Optimal atomic configurations, i.e. minimizers of an energy built from interatomic interactions, can be described and analysed explicitly for highly symmetric structures such as infinite carbon nanotubes. If the symmetry is broken, for instance by caps at the ends of the tube, explicit analysis becomes much harder or even out of reach. For given interatomic potentials, one can instead use computer-assisted proofs to rigorously establish the existence of true local minimizers near numerically computed ones. I will present this approach and several case studies comparing different interatomic potentials. This is joint work with Miguel Ayala and Rustum Choksi.