Valence One-Electron and Shake-Up Ionization Bands of Carbon Clusters. III. The Cn(n = 5,7,9,11) Rings

The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of odd-membered carbon rings (C 5, C 7, C 9, C 11 ) are investigated by means of the third-order algebraic diagrammatic construction [ADC(3)] scheme for the one-particle Green's function. Despite a severe dispersion of the σ- and π- ionization intensity over intricately dense sets of satellites, the present study undoubtedly confirms that structural fingerprints in ionization spectra could be usefully exploited to discriminate the cyclic C 5, C 7, C 9, and C 11 species from their linear counterparts in plasma conditions. Such spectra could also be used to indirectly trace very fine details of the molecular structure, such as bond length alternations, out-of-plane distortions, or the strength of cyclic strains. Both structurally and electronically, the cyclic isomers of the C 5 and C 9 clusters must be described as even-twisted cumulenic tori, whereas the C 7 and C 11 cyclic species are simply planar polyynic rings. In comparison with their linear counterparts, all species display an intrinsically lower propensity to electronic excitations, marked by a rather significant increase of the fundamental HOMO−LUMO band gap. On the other hand, the lower symmetry of the cyclic clusters, C 5 and C 9 in particular, permits many more configuration interactions in the cation. The ultimate outcome of these two opposite factors is, overall, a severe enhancement of the shake-up fragmentation of ionization bands, compared with the linear isomers.