  Electron transfer coupled to a collective vibronic degree of freedom is
studied in strongly condensed phase and at lower temperatures where quantum
fluctuations are essential. Based on an exact representation of the reduced
density matrix of the electronic+reaction coordinate compound in terms of path
integrals, recent findings on the overdamped limit in quantum dissipative
systems are employed. This allows to give for the first time a consistent
generalization of the well-known Zusman equations to the quantum domain.
Detailed conditions for the range of validity are specified. Using the Wigner
transform these results are also extended to the quantum dynamics in full phase
space. As an important application electronic transfer rates are derived that
comprise adiabatic and nonadiabatic processes in the low temperature regime
including nuclear tunneling. Accurate agreement with precise quantum Monte
Carlo data is observed.
