Geometries, stabilities and electronic properties of small Nb-doped gallium clusters: A density functional theory study

The host Ga n+1 and doped Ga n Nb ( n=1–9) clusters with several spin configurations have been systematically investigated by a relativistic density functional theory (DFT) with the generalized gradient approximation. The optimized equilibrium geometries tend to prefer the close-packed configurations for small Nb-doped gallium clusters up to n=9. The average binding energies per atom ( E b /atom), second-order differences of total energies ( Δ 2 E), fragmentation energies ( E f ) and HOMO–LUMO gaps of Ga n+1 and Ga n Nb ( n=1–9) clusters are studied. The results indicate the doping of Nb atom in gallium clusters improves the chemical activities. In particular, the clusters with sizes of Ga 4Nb and Ga 7Nb are found to be more stable with respect to their respective neighbors. Our calculated vertical ionization potentials (VIPs) exhibit an obvious oscillating behavior with the cluster size increasing, except for Ga 3 and Ga 4Nb, suggesting the Ga 3, Ga 5, Ga 7, GaNb, Ga 3Nb, Ga 6Nb and Ga 8Nb clusters corresponding to the high VIPs. In the case of vertical electron affinities (VEAs) and chemical hardness η, VEAs are slightly increasing whereas chemical hardness η decreasing as Ga n Nb cluster size increases. Besides, the doping of Nb atom also brings the decrease as the cluster sizes increases for atomic spin magnetic moments ( μ b ).