Mapping structure-property relationships in fullerene systems: a computational study from C20 to C60

Fullerenes, as characteristic carbon nanomaterials, offer significant potential for diverse applications due to their structural diversity and tunable properties. Numerous isomers can exist for a specific fullerene size, yet a comprehensive understanding of their fundamental properties remains elusive. In this study, we construct an up-to-date computational database for C20–C60 fullerenes, consisting of 5770 structures, and calculate 12 fundamental properties using DFT, including stability (binding energy), electronic properties (HOMO-LUMO gap), and solubility (partition coefficient logP). Our findings reveal that the HOMO-LUMO gap weakly correlates with both binding energy and logP, indicating that electronic properties can be tailored for specific uses without affecting stability or solubility. In addition, we introduce a set of topological features and geometric measures to investigate structure-property relationships. We apply atom, bond, and hexagon features to effectively predict the stability of C20–C60 fullerenes, surpassing the conventional qualitative isolated pentagon rule, and demonstrating their robust transferability to larger-size fullerenes beyond C60. Our work offers guidance for optimizing fullerenes as electron acceptors in organic solar cells and lays a foundational understanding of their functionalization and applications in energy conversion and nanomaterial sciences.