In this article, we shall present the theoretical treatment of both equilibrated and non equilibrated electron and energy transfer reactions. We discuss the rate constants of energy and electron transfer reactions occurring in photosynthetic bacteria. We would like to emphasis the importance of multi-mode effects on the rate constants and their temperature dependence. On the basis of the density matrix method, we construct the pump-probe stimulated emission spectra that have been observed experimentally for photosynthetic reaction centers. In the simulation, the vibrational population and coherence dynamics including their relaxation are taken into account. We demonstrate both strong and weak electronic coupling cases. We show the transient vibrational dynamics is a major contribution to the time-resolved spectra in its early time region for both cases. From our calculation, the electron transfer of RCs takes place under the weak electronic coupling case.