A Pedestrian Approach to the Aromaticity of Graphene and Nanographene: Significance of Huckel's (4n+2)π Electron Rule

In an attempt to describe and rationalize the elusive aromatic properties of graphene by first-principles calculations in a simple and transparent way, we have constructed numerous judicially chosen real-space models Of various sizes and symmetries, which lead to the aromaticity pattern of infinite graphene by a process of spatial evolution through successive peripheral additions, characterized by fundamental periodicities related to the traditional Huckel (4n+2)pi electron rule. In accord with the early expectations of Pauling, we have found that the electronic and aromatic properties of infinite graphene result from the superposition of two complementary primary aromatic configurations, in which full and empty rings ate interchanged. The primary pattern consists of a hexagonal superlattice in which each fully aromatic ring is surrounded by six nonaromatic rings, in full agreement with the empirical Clar aromatic sextet theory. We have found that, for finite nanographene(s), aromaticity patterns change periodically by addition/removal of one periphery of rings, which for hexagonal samples is equivalent to exchanging aromatic and nonatomatic rings, resulting in alternating (4n+2) and 4n pi electron numbers, characterizing, respectively, aromatic and anti-aromatic samples according to Huckel's (4n+2)pi electron rule. For infinite graphene, this interchange occurs naturally, resulting in a uniform pattern. The opposite route is also valid, subject to the restrictiohs of size and edge morphology, 'which determine and tune the aromaticity pattern(s). The observed periodicities in the aromaticity patterns of graphene nanoribbons and carbon nanotubes are rooted in such fundamental peripheral periodicities. These findings, on top of their fundamental importance, should be very useful for the technological functionalization of infinite and finite graphene and graphene-based materials.