As a continuation of our previous work (J. Phys. Chem. B, 2014, 118, 11330) On the solvation of C-60 by ionic liquids (ILs) using Molecular Dynamic simulations, this paper reports a systematic density functional theory (DFT) analysis on the interaction mechanism between C-60 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-C-60 interactions would be related with pi-pi stacking between the C-60 surface and anions such as salycilate ([SA]). Likewise, the electronic structure analysis pointed to a well-defined relationship between the energetics of IL-C-60 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 C-60 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 C-60 solvents.