A graph-theoretical model for ballistic conduction in single-molecule conductors

The tight-binding version of the source-and-sink potential (SSP) model of ballistic conduction can be cast in a graph-theoretical form where the transmission through a molecular wire depends on four characteristic polynomials: those of the molecular graph and the vertex-deleted subgraphs with one or both of the molecular vertices contacting the electrodes removed. This gives an explicit function for the dependence of transmission on energy, one that is well adapted for qualitative description of general classes of conductors and conduction behavior. It also leads directly to a selection-rule criterion for conduction in terms of counting zero roots of the polynomials, which for benzenoids and graphenes is shown to subsume literature approaches based on Kekule structure counting, bond order, and frontier-orbital matching. As explicitly demonstrated here, the SSP transmission function agrees with that derived by the Green's function (GF) method.