Density functional calculations have been performed for many isomers of neutral carbon clusters $C_n( 14 ≤ n ≤ 24, n even )$ using both local spin density (LSD) and generalized gradient approximations to the exchange-correlation energy. The stable isomers include chains, rings, cages, and graphitic structures, and we observe a fourfold periodicity in monocyclic rings as n changes. Stable cages exist for all clusters, and double rings are less stable than the monocyclic rings in all cases. Gradient corrections often change the ordering of the energies of the isomers, but the effects are remarkably regular within a given structural type. The bonding trends found should also apply to larger clusters.
We also calculated the first and second ionization energies of cage structure over a size range. The ionization energies decrease roughly as $\frac{1}{N}^{\frac{1}{2}}$ towards an asymptotic value close to the bulk work function of graphite.
