On the Problem of He–He Bond in the Endohedral Fullerene He2@C60

For more than twenty years, the endohedral fullerene cavity is attracting a permanent attention of experimenters and theorists, computational chemists and physicists, who apply their efforts to simulate encapsulated atoms and molecules in the fullerene cavity on computers and analyze the arising phenomena of atomic bonding. In this work, recent developments concerning the endohedral fullerene He2@C60, in particular, its experimental observation and relevant computational works, are reviewed. On the one hand, the dihelium He2 embedded into the C60 cavity is observed experimentally. On the other hand, the computer simulation shows that each of the He atoms is characterized by an insignificant charge transfer to C60, so that the He dimer exists as a partially charged (He+b)2 entity. The key issue of the work concerns the existence of a bond between those two helium atoms. Since the bond is created between two particles, we assert that it suffices to define the bond on the basis of the molecular L¨owdin’s postulate and use it to study the He dimer in the C60 cavity in terms of the He–He potential energy well. It was analytically demonstrated that this well can contain at least one bound (ground) state. Therefore, according to L¨owdin’s postulate, which is naturally anticipated in quantum theory, the conclusion is drawn that the (He+b)2 entity is a diatomic molecule, in which two heliums are bound with each other. On the basis of those arguments, the concept of endohedral fullerene stability is proposed to be extended.

Prediction of Fullerene Stability Using Topological Descriptors

In recent years, several attempts have been made to characterize the geometric structure of fullerenes by means of topological shape factors in order to predict their physical properties and stability. In this paper, we present a simple method to estimate the stability of fullerenes on the basis of quantitative topological criteria. This approach is based on the concept of the generalized combinatorial curvatures defined on the set of simple graphs embedded on a closed surface without boundary (sphere, torus, projective plane, Klein bottle). It is shown that starting with the computed generalized combinatorial curvatures several novel topological indices can be generated. From computations performed on a set of C40 and C60 fullerenes, we concluded that the four topological shape factors tested (Λ(-1), (-1), Λ(1) and (1)) could be successfully used to preselect the most stable fullerene isomers.