The electronic structures of the compounds [(HCO₂)₃M₂]₂(bridge), where M = Mo and bridge is C₂O₄²⁻, C₂S₄²⁻ or B₂O₄H₂²⁻ are compared based on calculations employing density functional theory. The planar structure, D_2h, for the oxalate and tetrathiooxalate is the ground state and the splitting of the two M₂δ orbitals is found to be significantly larger for the tetrathiooxalate due primarily to the lower energy of the C₂S₄²⁻ LUMO, which interacts with the in-phase combination of the M₂δ orbitals. An attempt to prepare the compound [(^tBuCO₂)₃Mo₂]₂(μ-S₂CCS₂) is reported, which yielded a material that was not soluble in organic solvents and has not been fully characterized. Calculations on the borinate bridged compound with μ-B₂O₄H₂²⁻ revealed the surprising prediction that the B–B bond is reductively cleaved and the [Mo₂⁴⁺] centers oxidized: the bridge is [O₂B(μ-H)]₂⁴⁻.