Electron transfer in a slow relaxation bath: Coherence and nonexponential kinetics

A fast reaction of an electron transfer in a slow relaxation environment is considered. In the framework of the spin-boson approach, the time-dependent probability, P(t), is shown to be essentially nonexponential at short times. P(t) exhibits coherent oscillations of the electron density with rather different types of decay, depending on the parameter values. The fast decay corresponds to large values of the reaction heat and small values of the transition matrix element. The slow decay, determined by P(t)similar or equal to cos(Delta t)/root t, corresponds to large values of the electronic matrix element and small barriers. The general expression for P(t) is interpreted as free coherent oscillations of the electron density. The heat of the reaction is treated as a random Gaussian variable centered at the value epsilon-E-r, where epsilon and E-r are the bias and reorganization energy, respectively. It is pointed out that such nonexponential behavior can be observed for fast reactions in matrices of inert gases or electron transfer in bacterial photosynthetic centers or photoexcited mixed-valence compounds. (C) 1999 American Institute of Physics. [S0021-9606(99)50935-5].