Electron dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an \textit{anharmonic} bath is found in a time-dependent Hartree approximation. The theory presented is a direct generalization of an oscillator medium to an \textit{arbitrary anharmonic environment}. The general expression for the transition probability is presented in terms of medium \textit{Keldysh} functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation (NIBA) where the rate constant does not exhibit activation dependence at high temperatures. The parameters similar to the reorganization energy, E$_{r}$, and the reaction heat, $\varepsilon $, are expressed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that E$_{r}$ and $\varepsilon $ are temperature dependent. Such a behavior is demonstrated in the case of a particular electron transfer reaction in nonpolar solvents experimentally studied by Zimmt \textit{et al}.