Structure of laser-pulse-plasma-induced carbon clusters: Explanation of the magic numbers

A simple explanation is offered for the magic numbers 11, 15, 19, and 23 for carbon clusters produced promptly by pulsed-laser ablation of carbon. The structure proposed for the eleven-member cluster has all C—C—C angles equal to 120° with three five-member rigns about two atoms whose $p_{\pi }$ orbitals are perpendicular to those of the other atoms. This structure allows one graphitic six-member ring to be formed on each of the three rings upon the addition of four more atoms, thereby accounting for 15, 19, and 23 and for the absence of 7, 27, 31, etc. Extended Hückel calculations indicate the eleven-member cluster is only about 1% less stable than carbon rings or chains under normal conditions. We also find that its highest occupied molecular orbitals have nonbonding character for all nearest-neighbor interactions, and argue that this explains why 11, 15, 19, and 23 are magic numbers for neutral and for positive clusters but not for negative clusters. When stacked together they produce very open structures with a density of 1.4 g/${\mathrm{cm}}^3$. It is proposed that they are common constituents of glassy carbon and of soot and account for the fact that the densities of these materials are much less than those of graphite and diamond. Thus, the observed clusters are present in the target before ablation; they need not form during the pulse.