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The unique properties of graphene are rooted in its peculiar electronic structure where effects of electron delocalization are pivotal. We show that the traditional view of delocalization as formation of a local or global aromatic bonding framework has to be expanded in this case. A modification of the π-electron system of a finite-size graphene substrate results in a scale-invariant response in the relaxation of interatomic distances and reveals self-organized criticality as a mode of delocalized bonding. Graphene is shown to belong to a diverse class of finite-size extended systems with simple local interactions where complexity emerges spontaneously under very general conditions that can be a critical factor controlling observable properties such as chemical activity, electron transport, and spin-polarization.

A family of small graphene patches, i.e., rectangular polyaromatic hydrocarbons (PAHs), that have both zigzag and armchair edges is investigated to establish their ground state electronic structure. Broken symmetry density functional theory (DFT) and plane wave DFT were used to characterize the onset of diradical character via relative energies of open-shell and closed-shell singlet states. The perfect pairing (PP) active space approximation of coupled cluster theory was used to characterize diradical character on the basis of promotion of electrons from occupied to unoccupied molecular orbitals. The role of zigzag and armchair edges in the formation of open-shell singlet states is elucidated. In particular, it is found that elongation of the zigzag edge results in an increase of diradical character whereas elongation of the arm chair edge leads to a decrease of diradical character. Analysis of orbitals from PP calculations suggests that diradical states are formally Mobius aromatic multiconfigurational systems.

A method of description of the chemical bonding combining the compactness and intuitive simplicity of Lewis theory with the flexibility and generality of canonical molecular orbital theory is presented, which is called adaptive natural density partitioning. The objects of chemical bonding in this method are n-center 2-electron bonds, where n goes from one (lone-pair) to the maximum number of atoms in the system (completely delocalized bonding). The algorithm is a generalization of the natural bonding orbital analysis and is based on the diagonalization of the blocks of the first-order density matrix in the basis of natural atomic orbitals. The results obtained by the application of the algorithm to the systems with non-classical bonding can be readily interpreted from the point of view of aromaticity/antiaromaticity concepts. The considered examples include Li4 cluster and a family of planar boron clusters observed in molecular beams.

Aromaticity is an important concept in chemistry primarily for organic compounds, but it has been extended to compounds containing transition-metal atoms. Recent findings of aromaticity and antiaromaticity in all-metal clusters have stimulated further research in describing the chemical bonding, structures and stability in transition-metal clusters and compounds on the basis of aromaticity and antiaromaticity, which are reviewed here. The presence of d-orbitals endows much more diverse chemistry, structure and chemical bonding to transition-metal clusters and compounds. One interesting feature is the existence of a new type of aromaticity-delta-aromaticity, in addition to sigma- and pi-aromaticity which are the only possible types for main-group compounds. Another striking characteristic in the chemical bonding of transition-metal systems is the multi-fold nature of aromaticity, antiaromaticity or even conflicting aromaticity. Separate sets of counting rules have been proposed for cyclic transition-metal systems to account for the three types of sigma-, pi- and delta-aromaticity/antiaromaticity. The diverse transition-metal clusters and compounds reviewed here indicate that multiple aromaticity and antiaromaticity may be much more common in chemistry than one would anticipate. It is hoped that the current review will stimulate interest in further understanding the structure and bonding, on the basis of aromaticity and antiaromaticity, of other known or unknown transition-metal systems, such as the active sites of enzymes or other biomolecules which contain transition-metal atoms and clusters.