Order-N Tight-Binding Molecular Dynamics : Application to Giant Fullerenes

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 carbon cage clusters with up to 3840 atoms using workstation HP755 (512MB). 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 C_ and larger clusters have lower energy per atom than the fullerene C_, and therefore should be possible to be synthesized. Concerning the spherical carbon cage clusters, 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 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