Exothermic rate restrictions on electron transfer in a rigid medium

Many highly exothermic (2–3 eV) electron transfer reactions are shown to be slower than moderately exothermic reactions by factors as large as 105. The decrease occurs in a regular way with increasing exothermicity, tending to confirm theoretical predictions of Franck–Condon restrictions on strongly exothermic electron transfer reactions. Deviations from the above trends occur if the reaction product, a molecular anion, has a low-lying electronic excited state into which the reaction may occur with more moderate vibrational exothermicity. Then greatly enhanced rates are found. The rates are enhanced to a lesser extent for acceptors likely to undergo configurational changes upon accepting an electron. These effects are found in measurements of rates of electron tunneling reactions between trapped electrons and 48 organic electron acceptors in rigid 2-methyltetrahydrofuran glass at 77 K. Electron tunneling rates were observed from 10−6 to 102 s. Measured tunneling distances were 15–40 Å. In most cases the observed kinetic decay curves are well simulated by a theory in which the only variable parameter is the effective Franck–Condon factor (F), which is a constant characteristic of the acceptor. For the various acceptors F ranges from 1 to 10−5, and scales the reaction rate at each distance. However in reactions of small vibration exothermicity, the Franck–Condon factors are expected to be very sensitive to small changes in reaction exothermicity caused by relaxations of trapped electrons, which deepen their trap depths with time and, possibly, a dispersion of trap depths. These effects cause F to change with time leading to changes in the shapes of the decay curves. The relationship between the shapes of the decay curves, Franck–Condon factors, and exothermicity allows a thorough and consistent semiquantitative interpretation of the present results and much of the earlier tunneling data on electron transfer reactions involving other solvents and solutes.