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.

富勒烯作为特征碳纳米材料，由于其结构多样性和可调特性，为各种应用提供了巨大的潜力。特定的富勒烯尺寸可以存在多种异构体，但对其基本性质的全面了解仍然难以捉摸。在本研究中，我们构建了由5770个结构组成的C ₂₀ –C ₆₀富勒烯的最新计算数据库，并使用DFT计算了12个基本性质，包括稳定性（结合能）、电子性质（HOMO-LUMO能隙）和溶解度（分配系数 logP）。我们的研究结果表明，HOMO-LUMO 间隙与结合能和 logP 均呈弱相关，这表明电子特性可以根据特定用途进行定制，而不会影响稳定性或溶解度。此外，我们引入了一组拓扑特征和几何测量来研究结构-性能关系。我们应用原子、键和六边形特征来有效预测C ₂₀ –C ₆₀富勒烯的稳定性，超越了传统的定性孤立五边形规则，并证明了它们对C ₆₀以上更大尺寸富勒烯的强大可转移性。我们的工作为优化富勒烯作为有机太阳能电池中的电子受体提供了指导，并为其在能量转换和纳米材料科学中的功能化和应用奠定了基础了解。