2. Computational details:
All electronic structure calculations have been carried out using the Gaussian 09[47 ] suite of the quantum chemistry program. For electronic structure calculations, M06-2X[48 ] functional in conjunction with 6–31G(d) basis set has been employed. M06-2X functional has been well-established for various theoretical studies such as kinetic and thermodynamic calculations related to Diels-Alder reactions of fullerenes and metallofullerenes[49 ].This functional is a hybrid meta-GGA functional which was developed by Zhao and Truhlar. It has been found that Quasi-Newton methods are inefficient in finding the transition-state structures (first-order saddle points) between the equilibrium geometries. In this regard, Gaussian incorporates Synchronous Transit-guided Quasi-Newton (STQN) method to search for a maximum along the parabola connecting the reactant and product[50 ]. A parallel intrinsic reaction coordinate (IRC) calculation [51 ] has also been performed to confirm whether the transition states connect the right minima or not. Normal-mode analysis has been carried out at the same level of theory to confirm whether the optimized structures are local minima (no imaginary frequency) or transition state geometries (one imaginary frequency).The relative energies of the intermediate adduct (ΔEA) and transition state (ΔETS) concerning the separated reactants are defined as:
ΔEA= E(intermediate adduct)-E(fullerene/metallofullerene)-E(1,3-butadiene);
ΔETS= E(transition state)-E(fullerene/metallofullerene)-E(1,3-butadiene).
The activation barrier (ΔEa) is defined as: ΔEa= ΔETS-ΔEA.
All energies reported in the article are zero-point-corrected electronic energy obtained at 0 K temperature and 1 atm pressure.
Moreover, kinetics study has also been performed to determine the rate of all Multi-Diels-Alder reactions by employing Transition State Theory (TST) [52, 53 ]. The entire kinetic study has been performed with The Rate program[54 ].In this program, the molecular rotations are treated classically and the vibrations are treated quantum mechanically within the harmonic approximation. The rate constant (k) values have been determined for a temperature range of 100 K - 1000 K with 100 K temperature interval, keeping the pressure fixed at 1 atm.