We present a molecular-dynamics study of the energetics and structures of very large carbon cage clusters, which has been performed using tight-binding methods, both empirical and ab initio. The use of an order-N scheme, which provides the solution of the electronic problem with an effort proportional to the size of the system, allowed us to study clusters with up to 3840 atoms. We have considered clusters with spherical and with toroidal topology, and systematically find that spherical clusters have lower energy than toroidal clusters of the same size. However, the toroidal ${\mathrm{C}}_{360}$ and larger clusters have lower energy per atom than the fullerene ${\mathrm{C}}_{60}$. Concerning the spherical fullerenes, we show that, in all cases, their minimum energy shape is markedly polyhedral rather than spherical. The clusters present nearly flat faces between each three contiguous protruding pentagon sites. The surfaces are nevertheless smooth, without sharp edges in the lines joining the pentagons, which would be present in a perfect truncated icosahedron. We also discuss the energetics of the clusters as a function of their size, and the validity of different functional forms proposed in the literature. © 1996 The American Physical Society.

• Received 26 July 1995

DOI:https://doi.org/10.1103/PhysRevB.53.2132