Theoretical study on the stabilities, electronic structures, and reaction and formation mechanisms of fullerenes and endohedral metallofullerenes

The elucidation of geometries is the fundamental to further investigate and develop fullerene chemistry, an epoch-making discipline since 1985. Although the geometries of fullerenes, including their derivatives, could be characterized by various experimental methods, single-crystal X-ray diffraction is the only precise one. Notably, the electronic structures and reaction mechanisms cannot be clearly studied in experiment. Theoretical study is a valid and credible choice with foresight. In this account, we highlight the advanced theoretical contributions to the structures, reaction mechanisms, and formation mechanisms of fullerenes, including endohedral fullerenes (EFs). Several rules previously proposed were highlighted to screen the stabilities of (endohedral) fullerenes. In addition, the semi-empirical molecular orbital methods (SEMOMs), molecular dynamics, and Hartree-Fock (HF) method are also performed to characterize the relative stability of EFs. Subsequently, with the developments of theoretical level and computational efficiency, density functional theory (DFT) computation combined with statistic thermodynamically analysis (STA) is successful for predicting the stable isomers of EFs, on which the first non-IPR EF, [email protected]70, was revealed. In addition, the results of the single-crystal X-ray diffraction results confirm many of theoretical predictions. The long-range corrections in DFT play a key role in the study of Sc2C2n system. Additionally, the electronic structures of EFs have also been studied in theory, and there is no choice but to the theoretical study on reaction mechanism of EFs. The experimental method is languorous on the fullerene-formation mechanism, including endohedral fullerenes, which is still ambiguous up to now, due to the ultra-formation conditions. There is much theoretical evidence for the fullerene-formation process based on top-down and bottom-up models. At the end, the machine learning is expected to be used in fullerene chemistry in the future.