Quantum interference through gated single-molecule junctions

We discuss the general form of the transmission spectrum through a molecular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green function properties into practical graphical rules for assessing beforehand the possible existence of antiresonances in an energy range for a given choice of connecting sites. The analysis is exemplified with a benzene molecule under a hypothetical local gate, which allows one to continuously tune the on-site energy of single atoms, for various connection topologies and gate positions.