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All possible types of Diels-Alder (DA) cycloadditions of 1,3-cis-butadiene to C60 (2 in total) and to C70 (8 in total) were theoretically investigated by the M06-2X density functional method in gas phase and solutions.An intermediate between the reactant and the transition state was located for each reaction.These intermediates except one have not been experimentally or theoretically reported.