Endohedral metallofullerenes (EMFs) are novel derivatives of fullerenes that can encapsulate metal atoms or clusters in their inner space.[1] Owing to their extraordinary properties attributed to significant electron transfer from the metal atoms to the fullerene cage, [2] EMFs have attracted wide interests since the discovery of fullerenes.[3] For instance, lanthanide metallofullerenes have been suggested for use as encapsulated contrasting agents for magnetic resonance imaging. [4] In EMFs, the internal metal atoms always donate electrons to the fullerene cage and carry considerable positive charges. It is interesting and highly significant to investigate the possible formation of metal-metal bonds between these metal atoms in EMFs. [5][6][7] From a theoretical point of view, the study of metal-metal bonds in EMFs gives an in-depth perspective of the metal-metal interaction and provides an approach for further experimental and theoretical explorations of metal-metal interactions. [6,8] On the other hand, in contrast to the fact that several kinds of metal-metal bonds have been studied, in other fields, [9] up to now only rare examples of metal-metal bonds are reported in fullerene chemistry.[7] Furthermore, the presence of metal-metal bonds produces unique structures and fascinating electronic properties of EMFs, which may extend their promising applications in electronics, magnetism, and photovoltaics. [7,10] Most importantly, previous studies have indicated that the encapsulated metal atoms can move around in fullerene cage at room temperature.[11] This dynamic motion makes it possible to design these EMFs as functional molecular devices with new magnetic and electronic properties. [12] It is also an interesting question whether other novel dynamic motion of the encapsulated metals exists in fullerene cage.Lots of efforts have been devoted to metal-metal bonds in EMFs during the past decades, but only a few single metal-metal bonds have been found and confirmed. [6][7][8][13][14][15] In fact, Stevenson et al. suggested the presence of a Sc À Sc bond between the shortest Sc À Sc distance with a newly experimentally determined structure of Sc 4 O 2 @C 80 .[14] Two kinds of metal-metal bonds have been found between Y atoms so far: one two-electron bond in the Y 2 @C 82 , [7] and another long single-electron bond in Y 2 @C 79 N.[15] In addition, a single-electron bond between Tb atoms was also proposed in Tb 2 @C 79 N.[15]Herein we present a thorough investigation on a newly isolated dimetallofullerene Lu 2 @C 76 , [16] and find that the two lutetium atoms prefer to bind together to form an unprecedented single metal-metal bond, in a formal valence state of [Lu 2 ] 4 + @C 76 4À by means of combined quantum chemical and statistical thermodynamic approaches. More interestingly, it is shown that the Lu atoms can hop rapidly between six equivalent configurations in the fullerene cage at room temperature, giving rise to a trajectory as a tetrahedron in C 76 (T d ). Systematic calculations on the di-, tetra-, he...