Graph theory of aromatic stabilization

Abstract

Aromaticity is very sensitive to the geometry of the ?-system. Topological resonance energy (TRE), defined graphtheoretically, represents an aromatic stabilization energy (ASE) arising from cyclic conjugation in the ?-system. TRE can be calculated for not only ground-state but also excited-state species. The TRE concept has since been extended analytically to solve many different problems concerning aromaticity and reactivity. Bond resonance energy (BRE), defined in harmony with TRE, is an excellent probe for exploring kinetic stability of cyclic ?-systems. It represents the contribution of individual ?-bonds to global aromaticity. The well-known isolated pentagon rule (IPR) for fullerenes was verified in terms of BRE. Superaromatic stabilization energy (SSE) defined for macrocyclic ?-systems finally confirmed the absence of macrocyclic aromaticity in kekulene. A novel local aromaticity index for polycyclic aromatic hydrocarbons (PAHs) was devised by reinterpreting the definition of SSE. We then found that aromatic properties of some PAHs are not compatible with Clar's aromatic sextet rule. We now feel that many fundamental problems with regard to aromatic stabilization and related phenomena have been solved conceptually.