Dynamics of the spin-boson Hamiltonian by the projection operator technique: applications to electron transfer reactions.

A perturbative treatment developed by using the projection operator technique is provided to find dynamics of the spin-boson Hamiltonian in the second order approximation of the subsystem-bath interaction. In the framework of the generalized master equations and in the Markovian approximation it leads to the Redfield/Bloch-type equations. The treatment can be applied to both fast and slow bath cases; in this paper we consider the fast bath case. The relaxation times, energy splitting, and bath-induced renormalization effect of the coherence frequency are discussed and applied to a Lorentzian-Ohmic fast bath. A good agreement between our results and those obtained by the path-integral formalism is obtained. The treatment is applied to electron transfer reactions to test the possibility of apparition of the electronic coherence in certain photosynthetic reaction centers.