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 novel topological features and geometric measures to investigate structure-property relationships. For the first time, 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.