  Quantum interference (QI) in molecular transport junctions can lead to
dramatic reductions of the electron transmission at certain energies. In a
recent work [Markussen et al., Nano Lett. 2010, 10, 4260] we showed how the
presence of such transmission nodes near the Fermi energy can be predicted
solely from the structure of a conjugated molecule when the energies of the
atomic p_z orbitals do not vary too much. Here we relax the assumption of equal
on-site energies and generalize the graphical scheme to molecules containing
different atomic species. We use this diagrammatic scheme together with
tight-binding and density functional theory calculations to investigate QI in
linear molecular chains and aromatic molecules with different side groups. For
the molecular chains we find a linear relation between the position of the
transmission nodes and the side group pi orbital energy. In contrast, the
transmission functions of functionalized aromatic molecules generally display a
rather complex nodal structure due to the interplay between molecular topology
and the energy of the side group orbital.
