Inverse sandwich complexes of B₇M₂^-, B₈M₂, and B₉M₂⁺(M = Zr, Hf): The nonclassical M-M bonds embedded in monocyclic boron rings

A number of doped boron clusters with metals have been achieved with intriguing electronic and structural properties. In this work, we found the inverse sandwich complexes of B7M2-, B8M2, and B9M2+ (M = Zr, Hf) to be a global minimum, where the M2 motif perpendicularly embeds in the B7, B8, and twist B9 monocyclic boron rings. The interactions between M2 and boron rings, including the dp-π interactions and the electrostatic interactions originating from the charge transfer from the M to the boron rings, provide driving forces that stabilize such title complexes. The effective charge transfer gives rise to perfectly delocalized (3π + 3σ) orbitals, leading to double aromaticity of the whole species, especially when the three delocalized σ orbitals of the boron rings are perpendicularly mixed with one negligible σ and two π bonds of the M2 motifs, giving rise to less pronounced and nonclassical bonding interactions between two short-contact M atoms.