Molecule-Lead Coupling at Molecular Junctions: Relation between the Real- and State-Space Perspectives

We present insights into the lead-molecule coupling scheme in molecular electronics junctions. Using a "site-to-state" transformation that provides direct access to the coupling matrix elements between the molecular states and the eigenstate manifold of each lead, we find coupling bands whose character depends on the geometry and dimensionality of the lead. We use a standard tight-binding model to elucidate the origin of the coupling bands and explain their nature via simple "particle-in-a-box" type considerations. We further show that these coupling bands can shed light on the charge transport behavior of the junction. The picture presented in this study is not limited to the case of molecular electronics junctions and is relevant to any scenario where a finite molecular entity is coupled to a (semi)infinite system.