Superior performance of the machine-learning GAP force field for fullerene structures

Carbon force fields are widely used for obtaining structural properties of carbon nanomaterials. We evaluate the performance of a wide range of carbon force fields for obtaining molecular structures of prototypical C-60 fullerenes. The reference geometries are optimized using the hybrid B3LYP-D3BJ density functional. The Gaussian approximation potential (GAP-20) machine-learning-based force field attains a root-mean-square deviation (RMSD) of merely 0.014 angstrom over a set of 29 unique C-C bond distances. This represents a significant improvement over traditional empirical force fields, which result in RMSDs ranging between 0.023 (LCBOP-I) and 0.073 (EDIP) angstrom. Performance of the GAP-20 force field is on par with that of the PM6 and AM1 semiempirical methods. Moreover, the GAP-20 force field attains a mean signed deviation of 0.003 angstrom indicating it is free of systematic bias toward underestimating or overestimating the fullerene bond distances. We therefore recommend the GAP-20 force field for optimizing the equilibrium structures of fullerenes and nanotubes.