Metal-metal bonding in d1d1 and d2d2 bioctahedral dimer systems:: A density functional study of face-shared M2X93- (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 M2X93- 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 Ti2Cl93-, the [a(1) x a(1)] broken-symmetry optimized structure, corresponding to significant delocalization of the metal-based a electrons, nicely rationalizes the strong antiferromagnetic coupling reported for Cs3Ti2Cl9. The ground-state geometries for Zr2Cl93- and Hf2Cl93- correspond to complete delocalization of the metal-based electrons in a metal-metal sigma bond. For V2Cl93-, 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 Cs3V2Cl9. For Nb2X93- (X = Cl, Br, I) and Ta2Cl93-, 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 (Delta E-ov1p) and spin polarization (Delta E-spe), the difference Delta E-spe - Delta E-ov1p determining the tendency of the metal-based electrons to delocalize in the dimer. For d(1)d(1) systems, Delta E-ov1p is always greater than Delta E-spe and therefore delocalized ground states result for all complexes of the titanium triad. Across the first transition series, the dramatic increase in Delta E-spe dominates Delta E-ov1p and therefore V2Cl93- and Cr2Cl93- have localized ground states. For the second and third transition series, the much larger Delta E-ov1p term ensures that all these complexes remain delocalized.