  Based on the reduced density matrix method, we compare two different
approaches to calculate the dynamics of the electron transfer in systems with
donor, bridge, and acceptor. In the first approach a vibrational substructure
is taken into account for each electronic state and the corresponding states
are displaced along a common reaction coordinate. In the second approach it is
assumed that vibrational relaxation is much faster than the electron transfer
and therefore the states are modeled by electronic levels only. In both
approaches the system is coupled to a bath of harmonic oscillators but the way
of relaxation is quite different. The theory is applied to the electron
transfer in ${\rm H_2P}-{\rm ZnP}-{\rm Q}$ with free-base porphyrin (${\rm
H_2P}$) being the donor, zinc porphyrin (${\rm ZnP}$) being the bridge and
quinone (${\rm Q}$) the acceptor. The parameters are chosen as similar as
possible for both approaches and the quality of the agreement is discussed.
