Experimental investigation of excited-state electron-transfer reaction: Effects of free energy and solvent on rates

Photoinduced electron-transfer reaction between phenanthrene substituted derivatives and a series of amines, such as N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) and N,N-diethylaniline, was studied in three solvent systems. Measured from fluorescence decay, electron-transfer quenching rate constants as a function of overall free energy change and solvent polarity were compared with the prediction of Marcus outer-sphere electron-transfer theory. The more negatve the free energy change of electron transfer in acetonitrile becomes, the more the electron-transfer quenching rate increases. When free energy change in the acetonitrile system is smaller than -15 kcal/mol, the quenching rate approaches the diffusion-controlled limit and almost remains constant; there is not inverted behavior region as predicted by Marcus theory. The relation between quenching rate and free energy change of electron transfer in N,N-dimethylformamide is similar to that in acetonitrile in the normal region. In the highly exergonic region of ΔG° < -35 kcal/mol, the electron-transfer quenching rate slightly decreases as the free energy change becomes more negative. This slightly inverted behavior is also observed in the exergonic region of ΔG° < -20 kcal/mol in the cyclohexane system. By fitting experimental rate data in the normal region, we are able to obtain reorganization free energies for acetonitrle and N,N-dimethylformamide systems. The results agree well with calculated polarization free energy change as estimated in Marcus theory. There is no need to invoke vibrational reorganization for the electron-transfer process. For the highly exergonic region, experimental rate is always larger than theoretical rate. We propose a simple explanation for this result in terms of electron-transfer distance. Either donor with low oxidation potential or excited donor is able to result in long-distance electron-transfer reaction, e.g., electron hopping through solvent molecules. Moreover, the lower the solvent LUMO energy is, the greater the average distance for electron transfer is. Such a solvent-assisted process would enhance the electron-transfer rate in the highly exergonic region.