Metal-Metal Bonding in d(1)d(1) and d(2)d(2) Bioctahedral Dimer Systems: A Density Functional Study of Face-Shared M(2)X(9)(3)(-) (M = Ti, Zr, Hf, V, Nb, Ta) Complexes.

Density functional theory is used to investigate the electronic and geometric structures and periodic trends in metal-metal bonding of d(1)d(1) and d(2)d(2) face-shared M(2)X(9)(3)(-) dimers of Ti, Zr, Hf (d(1)d(1)) and V, Nb, Ta (d(2)d(2)). For these systems three distinct coupling modes can be recognized, depending on the occupation of the trigonal t(2g)(a(1) + e) single-ion orbitals, which determine the ground-state geometry and extent of metal-metal bonding. For Ti(2)Cl(9)(3)(-), the [a(1) x a(1)] broken-symmetry optimized structure, corresponding to significant delocalization of the metal-based sigma electrons, nicely rationalizes the strong antiferromagnetic coupling reported for Cs(3)Ti(2)Cl(9). The ground-state geometries for Zr(2)Cl(9)(3)(-) and Hf(2)Cl(9)(3)(-) correspond to complete delocalization of the metal-based electrons in a metal-metal sigma bond. For V(2)Cl(9)(3)(-), the global minimum is found to be the ferromagnetic [a(1)e x e(2)] spin-quintet state giving rise to a long V-V separation, consistent with the known structure and reported weak ferromagnetic behavior of Cs(3)V(2)Cl(9). For Nb(2)X(9)(3)(-) (X = Cl, Br, I) and Ta(2)Cl(9)(3)(-), the [a(1)e x a(1)e] spin-triplet state, where complete delocalization of the sigma and delta(pi) electrons occur in a metal-metal double bond, is found to be the global minimum and consequently relatively short internuclear distances result, again, in good agreement with experiment. The periodic trends in metal-metal bonding in these and the isovalent d(3)d(3) complexes can be rationalized in terms of the energetic contributions of orbital overlap (DeltaE(ovlp)) and spin polarization (DeltaE(spe)), the difference DeltaE(spe) - DeltaE(ovlp) determining the tendency of the metal-based electrons to delocalize in the dimer. For d(1)d(1) systems, DeltaE(ovlp) is always greater than DeltaE(spe) and therefore delocalized ground states result for all complexes of the titanium triad. Across the first transition series, the dramatic increase in DeltaE(spe) dominates DeltaE(ovlp) and therefore V(2)Cl(9)(3)(-) and Cr(2)Cl(9)(3)(-) have localized ground states. For the second and third transition series, the much larger DeltaE(ovlp) term ensures that all these complexes remain delocalized.