Theoretical Study on Structural Properties and Infrared Spectra of M@B₁₂N₁₂ (M = La – Lu) Clusters

The geometric structure, electronic properties, electric dipole moment and infrared absorption spectra of M@B₁₂N₁₂ (M = La – Lu) clusters have been investigated systematically via first-principles based on density functional theory (DFT). The results show that the structural stability of the B₁₂N₁₂ cluster is significantly enhanced after embedding lanthanide atoms, and the molar volume decreases regularly with the increase of the atomic number of M, which is consistent with the lanthanide contraction effect. The spin multiplicity shows element dependence, Sm/Er/Yb@ B₁₂N₁₂ is a singlet, Pr/Pm/Ho/Tm/Lu@ B₁₂N₁₂ is a doublet, Ce/Gd/Dy@ B₁₂N₁₂ is a triplet, La/Eu/Tb@ B₁₂N₁₂ is a quartet, and Nd@ B₁₂N₁₂ is a quintet. The reduction of the HOMO-LUMO energy gap enhances the chemical activity, and the HOMO orbital is mostly distributed near the M and N atoms, while the LUMO orbital is mostly concentrated around the B atoms. The electric dipole moment shows a trend of first increasing and then decreasing after doping, and some structures are close to zero. The polarizability shows an oscillating feature, among which Tm@ B₁₂N₁₂ has the largest polarizability. With the increase of the atomic number of M, the number of infrared absorption peaks increases, and the absorption peaks of Nd/Sm/Er@ B₁₂N₁₂ show a blue shift, while the absorption peaks of the other doped structures show a red shift. The research results supplement and improve the theoretical data regarding the structure, electric dipole polarity, and infrared spectrum of lanthanide-embedded cage-like B₁₂N₁₂ clusters.