It
is illustrated and computationally verified by ab initio density
functional theory and simple but powerful order-of-magnitude arguments,
based on deformation energy ΔEdef 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) and the largest (a few 2) 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.