M@C 78 (M = U, Th): Inherent Topological Connectivity Existed in Thermodynamically Stable Isomers and the Possibility of an Endohedral Fullerene Containing One Heptagon Ring.

The density functional theory combined with statistical thermodynamic analyses of M@C 78 (M = U and Th) demonstrated that four isomers, M@ D 3h (24109)-C 78 , M@ C 2 v (24107)-C 78 , M@ C 1 (22595)-C 78 , and M@ C 1 (23349)-C 78 , and a nonclassical isomer, M@ C 1 (id7)-C 78 , containing one heptagon ring possess outstanding thermodynamic stabilities in the two M@C 78 series. Especially, the M@ C 1 (id7)-C 78 isomer is the first nonclassical C 78 fullerene that can exist stably. Importantly, these five fullerene cages are found to be related in the form of Stone-Wales (SW) transformations. Geometric analyses disclosed that, unlike lanthanide metals, actinide metals are more likely to bond with sumanene-type hexagonal rings when they are encapsulated in IPR C 78 cages. Frontier molecular orbital analysis showed that both U and Th atoms donate four electrons to the C 78 carbon cages.