Density functional calculations have been performed for many isomers of carbon clusters ${\mathrm{C}}_n$ ( $14\le n\le 24$, $n$ even) using both local spin density and gradient-corrected approximations to the exchange-correlation energy. The stable isomers include chains, rings, graphitic (“plate” and “bowl”), and cagelike structures, and we observe a fourfold periodicity in several structural classes, not only the monocyclic rings. Stable cages exist for all clusters, and double rings are less stable than the monocyclic rings. Gradient corrections are significant, but quite regular within a given structural type. The bonding trends found should also apply to larger clusters.

• Received 7 April 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.443