Stabilities Referring to the f Electron Effect in Erbium-Based Endohedral Metallofullerenes: Revisiting Er₂@C₈₀ and the Missing Er₂C₂@C₇₈

Endohedral metallofullerenes (EMFs) involving lanthanide elements exhibit unique physicochemical properties, with one of the key factors being the presence of 4f electrons. These 4f electrons contribute to complex metal-metal and metal-cage interactions. Despite extensive research on their properties, a thorough theoretical interpretation of the effect of 4f electrons on the EMF stability and structure remains lacking. In this study, building on previous findings that highlighted Er₂@C₈₀ as a potential magnetic molecule, the stabilities and metal-metal/metal-cage interactions of the Er₂C₈₀ system have been explored using density functional theory calculations combined with statistical thermodynamic analyses. Three thermodynamically stable isomers are identified: Er₂@<i>I</i>_h(31924)-C₈₀, Er₂C₂@<i>C</i>₁(23349)-C₇₈, and Er₂C₂@<i>C</i>₁(22595)-C₇₈. The Er₂@<i>I</i>_h-C₈₀ isomer features a two-center one-electron Er-Er bond stabilized by significant charge transfer to the C₈₀ cage. Extended Transition State-Natural Orbitals for Chemical Valence (ETS-NOCV) analysis reveals electron redistribution within the cage and stabilization of the Er-Er bond, which corroborates earlier model conclusion of the magnetic properties of Er₂@C₈₀. Analyses of different electronic configurations of the main Er₂C₈₀ isomers and Er₂ cluster reveal a significant impact on the exchange interaction of 4f electrons to the stability of the whole Er₂C₈₀ molecule.