Size- and charge-dependent geometric and electronic structures of Bi n (Bi(-)n) clusters (n=2-13) by first-principles simulations

Neutral and negatively charged bismuth clusters, Bi n and Bi(-)n (n=2-13), are investigated by first-principles simulations with the scalar-relativistic projector-augmented wave potential and the spin-polarized generalized gradient approximation. Both types of clusters show size-dependent odd-even oscillations in stability, density of states, and vertical and adiabatic electron affinities, in close agreement with experiment. The negative charge thoroughly reverses the oscillations and considerably influences the geometric structures, particularly of the odd-sized clusters. We note that most atoms in the ground states and the low-lying isomers are three coordinated with a quasilayerlike growth mode based on pentagon units, due to a weak s-p hybridization. The Bi12 cluster is found to prefer a small elongated tubelike structure with the surface consists of six curved-pentagon rings and two triangular facets, which may be the basis for the formation of bismuth nanotubes experimentally reported.