The ability to control electronic tunneling in complex molecular networks of multiple donor/acceptor sites is studied theoretically. Our past analysis, demonstrating the phenomenon of site-directed transport, was limited to the coherent tunneling regime. In this work we consider electronic coupling to a dissipative molecular environment including the effect of decoherence. The nuclear modes are classified into two categories. The first kind corresponds to the internal molecular modes, which are coupled to the electronic propagation along the molecular bridges. The second kind corresponds to the external solvent modes, which are coupled to the electronic transport between different segments of the molecular network. The electronic dynamics is simulated within the effective single electron picture in the framework of the tight binding approximation. The nuclear degrees of freedom are represented as harmonic modes and the electronic-nuclear coupling is treated within the time-dependent Redfield approximation. Our results demonstrate that site-directed tunneling prevails in the presence of dissipation, provided that the decoherence time is longer than the time period for tunneling oscillations (e.g., at low temperatures). Moreover, it is demonstrated that the strength of electronic coupling to the external nuclear modes (the solvent reorganization energy) controls the coherent intramolecular tunneling dynamics at short times and may be utilized for the experimental control of site-directed tunneling in a complex network.

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