Aromaticity and electron affinity of Carbo(k)-[3]radialenes, k=0, 1, 2

Aromaticity enhancement is a possible driving force for the low reduction potentials of buta-1,3-diynediyl-expanded [N]radialenes: this hypothesis is theoretically analyzed for the expanded [3]radialene prototype. This study is undertaken within a more general prospect, namely the evaluation of the variation of aromaticity with endocyclic and peripheral carbomeric expansion of [3]radialene and its mono- and dianions. The structures, denoted as [C-H](6) (h)[C-C](3) (k)carbo-[3]radialene(q) (h=0, 1; k=0, 1, 2; q=0, -1, -2), were optimized in relevant singlet, doublet, or triplet spin states at the B3PW91/6-31G** level. They were found to be all planar. The structural aromaticity was measured through the average bond length d(av) over the [C-C](3) (k)carbo-[3]radialene core, and by the corresponding bond-length equalization parameter sigma(d), related to Krygowski's GEO. The magnetic aromaticity was measured by Schleyer's NICS values at the center of the rings. Regarding the relative variation of NICS and sigma(d), two classes of species can be distinguished according to their endocyclic expansion level. The species with a nonexpanded (k=0) or doubly expanded (k=2) ring constitute the first class: they exhibit D(3h) symmetry and a strong correlation of NICS with sigma(d). The species with a singly expanded ring (k=1) fall far from the correlation line, and constitute the second class. This class distinction is related to the degeneracy scheme of the frontier orbitals of the neutral representative. A finer appraisal of the electron (de)localization is brought by the ELF (Electron Localization Function) analysis of the electron density. It allows for a weighting of relevant resonance forms. Unsubstituted species are well described by the superimposition of two or three resonance forms. For (doublet spin state) monoanionic species, their respective weights are validated by comparison with AIM spin density. The weighted mean, n, of the formal numbers of paired pi(z) electrons in the resonance forms was calculated and compared with the closest even integer of either forms 4m+2 or 4m. A density-based continuous generalization of the orbital-based discrete Hückel rule is then heuristically proposed through an analytical correlation of NICS versus sigma(d), n, and S, the spin of the species. The frontier-orbital-degeneracy pattern of neutral species is discussed with respect to structural and magnetic aromaticity criteria. A decreasing HOMO-LUMO gap versus endocyclic expansion is obtained, but [C-C](3) (1)carbo-[3]radialene possesses the highest HOMO and LUMO energies. Vertical and adiabatic electron affinities of neutral and monoanionic species were also computed and compared with related experimental data.