  We present here a formally exact model for electronic transitions between an
initial (donor) and final (acceptor) states linked by an intermediate (bridge)
state. Our model incorporates a common set of vibrational modes that are
coupled to the donor, bridge, and acceptor states and serves as a dissipative
bath that destroys quantum coherence between the donor and acceptor. Taking the
memory time of the bath as a free parameter, we calculate transition rates for
a heuristic 3-state/2 mode Hamiltonian system parameterized to represent the
energetics and couplings in a typical organic photovoltaic system. Our results
indicate that if the memory time of the bath is of the order of 10-100 fs, a
two-state kinetic (i.e., incoherent hopping) model will grossly underestimate
overall transition rate.
