Stable carbon configurations

Molecular Mechanics models molecules as configurations of particles interacting via classical potentials. The specific geometry of covalent bonding in carbon is described by the combination of an attractive-repulsive two-body interaction and a three-body bond-orientation part. We investigate the strict local minimality of specific carbon configurations under general assumptions on the interaction potentials. Carbyne, graphene, some fullerenes, and diamond are proved to be stable.