Insights of the role of shell closing model and NICS in the stability of NbGe_n (n = 7–18) clusters: a first-principles investigation

In the present report, the structures, energetics and electronic properties of neutral and cationic Nb-doped Ge_n (n = 7–18) clusters are systematically investigated under the first-principles density functional theory approach. The isomers in which the Nb atom is encapsulated inside a germanium cage are relatively stable compared to the exohedral surface doping. The thermodynamic stability and chemical activity of the ground-state isomers are analyzed through various energetic parameters. The results highlight the enhanced stability of the neutral NbGe₁₂ hexagonal prism-like structure with D_6h symmetry and cationic NbGe₁₆ fullerene isomers. The negative nucleus-independent chemical shift can explain the enhanced stability of neutral NbGe₁₂. However, the enhanced stability of cationic NbGe₁₆ is explained by shell closing model associated with the quasi-spherical geometry with a sequence 1S²1P⁶1D¹⁰1F⁶1G¹²2S²2P⁶IF⁸IG⁶2D¹⁰ following Hund's rule. To understand the effect of hybridization on stability, we have calculated density of states (DOS) and projected DOS (PDOS). From PDOS, it is clear that Nb-p and Ge-s and p orbitals are mainly take part in hybridization; however, near below Fermi level, the dominating contribution comes from Nb-d orbitals. In addition, IR and Raman spectra of clusters are also calculated to explain their vibrational properties of the isomers. Specifically, IR spectrum of the clusters in the range of 12–16 shows the possible application of these clusters in the IR sensing device.