The Geometry of C60: A Rigorous Approach via Molecular Mechanics

Molecular Mechanics describes molecules as particle configurations interacting via classical potentials. These configurational energies usually consist of the sum of different phenomenological terms which are tailored to the description of specific bonding geometries. This approach is followed here to model the fullerene C60, an allotrope of carbon corresponding to a specific hollow spherical structure of sixty atoms. We rigorously address different modeling options and advance a set of minimal requirements on the configurational energy able to deliver an accurate prediction of the fine three-dimensional geometry of C60 as well as of its remarkable stability. In particular, the experimentally observed truncated-icosahedron structure with two different bond lengths is shown to be a strict local minimizer.