Density functional study of carbon clusters C2n (2⩽n⩽16). I. Structure and bonding in the neutral clusters

Density functional calculations have been performed for many isomers of neutral carbon clusters ${\mathrm{C}}_n$ $\text{(4⩽n⩽32}$ , n even) using both local spin density (LSD) and gradient-corrected (Becke–Perdew) approximations to the exchange-correlation energy. The stable isomers include chains, rings, cages, and graphitic (“plate ” and “bowl”) structures, and we observe a fourfold periodicity in several structural classes as n changes. Stable cages exist for all clusters with $\text{n⩾8}$ , and double rings are less stable than the monocyclic rings in all cases. Most planar structures have low-frequency out-of-plane vibrations. Gradient corrections often change the ordering of the energies of the isomers, but the effects are remarkably regular within a given structural type.