Extending the source-sink potential method to include electron-nucleus coupling

The source-sink potential (SSP) method provides a simple tool for the qualitative analysis of the conductance of molecular electronic devices, and often analytical expressions for the conductance can be obtained. Here, we extend the SSP approach to account for decoherent, inelastic electron transport by including the non-adiabatic coupling between the electrons and the nuclei in the molecule. This coupling results in contributions to electron transport that can modify the qualitative structure-conductance relationships that we unraveled previously with SSP. In the approach proposed, electron-nucleus interactions are treated starting from the harmonic approximation for the nuclei, using a non-perturbative approach to account for the non-adiabatic coupling. Our method qualitatively describes experimentally observed phenomena and allows for a simple analysis that often provides analytical formulas in terms of the physical parameters of the junction, e.g., vibrational energies, non-adiabatic coupling, and molecule-contact coupling.