Theoretical Study On The Dynamic Metastable Characteristics Of Carbon Cages Embedded With Er₂C₂

Endohedral Metal Fullerenes（EMFs）can not only protect metal atoms or clusters from the external environment,but also transfer the electrons of central atoms to the carbon cage compare with traditional fullerenes.With such fascinating molecular structure and chemical properties,EMFs have great potential applications in materials science,electronics,optoelectronics,catalysis,biomedicine,and molecular devices.In the past decades,various types of endohedral metal fullerenes have been synthesized experimentally.In particular,Lu Group from Huazhong University of Science and Technology has conducted a large number of systematic studies on the synthesis and characterization of EMFs.However,the theoretical work is not rich at present,focusing on the internal chemical bond characteristics and electronic structure information.We believe that it is of great significance to further study the structural law of EMFs and its overall application basis and systematic evaluation by theoretical methods.Er₂C₂@C_s（6）-C₈₂system was selected as the research target,and its five molecular systems in the same series were modeled to investigate the internal bonding and interaction properties of Er₂C₂,the interaction characteristics of Er with the surrounding carbon cage,the disorder of multiple local locations shown in the characterization of Er atoms,and the geometrical variation of Er₂C₂core with different fullerene sizes will be solved and described in detail.Novel EMFs,such as 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 with in the stable EMF monomer,which is difficult to understand and explain from the point of experimental view.In this work,based on the density functional theoretical calculations,the Er₂C₂@C_s（6）-C₈₂has 73 directional isomers and Er atoms are far beyond from Er-Er single bonding and tend to be close to the cage side（marked as“shell”）,and the Er₂C₂units（simplified as"core"）,takes on a butterfly shape generally were 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 clusters EMF(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 same way and there are 30,37,39,and 43most stable Er oriented sites inside the cage,respectively,are obtained.In addition,the shape of the Er₂C₂could change gradually changed from butterfly to linear.Moreover,the electronic structure and molecular orbital analysis show that Er₂C₂@C_80⁸8is easy to form charge transfer state of[Er₂C₂]⁴⁺@[C_80-88]^4-via the dynamic core-shell coordination equilibrium.Er₂C₂with 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 e V compared with to fullerenes C_80-88,potentially providing favourable conditions for suitable energy level matching with EMF as electron acceptor used in organic solar cell devices.