A theoretical approach to the role of different types of electrons in planar elongated boron clusters

Abstract

We analyze the thermodynamic stability of some small elongated boron clusters and confirm the relationship between their planarity and their inherent electron configuration […σ²⁽ⁿ⁺¹⁾ π₁²⁽ⁿ⁺¹⁾ π₂²ⁿ]. Delocalized σ electrons in an elongated bare boron cluster and 2c-2e C–H bonds in a corresponding elongated hydrocarbon play a vital role in maintaining their planar structure. Through the eigenstates derived from a model of a particle moving in a rectangle, the rectangle model, our study suggests that the larger planar elongated boron clusters are not thermodynamically stable. A partition of the electron densities which is consistent with the electron count, points out that the dianionic, neutral and dicationic B₁₀^2−/0/2+ clusters are doubly σ and π aromatic, singly π aromatic, and doubly σ and π antiaromatic, respectively.