Probing the balance between localization and delocalization of the metal-based electrons in face-shared bioctahedral complexes

The electronic structures of a variety of metal nonahalides, MM'X-9, with the {d(3)d(3)} configuration are examined using broken-symmetry density functional theory. Complexes containing trivalent ions of the chromium triad and tetravalent ions of the manganese triad are considered, where metal-metal interactions range from strong multiple bonding to weak antiferromagnetic coupling. The division of the metal-based electrons into symmetry-distinct sigma and delta(pi) subsets also gives rise to an intermediate group of complexes, where the a electrons are involved in a strong bond, but the delta(pi) subset remain weakly coupled. The balance between localization and delocalization of the metal-based electrons is determined by two distinct factors. The overlap of metal-based orbitals favors delocalization, whereas the high single-ion spin polarization energy associated with an isolated d(3) ion favors localization. Independent estimates of these two factors are made, and their contribution to the observed periodic trends is assessed. On descending a triad, the radial expansion of the d orbitals reduces the single-ion spin polarization energy and also increases overlap between orbitals on adjacent centers. Both factors contribute approximately equally to the increased tendency of the metal-based electrons to delocalize in the heavier congeners. Moving across a period, the greater covalence of the M-IV-Cl bond in complexes of the manganese triad reduces the spin polarization energy, favoring delocalization. The contracted orbitals of the M-IV ion, however, reduce the orbital overlap term, favoring localization. Changes in the overlap term dominate, and hence the overall trend is toward greater localization of the metal-based electrons in complexes of the manganese triad.