An analytical model for steady-state currents in conjugated systems

The ‘source-and-sink-potential’ approach is used to treat the steady-state currents created by injection of ballistic electrons via external contacts into unsaturated π systems. An analytical expression is derived, within the tight-binding approximation, for the molecular transmission as a function of energy, which is cast in terms of four characteristic polynomials: those of the molecular graph and three vertex-deleted sub-graphs. The dependence of transmission on both the molecular skeleton and its mode of connection is thereby made explicit.