Recently, one η1-coordinated complex of endohedral metallofullerene (EMF) Y@C2v(9)-C82[Re(CO)5] has been synthesized and characterized with a highly efficient radical-coupling methodology by performing a photochemical reaction between Y@C2v(9)-C82 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@C2v(9)-C82 (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@C2v(9)-C82. In the reactions of Y@C2v(9)-C82 with various transition-metal complexes [M'Ln]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 dσ orbital of the M'Ln species. Moreover, the very-low-energy dσ 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@Cs(6)-C82 and La@C72 have been investigated. The Y@Cs(6)-C82 structure is more reactive toward the [M'Ln]2 complexes than Y@C2v(9)-C82 thanks to a lower SOMO of Y@Cs(6)-C82 than that of Y@C2v(9)-C82, which derives from position change of the Y atom in Cs(6)-C82 during the reactions. However, the formation of [Y@Cs(6)-C82]2 suppresses the formation of several C-M' bonds. The reactivity of La@C72 is weak due to a high LUMO+1 of C72, which leads to a high SOMO of La@C72. 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.