  We present a real-time path integral theory for the rate of electron transfer
reactions. Using graph theoretic techniques, the dynamics is expressed in a
formally exact way as a set of integral equations. With a simple approximation
for the self-energy, the rate can then be computed analytically to all orders
in the electronic coupling matrix element. We present results for the crossover
region between weak (nonadiabatic) and strong (adiabatic) electronic coupling
and show that this theory provides a rigorous justification for the salient
features of the rate expected within conventional electron transfer theory.
Nonetheless, we find distinct characteristics of quantum behavior even in the
strongly adiabatic limit where classical rate theory is conventionally thought
to be applicable. To our knowledge, this theory is the first systematic
dynamical treatment of the full crossover region.
