Element effects in endohedral metal-metal-bonding fullerenes M₂@C₈₂ (M = Sc, Y, La, Lu)

Endohedral metal-metal-bonding fullerenes have recently emerged, in which encapsulated metals form a metal-metal bond. However, the physical reasons why some metal elements prefer to form metal-metal bonds inside fullerene are still unclear. Herein, we reported first-principles calculations on electronic structures, bonding properties, dynamics, and thermodynamic stabilities of endohedral metallofullerenes M-2@C-82 (M = Sc, Y, La, Lu). Multiple bonding analysis approaches unambiguously reveal the existence of one two-center two-electron sigma covalent metal-metal bond in M-2@C-82 (M = Sc, Y, Lu); however, the La-La bonding interaction in La-2@C-82 is weaker and could not be categorized as one metal-metal covalent bond. The energy decomposition analysis on bonding interactions between an encapsulated metal dimer and fullerene cages suggested that there exist two electron-sharing bonds between a metal dimer and fullerene cages. The reasons why La-2 prefers to donate electrons to fullerene cages rather than form a standard sigma covalent metal-metal bond are mainly attributed to two following facts: La-2 has a lower ionization potential, while the hybridization of ns, (n - 1)d, and np atomic orbitals in La-2 is higher. Ab initio molecular dynamic simulations reveal that the M-M bond length at room temperature follows the trend of Sc < Lu < Y. The statistical thermodynamics calculations at different temperatures reveal that the experimentally observed endohedral metal-metal-bonding fullerenes M-2@C-82 have high concentrations in the endohedral fullerene formation temperature range.