Unraveling the Origin of the Relative Stabilities of Group 14 M₂N₂²⁺ (M, N = C, Si, Ge, Sn, and Pb) Isomer Clusters

Abstract

We analyze the molecular structure, relative stability, and aromaticity of the lowest-lying isomers of group 14 M₂N₂²⁺ (M and N = C, Si, and Ge) clusters. We use the gradient embedded genetic algorithm to make an exhaustive search for all possible isomers. Group 14 M₂N₂²⁺ clusters are isoelectronic with the previously studied group 13 M₂N₂^2– (M and N = B, Al, and Ga) clusters that includes Al₄^2–, the archetypal all-metal aromatic molecule. In the two groups of clusters, the cyclic isomers present both σ- and π-aromaticity. However, at variance with group 13 M₂N₂^2– clusters, the linear isomer of group 14 M₂N₂²⁺ is the most stable for two of the clusters (C₂Si₂²⁺ and C₂Ge₂²⁺) , and it is isoenergetic with the cyclic <i>D</i>_4<i>h</i> isomer in the case of C₄²⁺. Energy decomposition analyses of the lowest-lying isomers and the calculated magnetic- and electronic-based aromaticity criteria of the cyclic isomers help to understand the nature of the bonding and the origin of the stability of the global minima. Finally, for completeness, we have also analyzed the structure and stability of the heavier Sn and Pb group 14 M₂N₂²⁺ analogues