Several of the lowest energy structures of small and medium sized boron clusters are two-dimensional systems made up of a pair of concentric rings. In some cases, the barriers to the rotation of one of those rings relative to the other are remarkably low. We find that a combination of electronic and geometrical factors, including apparently the relative sizes and symmetries of the inner and outer rings, are decisive for the diminished barriers to in-plane rotation in these two dimensional clusters. A sufficiently large outer ring is important; for instance, expansion of the outer ring by a single atom may reduce the barrier significantly. A crucial factor for an apparent rotation is that the σ-skeleton of the individual rings remains essentially intact during the rotation. Finally, the transition state for the rotation of the inner ring comprises the transformation of a square into a diamond, which may be linked to a mechanism suggested decades ago for the isomerization of carboranes and boranes.

The potential energy surfaces of a series of clusters with the formula CAl ₃ E (E = P, As, Sb, Bi) are systematically explored using density functional theory and high level ab initio calculations.

B ₁₂ is a rigid cluster with a high inner ring rotational energy barrier. However, doping it with Ir lowers the barrier significantly, transforming the IrB ₁₂ ⁻ cluster in a Wankel motor.

Viable planar pentacoordinate carbon (ppC) systems with a ppC bonded to a transition metal and embedded in a metallocene framework are reported. Our detailed global minima search shows that CAl₄MX₂ (M = Zr and Hf; X = F–I and C₅H₅) clusters with ppCs are appropriate candidates for experimental realization in the gas phase. The fulfillment of the 18 electron rule and electron delocalization is found to be crucial for the stabilization of these ppC arrangements.