Calculus of Variations and Geometric Measure Theory

M. Friedrich - P. Piovano - U. Stefanelli

The geometry of $C_{60}$: a rigorous approach via Molecular Mechanics

created by friedrich on 08 Apr 2016
modified by piovano on 19 May 2023


Published Paper

Inserted: 8 apr 2016
Last Updated: 19 may 2023

Journal: SIAM J. Appl. Math.
Volume: 76
Number: 5
Pages: 2009-2029
Year: 2016


Molecular Mechanics describes molecules as particle configurations interacting via classical potentials. These {\it 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 $C_{60}$, 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 $C_{60}$ 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.

Keywords: Fullerene, $C_{60}$ , configurational energy minimization, local stability