In this paper, based on the perturbative density matrix method, we calculate femtosecond (fs) transient spectra of initial electron transfer (ET) in the bacterial reaction centers (RCs) of Rhodobacter (Rb.) capsulatus at 20 K and compare them with experimental data. It is believed that the lowering of temperature will decrease the intermolecular distance in the special pair, which will in turn affect the energy levels of the excitonic-coupled dimer (special pair) P, i.e., P-*, P+*, P-+ and P++ where, for instance, P-* and P++ represent the lowest excited and the second charge-separated states of the P, respectively. The absorption spectrum of the P-* band is analyzed to obtain the small vibrational modes and their coupling constants (Huang-Rhys factor). By taking into account the anion and cation states of the bacteriochlorophyll a molecule (B) and the cation state of the bacteriopheophytin a molecule (H), the excitonic-vibronic model including the six electronic states P-*BH, P-+B-H, P-+BH-, PB+H-, P++B-H and P++BH- is applied to simulate the fs time-resolved three-dimension spectra of Rb. capsulatus. We find only the three electronic states P-*BH, P++B-H and P++BH- are mainly involved in the ET dynamics. We shall theoretically analyze the quantum beats appearing in the fs pump-probe stimulated emission profiles of the Dll mutant RCs of Rb. capsulatus at 10 K. The conventional ET theory assumes that vibrational relaxation is much faster than ET so that vibrational equilibrium is established before ET takes place. However, several recent fs measurements on RCs show quantum beats in their time-resolved profiles. This implies that the non-equilibrated vibrational motions of RCs should be investigated. The Dll mutant RC, lacking of the Hll, is incapable of ET on a time scale of the fs measurements. Thus, analyzing the quantum beats appearing in the fs time-resolved profiles, we shall extract the information of transient vibrational motions and their decays of the electronically lowest excited state P-*. The multi-mode effect on the quantum beats is also investigated.
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