Boron nitride clusters play an important role as precursors in the formation of ultra-hard thin solid boron nitride films, which have received considerable attention in material science. In this contribution, we investigated the ground and low-lying electronic states of B2N(∓,0) and N2B(∓,0). Triatomic NBN and BNB have been previously investigated using a variety of spectroscopic and calculational methods, and it is generally agreed that both of them are linear in their ground electronic states. The six ions including B2N (-), B2N (+), B2N (0) , BN2 (-), BN2 (+) and BN2 (0) have been studied and been also compared with one another in terms of various basis sets and predication of the symmetry breaking (SB) phenomenon. Artifactual symmetry breaking along the v3 coordinate is observed in the ab initio wave functions for the neutral ground state up to the coupled-cluster level of theory, even when Brueckner orbitals are used. In the D∞h point group of B2N(∓,0) and N2B(∓,0) variants, the unpaired electrons are delocalized, while in the asymmetric C∞v point group, they are localized on either one of the B atoms or N atoms of B2N(∓,0) and N2B(∓,0) , respectively. Structures with broken symmetry,C∞v, can be stable by interaction to the D∞h point group. In viewpoint of quantum chemistry, the second-order Jahn-Teller effect permits the unpaired electron to localize on boron atom, rather than being delocalized. Finally, from a statistical thermodynamical analysis, we calculated the thermochemical stabilities of those six ions.