4n + 2 = 6n? A Geometrical Approach to Aromaticity?

Using a simple but powerful geometrical/topological notion of aromaticity based on the shell model (Zdetsis, A. D. J. Phys. Chem. C 2018, 122, 17526-17536) and the bipartite topology, we uncover, on top of the geometrical virtual "equivalence" of the fundamental Hückel and Clar rules of aromaticity, the significance of empty peripheral rings, which are shown to be linked to zigzag edge states. Such empty rings can be thought of as "inversion symmetry incompatible". Thus, the elimination of these rings under the existing symmetry constrains preserves the aromaticity pattern and leads to a substantial improvement in the stability and/or sublattice imbalance, resulting in larger electronic band gaps and a lack of zigzag edge/end states. Using these ideas, we can illustrate that trigonal D₃-symmetric nanographens cannot be graphene-like because they are either armchair without Dirac points or zigzag-bonded (triangulenes) topologically frustrated with high spin states. This is also true for hexagonal heteroatomic BN or SiC structures, contrary to homoatomic silicene, germanene, and so forth. Existing paradigms are highly suggestive that such an elimination process could occur naturally.