Generalized Breit-Wigner treatment of molecular transport: Charging effects in a single decanedithiol molecule

We examine the relative contribution of ballistic and elastic cotunneling mechanisms to the charge transport through a single decanedithiol molecule linked to two terminal clusters of gold atoms. For this, we first introduced a conceptual model that permits a generalization of the Breit-Wigner scattering formalism where the cation, anion, and neutral forms of the molecule can participate with different probabilities of the charge transfer process, but in a simultaneous manner. We used a density functional theory treatment and considered the fixed geometry of each charge state to calculate the corresponding eigenvalues and eigenvectors of the extended system for different values of the external electric field. We have found that for the ballistic transport the HOMO and LUMO of the neutral species play a key role, while the charged states give a negligible contribution. On the other hand, an elastic cotunneling charge transfer can occur whenever a molecular orbital (MO) of the cation or anion species, even if localized in just one side of the molecule-gold clusters complex, has energy close to that of a delocalized MO of the neutral species. Under these conditions, a conduction channel is formed throughout the entire system, in a process that is controlled by the degree of resonance between the MOs involved. Our results indicate that while different charge transfer mechanisms contribute to the overall charge transport, quantum effects such as avoided-crossing situations between relevant frontier MOs can be of special importance. In these specific situations, the interchange of spatial localization of two MOs involved in the crossing can open a new channel of charge transfer that otherwise would not be available.