Propensity rules for inelastic electron tunneling spectroscopy of single-molecule transport junctions

Using a perturbative approach to simple model systems, we derive useful propensity rules for inelastic electron tunneling spectroscopy (IETS) of molecular wire junctions. We examine the circumstances under which this spectroscopy (that has no rigorous selection rules) obeys well defined propensity rules based on the molecular symmetry and on the topology of the molecule in the junction. Focusing on conjugated molecules of C2h symmetry, semiquantitative arguments suggest that the IETS is dominated by ag vibrations in the high energy region and by out of plane modes (au and bg) in the low energy region. Realistic computations verify that the proposed propensity rules are strictly obeyed by medium to large-sized conjugated molecules but are subject to some exceptions when small molecules are considered. The propensity rules facilitate the use of IETS to help characterize the molecular geometry within the junction.