In addition to E g , other fundamental quantities related to electronic properties have also been computed, such as the fundamental gap E f und between IP and EA, and the energy difference between triplet and singlet states ∆E T -S , which are also crucial for the stability and catalytic activity of materials. As shown in Figure , E g values show strong correlations with both E f und and ∆E T -S across the C 20 -C 60 database, with R 2 values exceeding 0.9, whereas the linear correlation between fundamental gap and triplet-singlet energy difference exhibits cage size dependence with a lower R 2 of 0.774. Indeed, Table reveals that, for fullerene cages of the same size, R 2 values for the E g , E f und , and ∆E T -S all exceed 0.94, with the exception of C 36 , which are consistent with the previous studies. Besides its significance in photovoltaic applications, E g is also connected to other essential properties in electrochemistry. For instance, E g is linked to the redox potential, a key factor in processes such as cyclic voltammetry (CV), energy storage in batteries and fuel cells, and electrocatalysis.