Local curvature as a reactivity index of fullerene molecules in the cycloaddition reactions

Using the density-functional theory computations, the curvature features of fullerenes C20 (Ci), C24 (D6), C30-3 (C2v), C40 (D2), C60 (Ih), C70 (D5h), and C76 (D2) were studied as well as their cycloaddition reactions with various substrates (carbene, nitrene, azomethine ylide, and hydrogen azide). Linear correlations were found between the curvature indices of the reaction centers in the fullerene molecules and the computed heat effects of cycloaddition reactions. These correlations have a general nature, allow considering the reactivity of the fullerenes as a whole class of compounds, and take into account the nature of the reaction centers of fullerenes, features of the attached addend, and type of the reaction. The rule was deduced from the correlations about the reactivity of fullerenes toward two reactants, Y1 and Y2: if the reaction proceeds according to the same mechanism and one fullerene is known to be more reactive toward Y1 then other representatives of the fullerene family also exhibit greater reactivity toward Y1.