Structural peculiarities of fullerenes C-20, C-24, C-30, C-36, C-40, C-60, C-70, and C-76 and their adducts with 1,3-dipolarophiles (ozone and diazomethane) were investigated by the DFT method with the PBE functional. A correlation between the heats of 1,3-dipolar addition reactions and the carbon surface curvatures at reaction sites in the original fullerene molecules was found.