) and k 11 for the bis-N,N-bicyclic hydrazine, 9,9‘-bi-9-azabicyclo[3.3.1]nonane, to be 8.7(0.5) × 103 M-1 s-1 (25 °C, CH2Cl2). These self-exchange rate constants are used to analyze cross reactions of these molecules with hydrazines, ferrocenes, and tetramethyl-p-phenylenediamine (TMPD) using Marcus theory. Cross-reaction rate constants for eight reactions are reported. Included are six cross-reactions between methylferrocenes and four cyclic hydrazines, one hydrazine, hydrazine−reaction, and the reduction of TMPD + by a cyclic hydrazine. These are the first cross-reaction rate constants reported for hydrazine−hydrazine and hydrazine−TMPD + ET reactions. The cross-reaction rate constants are used to test the application of Marcus theory to hydrazine ET reactions and to extract estimates of hydrazine self-exchange ET rate constants in systems for which direct measurement is presently impossible.

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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.

Electron-transfer cross-reactions between neutral molecules and their radical cations spanning a wide range of structural type and intrinsic reactivity have been analyzed using classical Marcus theory. The principal factor found to govern intrinsic reactivity is the inner-shell bond reorganization energy. The HOMO-LUMO overlap of alkyl groups on reacting molecules is generally sufficient to provide facile electron transfer; however, a significant steric effect on this overlap is observed for hydrazines with alkyl groups larger than methyl.