Charge hopping in molecular wires as a sequence of electron-transfer reactions

Charge transport in molecular wires is investigated theoretically within the framework of a simple hopping model. The model suggests that each elementary hopping step can be treated as an electron-transfer reaction between ionic and neutral states of π-conjugated structural units coupled through σ-bonded spacers. Within this mechanistic picture, the ability of wire to transport a charge depends crucially on the internal reorganization energy, λ. Using unrestricted Hartree-Fock and density functional theory methods, we evaluate λ for benzene, 3-methylbiphenyl, 2,6-dimethyl-1-phenyl-pyridinium (DMPP), and 4-(p-suflhydrylphenylpyridinium-1′-yl)-2,6-dimethylpyridinium, selected as representative examples of structures used for chemical attachment to σ-bonded structural spacers in real molecular wires. The results are exploited to estimate the upper and lower limits of hole and electron mobility in wires that consist of aromatic ring units linked to the antipodal bridgeheads of σ-bonded molecular "cages", bicyclo[1.1.1]pentane (BCP), cubane (CUB), and bicyclo[2.2.2]-octane (BCO). Our calculations show that the highest mobility of holes is expected for coplanar alignment of aromatic rings at the end of molecular cages as, in this configuration, the electron coupling is most efficient. We also analyze the situation in which thermally induced twisting motion destroys coplanarity of aromatic rings. The obtained results suggest that, for wires with the BCO spacer, hopping transitions are slower than twisting motion and, therefore, the mean hole mobility is determined by the equilibrium average twist angles. In the opposite case, relevant to the benzene/BCP and benzene/CUB systems, large deviations of the twist angles from the equilibrium value represent a bottleneck for the transport process.