Langevin-Schroedinger formulation of electronic tunneling through a molecular bridge with a dissipative acceptor

Modeling electronic tunneling through molecular bridges is desired in order to understand the mechanism of long-range electron transfer reactions in nature, as well as for the design of novel molecular electronics devices. Particularly interesting is the effect of the nuclear motion at the molecular bridge on the electron transfer mechanism and rate. In this work we study the effect of electronic nuclear coupling at the molecular bridge on a unidirectional electronic tunneling process from an electron donor into a dissipative acceptor, as may appear in controlled electron transfer reactions at biological membranes, or in heterogeneous electron transfer reactions. The model includes a collection of harmonic bath modes coupled to the dissipative acceptor site and a single mode at the molecular bridge. The parameters of the dissipative bath are tuned such that the electronic population decays from the donor to the acceptor. This process is simulated using a time-dependent nonlinear Langevin-Schroedinger equation, based on a mean-field approximation for the electronic-nuclear coupling at the acceptor site and a numerically exact treatment of the electronic-nuclear coupling at the molecular bridge. The simulations at zero temperature and weak electronic-nuclear coupling demonstrate that electronic tunneling is promoted by coupling to the nuclear mode at the bridge. This result is consistent with our previous studies of electronic tunneling oscillations in a symmetric donor-bridge-acceptor complex, and it emphasizes the importance of electronic nuclear coupling in analyzing long-range electron transfer processes through molecular bridges or wires.