The geometry of C_60: a rigorous approach via Molecular Mechanics

TL;DR

This paper rigorously models the $C_{60}$ fullerene's geometry using Molecular Mechanics, establishing minimal energy conditions that predict its stable truncated-icosahedron structure with two bond lengths.

Contribution

It introduces a rigorous approach to modeling $C_{60}$ geometry via Molecular Mechanics and identifies minimal energy conditions for its stability.

Findings

$C_{60}$ structure is a strict local energy minimizer.

The model accurately predicts the truncated-icosahedron geometry.

Two different bond lengths are confirmed as stable features.

Abstract

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.