Recent advances in the engineering of picoscale gaps between electroburnt graphene electrodes provide new opportunities for studying electron transport through electrostatically gated single molecules. But first we need to understand and develop strategies for anchoring single molecules to such electrodes. Here, for the first time we present a systematic theoretical study of transport properties using four different modes of anchoring zinc-porphyrin monomer, dimer, and trimer molecular wires to graphene electrodes. These involve either amine anchor groups, covalent C-C bonds to the edges of the graphene, or coupling via π-π stacking of planar polyaromatic hydrocarbons formed from pyrene or tetrabenzofluorene (TBF). π-π stacked pyrene anchors are particularly stable, which may be advantageous for forming robust single-molecule transistors. Despite their planar, multiatom coupling to the electrodes, pyrene anchors can exhibit both destructive interference and different degrees of constructive interference, depending on their connectivity to the porphyrin wire, which makes them attractive also for thermoelectricity. TBF anchors are more weakly coupled to both the graphene and the porphyrin wires and induce negative differential conductance at finite source-drain voltages. Furthermore, although direct C-C covalent bonding to the edges of graphene electrodes yields the highest electrical conductance, electron transport is significantly affected by the shape and size of the graphene electrodes because the local density of states at the carbon atoms connecting the electrode edges to the molecule is sensitive to the electrode surface shape. This sensitivity suggests that direct C-C bonding may be the most desirable for sensing applications. The ordering of the low-bias electrical conductances with different anchors is as follows: direct C-C coupling > π-π stacking with the pyrene anchors > direct coupling via amine anchors > π-π stacking with TBF anchors. Despite this dependency of conductances on the mode of anchoring, the decay of conductance with the length of the zinc-porphyrin wires is relatively insensitive with the associated attenuation factor β lying between 0.9 and 0.11 Å-1.
Keywords: Single molecule electronics; attenuation factor; covalent/π−π anchor; graphene electrode; porphyrin.