Metal-metal interactions in mixed-valence [M₂Cl ₉]^2- species: Electronic structure of d¹d ² (V, Nb, Ta) and d⁴d⁵ (Fe, Ru, Os) face-shared systems

The molecular and electronic structures of mixed-valence d ¹d² (V, Nb, Ta) and d⁴d⁵ (Fe, Ru, Os) face-shared [M₂Cl₉]^2- dimers have been calculated by density functional methods in order to investigate metal-metal bonding in this series. General similarities are observed between d ¹d² and d⁴d⁵ systems and can be considered to reflect the electron-hole equivalence of the individual d ¹-d⁵ and d²-d⁴ configurations. The electronic structures of the dimers have been analyzed using potential energy curves for the broken-symmetry and other spin states resulting from the d ¹d² and d⁴d⁵ coupling modes. In general, a spin-doublet (S = 1/2) state, characterized by delocalization of the metal-based electrons in a metal-metal bond with a formal order of 1.5, is favored in the systems containing 4d and 5d metals, namely, the Nb, Ta, Ru, and Os dimers. In contrast, the calculated ground structures for [V ₂Cl₉]^2- and [Fe₂Cl₉] ^2- correspond to a spin-quartet (S = 3/2) state involving weaker coupling between the metal centers and electron localization. In the case of [Ru₂Cl₉]^2-, both the spin-doublet and spin-quartet states are predicted to be energetically favored suggesting that this species may exhibit double-minima behavior. A comparison of computational results across the (d¹d¹, d¹d², d²d²) [Nb₂Cl₉]^z- and [Ta₂Cl₉]^z- and (d⁴d⁴, d⁴d⁵, d⁵d⁵) [Ru₂Cl ₉]^z- and [Os₂Cl₉]^z- series has revealed that, in all four cases, the shortening of the metal-metal distances correlates with an increase in formal metal-metal bond order.