Sructures and stabilities B₉, B₉⁺ and B₉^- clusters

28 isomers of B₉ (1-10), B₉⁺ (1 ⁺-8⁺) and B₉^- (1^--10 ^-) clusters, including five isomers reported previously, have been optimized at the B3LYP/6-311+G* and MP2/6-311+G* levels of theory. To confirm the global minimum, some low-energy isomers were recalculated with CCSD(T)/AVDZ method. The CCSD(T)/AVDZ results suggest that B₉, B ₉⁺ and B₉^- clusters have their global minima to be the D^7h-symmetry heptagonal bipyramid structure 2, the C_s-symmetry wheel-shaped structure 1⁺ and the D_gh-symmetry planar wheel-shaped structure 1^-, respectively. Natural bond orbital analysis suggests that multi-centered σ bonds and delocalized π bonding play an important role in stabilizing the most stable isomers of all the B₉/B₉⁺/B ₉^- clusters. The bonding nature and aromaticity of all the clusters are discussed according to their nucleus-independent chemical shifts. Moreover, the adiabatic ionization potentials and electron affinities are also calculated for various B₉ isomers, which express a proof for the clusters' stability.