Probing the multiple (δ- and π-) aromaticity of [Hf3F3]− anion, [Hf3F3X2]+ (X = Li, Na, and K), and [Hf3F3Y]+ (Y = Be and Mg) clusters

Investigation of equilibrium geometries, total energies, harmonic vibrational frequencies, natural population analysis, and nucleus-independent chemical shifts (NICS) of the low-lying states for the multinuclear low-fluorination-state transition-metal [Hf3F3]− cluster and its pyramidal [Hf3F3Y]+ (Y = Be and Mg) and bipyramidal [Hf3f3X2]+ (X = Li, Na, and K) complexes were done with two density functional theory (DFT) methods. The calculations reveal three types of d-bonding interaction existing in the planar regular hexagonal [Hf3F3]− (D3h, 1 A 1 ′ ) cluster, [Hf3F3X2]+ (D3h, 1 A 1 ′ ) (X = Li, Na, and K) and [Hf3F3Y]+ (C3v, 1A1)(Y = Be and Mg) complexes. They separately possess two delocalized π-electrons and two delocalized δ-electrons, exhibiting characteristics of multiple (δ- and π-) aromaticity (satisfying the (4n + 2) Hückel electron counting rule).