Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches.

Benzene is the emblematic example of an aromatic molecule, and the problem of its structure has given rise to a chemical serial story running over several decades. The epistemological digest of this story written by Stephen G. Brush1,2 shows how this problem has been at the root of important concepts such as those of mesomery and resonance. Before the advent of quantum mechanics, chemists had thought of the benzene structures in terms of two center bonds attempting to preserve the valence of the carbon atom and to explain its chemical properties. Kekulé’s theory of the structure of the benzene molecule3 invokes the oscillatory hypothesis in which “the fourth valence of each carbon oscillates between its neighbors, synchronously with all the other fourth valences, so that the structure switches rapidly between the two structures”,1 whereas Claus proposed a diagonal hypothesis4 in which the fourth valence of each carbon is directed toward the carbon in the para position. The latter hypothesis has been rejected because it enables only two derivatives, and it has been revised to remove this inconsistency: instead of forming a bond, the fourth valence stops near the center of the ring in the Armstrong-Baeyer formula,5 or there is only one bridging bond as in the Dewar’s bridged benzene formula.6 In Thiele’s partial valence model,7 the adjacent carbon-carbon bonds are considered as intermediate between single and double bonds. These formulas were later considered by K. C. Ingold to set up his intra-annular tautomerism,8 which appears to be the generalization of Kekulé’s oscillatory hypothesis. Ingold’s tautomerism hypothesis was later called mesomerism.9 The mesomery is an important concept in chemistry, which implicitly introduces the electron delocalization in the context of the prequantum electronic theory. The first applications of quantum chemistry to the benzene problem led on the molecular orbital (MO) side Erich Hückel to propose his famous 4n + 2 rule10 and on the valence bond (VB) side Pauling and Wheland to identify resonance with Ingold’s mesomerism.11,12 An enlighting contribution of modern VB theory on the benzene structure has been brought by Shaik et al.,13 who have shown that the hexagonal symmetry of benzene is due to the σ-system because the π component is distortive along a Kekulean distortion. * Authors to whom correspondence should be addressed (telephone +34-972-418912; fax +34-972-418356; e-mail miquel.sola@ udg.es or [email protected]). ‡ Universitat de Girona. § Université Pierre et Marie Curie. 3911 Chem. Rev. 2005, 105, 3911−3947