Dynamic solvent effects on electron transfer rates in the inverted regime: Ultrafast studies on the betaines

Abstract

Transient pump–probe measurements have been made on betaine-30, the solvent polarity probe. Betaine-30 is composed of organic donor and acceptor groups, D+A−⇄kethνDA (excited state). The transient data has been analyzed to measure ket, the electron transfer (et) rate constant, in polar solvents for this inverted regime et. The observed rate constant ket,obs in various polar solvents is as much as a factor of 108 larger than is predicted by the standard, classical, implementation of the theory of Sumi and Marcus, using Kjaer and Ulstrup’s estimates for necessary parameters. In contrast, a quantum treatment of the vibrational modes by Jortner and Bixon, which includes the dynamic solvent effect, predicts that the rate should be approximately ket,JB≂1/〈τs〉. This is close to the experimental results (≂1012 s−1) in typical polar aprotic solvents. However, in highly viscous, slowly relaxing solvents, ket,JB≪ket,obs. This is taken as evidence that the efficient coupling modes for the et in these environments is not the ‘‘conventional solvent coordinate.’’ It is shown that a hybrid of the Jortner/Bixon and Sumi/Marcus theories can physically account for the results. The kinetic behavior of betaine-30 in slowly relaxing solvents is shown to be in the ‘‘diffusionless limit’’ of the hybrid, generalized Sumi–Marcus/Jortner–Bixon picture.