A Pedestrian Approach to the Aromaticity of Graphene and Nanographene: Significance of Huckel’s (4n+2)π Electron Rule Aristides D. Zdetsis* ,†,‡ and E. N. Economou ‡ † Molecular Engineering Laboratory, Department of Physics, University of Patras, Patras 26500 GR, Greece ‡ Institute of Electronic Structure and Laser, Foundation for Research &Technology Hellas, Vassilika Vouton, P.O. Box 1385, Heraklion, Crete GR 71110, Greece ABSTRACT: 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)π 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 are 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 nonaromatic rings, resulting in alternating (4n+2) and 4n π electron numbers, characterizing, respectively, “aromatic” and “anti-aromatic” samples according to Huckel’s (4n+2)π electron rule. For infinite graphene, this interchange occurs naturally, resulting in a uniform pattern. The opposite route is also valid, subject to the restrictions 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. 1. INTRODUCTION The electronic properties of graphene are characterized primarily by the network of mobile (delocalized) π electrons based on the atomic p z orbitals, while the σ bonding is assumed to be a rigid honeycomb framework built out of “localized” (sp 2 hybridized) two-center two-electron (2c-2e) C-C σ bonds. Delocalized π bonding is naturally described by the concept of aromaticity, 1,2 which, however, is not free of controversial and conflicting views open to debate, even today. 1-3 Aromaticity, initially described by the traditional Huckel (4n+2)π electron rule (which is strictly applied to monocyclic systems as benzene), is not a measurable quantity and is usually described by various “aromaticity indices” (or aromaticity criteria), based on bonding, electronic, magnetic, etc., characteristics, which, however, are neither unique nor fully compatible among themselves. 1-3 In general, aromaticity involves planarity and extra stability due to electron delocalization, like benzene. In fact, the qualitative meaning of aromaticity is “like benzene”. Therefore, since benzene is considered as the prototypical aromatic molecule, then graphite, and par excellence graphene, should be thought of as more aromatic than benzene, since the resonance energy per π electron of graphite is greater than that in benzene. 4 Then, the answer to the question “is graphene aromatic?” 5 should, apparently, be affirmative but not as trivial as in the case of benzene. In graphene, the number of π electrons which could be assigned to a particular ring is two Received: May 5, 2015 Revised: June 25, 2015 Article pubs.acs.org/JPCC © XXXX American Chemical Society A DOI: 10.1021/acs.jpcc.5b04311 J. Phys. Chem. C XXXX, XXX, XXX-XXX