Broken-symmetry density functional theory is used to examine the coupling between metal ions in the face-shared bioctahedral complexes M2Cl93-, M = Fe, Ru, Os. In the ruthenium and osmium systems, the metal ions have low-spin configurations, and strong coupling results in the formation of a metal-metal sigma bond. In contrast, the iron system contains two weakly coupled high-spin Fe-III centers, the different behavior being due to the high spin-polarization energy in the smaller Fe atom. At Fe-Fe separations shorter than 2.4 Angstrom, however, an abrupt transition occurs and the ground state becomes very similar to that for the heavier congeners (i.e., strongly coupled low-spin Fe-III). The intrinsic link between high-spin/low-spin transitions on the individual metal centers and the onset of metal-metal bond formation is traced to the spin-polarization energy, which plays a central role in both processes.