Metal-metal Bonding in M₂Cl₆(H₂PCH₂PH₂) ₂ M₂Cl₆(PH₃)₄, and M₂Cl₁₀^4- (M = Cr, Mo, W) edge-shared dimer systems

Density functional theory is used to determine the electronic structures, geometries, and periodic trends in metal-metal bonding in the homo- and heterobimetallic d³d³ edge-shared systems M₂Cl₁₀^4-, M₂Cl₆(PH₃)₄, and M₂-Cl₆(H₂PCH₂PH₂) ₂ (M = Cr, Mo, W). The much shorter metal-metal distances in these complexes relative to M₂Cl₁₀^4- (M = Mo, W) are shown to arise solely from electronic differences between chlorine and phosphine donors. Due to inversion of the δand δ*orbitals, the complexes M₂Cl₆(PH₃)₄ and M₂Cl₆(H₂PCH₂PH₂) ₂ (M = Mo, W) are found to possess formal metal-metal double bonds. The periodic trends in metal-metal bonding in these systems are rationalized in terms of the energetic contributions of orbital overlap (ΔE_ovlp) and spin polarization (ΔE_spe). The reduction in ΔE_spe and increase in ΔE_ovlp on replacement of axial chlorides with phosphine both favor stronger metal-metal bonding in the phosphine-based complexes. The strong linear dependence observed between ΔE_spe and ΔE_ovlp enables the metal-metal bonding in these systems to be predicted simply from singleion spin-polarization energies. The antiferromagnetic coupling in M₂Cl₆(H₂PCH₂PH₂) ₂ (M = Mo, W) and MoWCl₆(H₂PCH₂PH₂)₂ is shown to be mostly due to coupling of the metal δ electrons, with a smaller contribution from the π electrons, particularly for the dimolybdenum complex.