3. Results and Discussion:
In our previous study [46 ], we have already explored the DA reaction of single 1,3-butadiene moiety with normal fullerene and its mono- and di-encapsulated fullerene derivatives. In the present work, we have extended the study to investigate the MDA reaction on normal fullerene and its mono-encapsulated derivative. The exploration of the Multi-Diels-Alder (MDA) reaction has been commenced by considering the first DA product (first functionalization) and 1, 3-butadiene as the initial reactants. Initially, two different approaches have been adopted for the attachment of the second butadiene on the surface of the first DA product (for both 6-6 and 6-5 connectivity separately). The pictorial diagram of 6-6 and 6-5 bonds are shown in Figure 1 . The double bond (either 6-6 or 6-5), placed almost opposite to the first functionalization, has been considered for the second butadiene attachment (Direct Approach) followed by sequential addition of another two butadiene moieties on the residual 6-6 or 6-5 bonds. In the other approach, designated as the Alternative Approach , the double bond adjacent to the first functionalization undergoes a second DA reaction followed by sequential attachment of the other two butadiene molecules on the remaining 6-6 or 6-5 double bonds. The schematic representation of the approaches considered here is depicted in Scheme 1 . Incidentally, the product formed after two successive DA reactions to the first functionalization, following these two approaches separately, are identical. Each of the six-membered cyclic transition states corresponding to the cyclo-addition is observed to be concerted. The optimized geometries of the TSs for MDA reaction on 6-6 bonds of neutral C60 and Li+@C60 and their associated PES diagram are depicted in Figure 2 andFigure 3 for the ’Direct’ approach and Figure 4 andFigure 5 for the ’Alternative’ approach, respectively. The graphical representation of ∆Ea on varying the steps of MDA reactions associated with 6-6 bonds for neutral C60and Li+@C60 in ‘Direct’ and ‘Alternative’ approaches is shown in Figure 6 andFigure 7 .