Density functional theory (DFT) calculations have been carried out at the hybrid Becke 3-Lee-Yang-Parr; B3LYP/3-21G** level of theory to study two series of hydroxy-chalca-acetic acid-(4-pyrrolidin-1-yl-phenyl) ester [C(60)-C(2)H(4)N-(4-XCOCH(2)OH)C(6)H(4)] and hydroxy-chalcoacetic acid-[2-(2-hydroxy-acetylchalcanyl)-4-pyrrolidin-1-yl-phenyl] ester[C(60)-C(2)H(4)N-(3,4-XCOCH(2)OH)C(6)H(4)]. The X atom is O, S or Se for the two series. The vibrational spectra, physical, chemical, thermodynamics and Quantitative Structure Activity Relationship (QSAR) properties of the studied molecules are calculated and discussed. We have evaluated these molecules as HIV-1 protease inhibitors based on the hydrogenation interaction between the hydroxymethylcarbonyl (HMC) groups and the two aspartic acid of the HIV-1 protease active site. Results show that some of the investigated fullerene-based derivatives can be considered promising as HIV-1 protease inhibitors.