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

Carbon force felds are widely used for obtaining structural properties of carbon nanomaterials. We evaluate the performance of a wide range of carbon force felds for obtaining molecular structures of prototypical C₆₀ fullerenes. The reference geometries are optimized using the hybrid B3LYP-D3BJ density functional. The Gaussian approximation potential (GAP-20) machine-learning-based force feld attains a root-mean-square deviation (RMSD) of merely 0.014 Å over a set of 29 unique C–C bond distances. This represents a signifcant improvement over traditional empirical force felds, which result in RMSDs ranging between 0.023 (LCBOP-I) and 0.073 (EDIP) Å. Performance of the GAP-20 force feld is on par with that of the PM6 and AM1 semiempirical methods. Moreover, the GAP-20 force feld attains a mean signed deviation of 0.003 Å indicating it is free of systematic bias toward underestimating or overestimating the fullerene bond distances. We therefore recommend the GAP-20 force feld for optimizing the equilibrium structures of fullerenes and nanotubes.