Clar's Sextet Rule Is a Consequence of the σ-Electron Framework

Abstract

A number of condensed PAHs are examined to identify the underlying reasons governing empirical Clar's rule taking benzene as a limiting case. It is found that the so-called Clar's structures are the only minima on the MP2(fc) potential energy hypersurfaces, meaning that other conceivable valence isomers are nonexistent. The influence of the electron correlation energies to the stability of Clar's structures is substantial with predominating influence of the sigma-electrons. However, the contributions arising from the sigma- and pi-electron correlation energies are approximately the same, if Clar's structures are compared with some artificial pi-electron localized or graphite-like delocalized planar systems. Analysis of the Hartree-Fock (HF) energies provides a compelling evidence that the origin of stability of Clar's structures lies in a decrease of the positive T, V(ee) and V(nn) energy terms relative to some characteristic virtual "delocalized" or "localized" model geometries. Partitioning of the mixed and terms in the sigma- and pi-type contributions, by using the stockholder (SHR), equipartitioning (EQP) and standard pi (SPI) schemes, unequivocally shows that the driving force leading to Clar's structures are more favorable sigma-type interactions. All these conclusions hold for the archetypal benzene too, which could be considered as a limiting Clar system. Finally, the boundaries of Clar's hypothesis and some common misconceptions are briefly discussed. Perusal of the geometric parameters and pi-bond orders reveals that there are no benzene rings completely "vacant" or "fully occupied" by the pi-electrons, envisaged by Clar in his picture of condensed benzenoid compounds. Instead, there are six-membered rings with higher and lower total pi-electron density. The bond length anisotropy of the former rings is smaller. It is concluded that Clar's proposition is a useful rule of thumb providing qualitative information on the stability of the PAH systems, which in turn should not be overinterpreted.