  We theoretically investigate the electron transport in armchair and zigzag
graphene nanoribbons (GNRs) chemically functionalized with p-polyphenyl and
polyacene groups of increasing length. Our nearest-neighbor tight-binding
calculations indicate that, depending on whether the number of aromatic rings
in the functional group is even or odd, the resulting conductance at energies
matching the energy levels of the corresponding isolated molecule are either
unaffected or reduced by exactly one quantum as compared to the pristine GNR,
respectively. Such an even-odd effect is shown to originate from a subtle
interplay between the electronic states of the guest molecule that are
spatially localized on the binding sites and those of the host nanoribbon. We
next generalize our findings by employing more accurate tight-binding
Hamiltonians along with density-functional theory calculations, and critically
discuss the robustness of the observed physical effects against the level of
theory adopted. Our work offers a comprehensive understanding of the influence
of aromatic molecules bound to the edge of graphene nanoribbons on their
electronic transport properties, an issue which is instrumental to the
prospective realization of graphene-based chemosensors.
