Periodic trends in metal–metal bonding in cubane clusters, (C5H5)4M4E4 [M = Cr, Mo, E = O, S]

Abstract

Trends in structure and bonding in a series of metal cubane clusters are examined using broken-symmetry density functional theory. For the metal–sulfur clusters, (C₅H₅)₄Mo₄S₄ and (C₅H₅)₄Cr₄S₄, the twelve cluster valence electrons are delocalised in six metal–metal single bonds, giving an approximately tetrahedral metal core. In (C₅H₅)₄Cr₄O₄, however, no strong Cr–Cr bonds are present, and three cluster valence electrons remain localised on each of the chromium centres. Antiferromagnetic coupling across four of the six edges of the tetrahedron, and ferromagnetic coupling across the remaining two give rise to a spin-singlet ground state and a distinct rhombic distortion. The driving force for the distortion is only 12 kJ mol^–1, and consequently inter- and intra-molecular steric effects may play a major role in determining the structure of the cluster in the solid state. Both chromium clusters have low-lying excited states in which the bonding pattern is completely reversed, with six Cr–Cr bonds present in (C₅H₅)₄Cr₄O₄ but none in (C₅H₅)₄Cr₄S₄. In each case the excited state lies less than 45 kJ mol^–1 above the ground state, despite the fact that a substantial structural rearrangement is involved. Changes in metal–metal bond strength and spin polarisation energy are found to contribute approximately equally to the periodic trend towards electron localisation in the chromium clusters.