As a continuation of our previous work (J. Phys. Chem. B, 2014, 118, 11330) on the solvation of C60 by ionic liquids (ILs) using Molecular Dynamic simulations, this paper reports a systematic density functional theory (DFT) analysis on the interaction mechanism between C60 and 24 different ionic liquids (belonging to the imidazolium, piperazinium, and cholinium groups). Properties such as binding energies, charge distributions, intermolecular interactions, or electronic structure were analyzed as a function of the selected ILs. The stronger IL-C60 interactions would be related with π-π stacking between the C60 surface and anions such as salycilate ([SA]). Likewise, the electronic structure analysis pointed to a well-defined relationship between the energetics of IL-C60 systems and IL features. Therefore, ILs with deep HOMO energies as well as weak interaction between both ions would be a priori good candidates for C60 solvation. Although only short-range interactions are studied in the framework of DFT, this work provides useful information for the rational design of ILs that could exhibit suitable features as C60 solvents.