Evolution of the structural and electronic properties, and dynamical fluxionality of B₂Ge_n^−/0 (n = 3–12) clusters: emergence of B₂ unit endohedral pentagonal structure and aromaticity at n = 10

ABSTRACT

The evolution of structural and electronic properties, and dynamical fluxionality of B₂Ge_n^−/0 (n = 3–12) clusters are investigated using DFT calculations combined with CALYPSO global searching algorithm. The B atoms in B₂Ge_n^−/0 incline to bond with each other and more Ge atoms. The theoretical calculations show that B₂Ge₃^−/0 have planar 2D structures, while the geometries of B₂Ge_4-7^−/0 are all exohedral 3D structures dominated by bipyramid-shaped or bowl-shaped based configurations and those of B₂Ge_8-12^−/0 majorly hold prism-shaped based geometries. B₂Ge₁₀⁻ and B₂Ge₁₀ are confirmed as the threshold sizes of transiting from B₂-exohedral to B₂-endohedral geometries for anions and neutrals, respectively. Natural population analysis indicates that the electron transfers from Ge_n skeletons to B atoms. Interestingly, the low-lying isomers of B₂Ge₄⁻, B₂Ge₆⁻, B₂Ge₇^−/0, B₂Ge₈^−/0, B₂Ge₉⁻, and B₂Ge₁₂⁻ clusters exhibit dynamical fluxionality. The ΔE^I, Δ₂E, and ΔE^I values versus number of Ge atoms suggest that B₂Ge_n⁻ anions are more stable than B₂Ge_n neutrals, except that B₂Ge₁₀ has higher stability than B₂Ge₁₀⁻. Molecular orbitals analysis of B₂Ge₁₀ indicates that it has σ + π double delocalised bonding patterns and electronic closed-shell configuration with a HOMO–LUMO gap of 2.17 eV. The nucleus-independent chemical shift (NICS) calculations indicate that B₂Ge₁₀^−/0 clusters have aromaticity.

GRAPHICAL ABSTRACT

Keywords:

• Structural evolution
• electronic properties
• dynamical fluxionality
• aromaticity
• germanium

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Natural Science Foundation of Shandong Province: [Grant Number ZR2018BB040]; Research Start-up Funds (Doctoral Science Foundation) of Heze University: [Grant Number XY18BS02]; Open Funds of Beijing National Laboratory for Molecular Sciences: [Grant Number Z191100007219009 and BNLMS201804].