Interaction between Er atoms and the carbon cageC82

The study of ${\mathrm{Er}}_2@{\mathrm{C}}_{82}$ by using an ab initio discrete-variational method based on the local-density approximation is reported. The trapping of two erbium atoms has caused significant rearrangement of the energy levels of the cage throughout the band. Due to the localized characteristic of $4f$ electrons of erbium, the on-site Coulomb interaction, “Hubbard U term,” is taken into consideration and the local-spin-density approximation +U method is used to investigate the behavior of $4f$ electrons of Er and the electronic structure of ${\mathrm{Er}}_2@{\mathrm{C}}_{82}.$ The description of the electronic structure of this system is greatly improved after taking on-site Coulomb interaction into consideration, and the $4f$ states are split into lower occupied states and higher unoccupied states and the splitting is 4.9 eV. Four new peaks appear below the Fermi level, and this result is in agreement with absorption spectra of ${\mathrm{Er}}_2@{\mathrm{C}}_{82}.$ It is shown that the valence of Er ions in ${\mathrm{Er}}_2@{\mathrm{C}}_{82}$ is divalent and in ${\mathrm{C}}_{82}$ cage the Er ion has a magnetic moment of $9.59{\mu }_B.$ The characteristics of the states near the Fermi level are discussed.