Recently, one η 1 -coordinated complex of endohedral metallofullerene (EMF) Y@C 2v (9)-C 82 [Re(CO) 5 ] has been synthesized and characterized with a highly efficient radicalcoupling methodology by performing a photochemical reaction between Y@C 2v (9)-C 82 and [Re(CO) 5 ] 2 complexes. Theoretical investigations with the density functional theory reveal that this complex is stabilized by an ionic C−Re bond. The reactions of M@C 2v (9)-C 82 (M = Sc, Y, La) with [Re(CO) 5 ] 2 suggest that the reaction energies differ little because of similar single occupied molecular orbitals (SOMOs) of M@C 2v (9)-C 82 . In the reactions of Y@C 2v (9)-C 82 with various transition-metal complexes [M′L n ] 2 (M′ = Mn, Tc, Re, Fe, Ru, Os, Co, Rh, Ir), the C−M′ bonds with Mn, Tc, Re, Fe, Ru, and Os can stably exist, whereas those with Co, Rh, and Ir are unstable. Further analyses disclose that, in each element group, the stability of the C−M′ bond is mainly determined by the bond energy of the M′−M′ bond, which is related to the d σ orbital of the M′L n species. Moreover, the very-low-energy d σ orbitals and large geometrical distortions of M′(CO) 4 (M′ = Co, Rh, Ir) lead to poor stabilities of the C−M′ (M′ = Co, Rh, Ir) bonds. As comparison, the reactions of Y@C s (6)-C 82 and La@C 72 have been investigated. The Y@C s (6)-C 82 structure is more reactive toward the [M′L n ] 2 complexes than Y@C 2v (9)-C 82 thanks to a lower SOMO of Y@C s (6)-C 82 than that of Y@C 2v (9)-C 82 , which derives from position change of the Y atom in C s (6)-C 82 during the reactions. However, the formation of [Y@C s (6)-C 82 ] 2 suppresses the formation of several C−M′ bonds. The reactivity of La@C 72 is weak due to a high LUMO+1 of C 72 , which leads to a high SOMO of La@C 72 . We believe that this theoretical study provides primary principles of radical-coupling reactions of EMFs and will be valuable for future research of organometallic complexes of fullerene.