Persistent/transient spectral hole burning (HB) and computer simulations are used to provide new insight into the excitonic structure and excitation energy transfer of the widely studied bacterial reaction center (bRC) of Rhodobacter (Rb.) sphaeroides. We focus on site energies of its cofactors and electrochromic shifts induced in the chemically oxidized (P+) and charge-separated (P(+)Q(M)(-)) states. Theoretical models lead to two alternative interpretations of the H-band. On the basis of our experimental and simulation data, we suggest that the bleach near 813-825 nm in transient HB spectra in the P(+)Q(M)(-) state, often assigned to the upper exciton component of the special pair, is mostly due to different electrochromic shifts of the B-L/M cofactors. From the exciton compositions in the charge-neutral (CN) bRC, the weak fourth excitonic band near 780 nm can be denoted that is, the upper excitonic band of the special pair, which in the CN bRC behaves as a delocalized state over P-M and P-L pigments that weakly mixes with accessory BChls. Thus, the shoulder in the absorption of Rb. sphaeroides near 813-815 nm does not contain the PY+, exciton band.