Dynamic Metastable Characteristics of Carbon Cages Embedded with Er₂C₂

Novel endohedral metallofullerenes (EMFs), namely, Er₂C₂@C_2v(5)-C₈₀, Er₂C₂@C_s(6)-C₈₂, Er₂C₂@C_s(15)-C₈₄, Er₂C₂@C_2v(9)-C₈₆, Er₂C₂@C_s(15)-C₈₆, and Er₂C₂@C_s(32)-C₈₈, had been experimentally synthesized, and the unique structures and many fascinating properties had also been widely explored. Nevertheless, the position of the Er atoms inside the cage shows a severe disorder within the stable EMF monomer, which is difficult to understand and explain from the experimental point of view. In this work, based on the density functional theoretical calculations, the Er₂C₂@C_s(6)-C₈₂ has 73 directional isomers and 2 Er atoms that are far beyond from Er-Er single bonding and tend to be close to the cage side (marked as "shell"), and the core (Er₂C₂ units) takes on a butterfly shape as generally revealed. The energy difference between any two of the isomers is in the range of 0.05 to 25.6 kcal/mol, indicating a relatively easy thermodynamic transition between the isomers. The other five Er carbide cluster EMFs (Er₂C₂@C_2v(5)-C₈₀, Er₂C₂@C_s(15)-C₈₄, Er₂C₂@C_2v(9)-C₈₆, Er₂C₂@C_s(15)-C₈₆, and Er₂C₂@C_s(32)-C₈₈) are also studied in the same way, and 30, 37, 39, and 43 most stable Er-oriented sites inside the cage, respectively, are obtained. In addition, the shape of the Er₂C₂ gradually changed from butterfly to linear. Moreover, the electronic structure and molecular orbital analyses show that it is easy for Er₂C₂@C_80-88 to form a charge transfer state of [Er₂C₂]⁴⁺@[C_80-88]^4- via the dynamic core-shell coordination equilibrium. Er₂C₂ with a steep drop in chemical stability is restricted to forming varying degrees of metastable states in the shell, determined by the shell size, to ensure the overall stability. The lowest unoccupied molecular orbital energy level of these EMFs is increased by 0.5-1.1 eV compared with fullerenes C_80-88, potentially providing favorable conditions for suitable energy level matching with EMF as an electron acceptor used in organic solar cell devices.