The shapes of hypoelectronic six-vertex anionic bare boron clusters: Effects of the countercations

RHF/6-31G(d) calculations have been carried out on the hypoelectronic six-vertex boron cluster anions B₆^z− (z = 6 and 4) as well as the corresponding alkali metal derivatives B₆M_z (z = 6 and 4; M = Na and Li) and the isoelectronic B₆H₆ and B₆H₆²⁺. Using such computational methods, the introduction of alkali metal counterions was found to have relatively little effect on the general structural patterns of the lowest lying structures for these clusters. However, introduction of external hydrogen atoms (i.e., protonation of B₆⁶⁻ to B₆H₆ and B₆⁴⁻ to B₆H₆²⁺) was found to lead to more open structures in the boron network relative to the corresponding alkali metal derivatives because of the need to divert boron valence orbitals from skeletal bonding to covalent bonds to the external hydrogens. The preferred structures of a bicapped tetrahedron for 12 skeletal electron systems derived from B₆⁶⁻ and a planar network of four fused triangles for 10 skeletal electron systems derived from B₆⁴⁻ can be rationalized both by localized and delocalized chemical bonding models.