Growth regimes of carbon clusters

We calculated the relative stabilities of carbon clusters with up to 60 atoms. Equilibrium geometries have been obtained by combining an adaptive simulated annealing method and a simple tight-binding-type Hamiltonian for total energies. We found that ${\mathrm{C}}_{\mathit{n}}$ clusters favor one-dimensional structures for n≲20. For n≳20, closed fullerene cages show a larger stability than both the one-dimensional and two-dimensional structures (such as graphite flakes and buckled fullerene ‘‘caps’’). Isomers with linear and ‘‘fullerene’’ structure should coexist near the critical cluster size n≊20. We find the ${\mathrm{C}}_{60}$ fullerene to be the most stable structure, with a binding energy of 6.99 eV/atom.