In the present study, we have investigated the energy differences between the lowest-energy singlet and triplet states of a large set of small fullerenes with density functional theory (DFT), and the related quantities of ionization energy (IE) and electron affinity (EA). The DFT methods generally show consistent qualitative observations. For the full set of 812 fullerene isomers, ~80–90% have a singlet ground state, with the rest being ground-state triplets" some of them may complement existing singlet-fission materials to improve the efficiency for light harvesting. The triplet–singlet energy difference correlates well with the IE–EA differences, which are indicators for charge-transfer capabilities. We have surveyed larger fullerenes in search of candidates with superior charge-transfer properties, with the results suggesting that optimally shaped medium-sized fullerenes may be the most promising.