Classics Illustrated: Clar’s Sextet and Hückel’s (4n + 2) π-Electron Rules

By revealing and invoking a novel concrete (topological and electronic) shell structure, inherent in hexagonal polycyclic aromatic hydrocarbons (PAHs), it is illustrated that the celebrated but largely empirical Hückel and Clar rules for aromaticity and stability can be derived, interrelated, and connected to shell closures, with well-identified stability and aromaticity maxima versus the number of π-electrons, analogous to the ionization energy curves in the periodical table of the elements, versus atomic number. This is because such shell structure is described in terms of topological/geometrical indices, n, l, m l, s, m s, analogous to the corresponding atomic quantum numbers, demanding (2 l + 1) × (2 s + 1) occupied π-electrons for given l. The frontier orbitals are composed of core and valence (annulene) orbitals in such a way that the benzene “core orbitals” ( l = 0) are expanded and combined, “propagating” successively from benzene to the larger layers, like gigantic superbenzenes, distinguished in those with an aromatic central benzene core, odd n, and satisfying the traditional Hückel/Clar rules, and those with a nonaromatic central ring following the opposite trends. All “superbenzenes” are fully aromatic, satisfying the generalized Hückel’s law suggested here. These results can be projected and/or expanded to other PAHs of all sizes up to infinite graphene, elucidating, among other things, graphene’s sensitivity to edge morphology and size.