The effect of the energy gap between donor and bridge states in the electron transfer of a double mutant photosynthetic purple bacterial reaction center is thoroughly investigated using a recently introduced modified on-the-fly filtered propagator important path integral formalism. By decomposition of the reduced density matrix of a system coupled to a dissipative environment, partial contributions of incoherent hopping, coherent superexchange, and partially coherent hopping transport to the overall electron or charge transfer are evaluated. Within the tight-binding donor-bridge-acceptor model, the three mechanisms coexist for a wide range of donor-bridge energy gap values, and the governing mechanism changes from incoherent hopping to partially coherent hopping and eventually to coherent superexchange as the donor-bridge energy gap becomes large.