The large range of chromium-chromium quadruple bond distances: structural and theoretical analysis

Pyramidality effect on metal–metal single bonds

“…It will be shown that, for some families, the torsion angle τ is correlated with the metal-metal distance. For this group of cobalt() complexes, however, inclusion of the torsion angle in the least-squares fitting does not improve the correlation [equation (3), r = 0.989] and the resulting coefficients are quite d(Co᎐Co) = 2.254 ϩ 4.849 cos α Ϫ 0.147 cos 2τ (3) similar to those in equation (2). Therefore, for the cobalt() compounds it suffices to consider the effect of the pyramidality to account for the variations in the metal-metal bond distances.…”

“…Let us now examine the corresponding family of tetrakis-(bridge) complexes of Co II , in which carboxylato or analogous bidentate ligands act as bridges between two metal atoms, with possibly one or two extra ligands co-ordinated to Co in axial positions (2). In Table 1 we show the Co᎐Co distance and the pyramidality (α, defined in 1) for these species.…”

“…However, other factors can affect the metal-metal bond length, such as the pyramidality α (the average of all M᎐M᎐X angles) and the internal rotation τ (average of the X᎐M᎐M᎐X torsion angles). [2][3][4][5] For instance, the wide range of values of α found for the quadruple-bonded Cr᎐Cr compounds accounts for the large dispersion of Cr᎐Cr distances, which span the range between 1.8 and 2.6 Å. 6 In these compounds the relationship between the M᎐M bond strength and the extent of pyramidalization of the metal atoms can be associated with changes in the hybridization of the σ and π orbitals, whereas the δ component is insensitive to pyramidalization.…”

“…Hence, we will use in this paper α for graphical display, but cos α for the least-squares fitting of the experimental data. The square planar Rh II X 4 fragment has an unpaired electron in its d z 2 orbital, and one can simply describe the Rh᎐Rh bonding in Rh 2 X 8 molecules as resulting from the interaction between the d z 2 orbitals of the two RhX 4 fragments. However, the rhodium p z orbital has the right symmetry to mix with the d z 2 orbitals, and an appropriate orbital diagram to describe such interactions is that presented in Fig.…”

Band Structures of Quasi-One-Dimensional Incommensurate Helical Systems: A Case Study of Infinite Chromium Extended Metal Atom Chain

“…Second, the knowledge of conduction band, valence band and Fermi level helps to predict and design suitable conductive properties of EAMCs . Third, it is known that finite EMACs are subject to chain end effects such as axial ligand properties − and pyramidality angles. − Considering the infinite EMACs not only avoids the above complications but also helps us to focus on the essence of metal–ligand interactions.…”