Interrelation of Aromaticity and Conductivity of Graphene Dots/Antidots and Related Nanostructures

It is illustrated and computationally verified by ab initio density functional theory and simple but powerful order-of-magnitude arguments, based on deformation energy ΔE_def in relation to the uncertainty principle, that the conductivity and aromaticity of graphene and graphene-based structures, such as graphene dots, antidots, and nanoribbons, are negatively interrelated for π aromatic structures, in agreement with recent experimental data. However, for σ aromaticity, the interrelation could be positive, especially for extended periodic structures. We predict that the conductivity of rectangular graphene dots and antidots, is anisotropic with much larger magnitude along the direction perpendicular to the zigzag edges, compared to the conductivity in direction parallel to them. The same is true for the polarizability and electron mobility. This is directly connected with the much higher aromaticity around the armchair edges compared to the aromaticity near the zigzag edges. Furthermore, contrary to what would be expected on the basis of simple arguments for defect states, we predict that antidot patterning could significantly improve the conductivity (sometimes by 1 order of magnitude) in one or both directions, depending on their number, arrangement, and passivation. For narrow atomically precise armchair nanoribbons (AGNRs) of finite length, both conductivity and energy gaps are dominated by lateral and longitudinal quantum confinement, which decrease with increasing length (for a given width), leading to a peculiar behavior of monotonically increasing "maximum conductivity" as the band gaps monotonically decrease. The electron distribution at the band edges of the AGNRs, in agreement with recent experimental data are well-localized at the zigzag edges. Using the concept of gap-determining LUMO-HOMO frontier states to avoid HOMOs and LUMOs localized at the zigzag edges, we can predict with very high accuracy the recently measured band gaps of AGNRs of widths N = 7 and N = 13. Both the smallest (10^-3-10^-4[Formula: see text]) and the largest (a few 2[Formula: see text]) calculated values of conductance and conductivity for the smaller structures and the larger nanographenes, respectively, are in full accord with the corresponding experimental values of single-molecule junction conductance and the measured minimum conductivity of graphene at 1.6 K.