Authors: Olivier Charles Gagné | F. C. Hawthorne
Source: IUCrJ (review, 2020-06-09)
Field: Materials Science — Materials Chemistry

Bond-length distributions for ions bonded to oxygen: results for the transition metals and quantification of the factors underlying bond-length variation in inorganic solids Bond-length distributions are examined for 63 transition metal ions bonded to O<sup>2-</sup> in 147 configurations, for 7522 coordination polyhedra and 41 488 bond distances, providing baseline statistical knowledge of bond lengths for transition metals bonded to O<sup>2-</sup>. <i>A priori</i> bond valences are calculated for 140 crystal structures containing 266 coordination polyhedra for 85 transition metal ion configurations with anomalous bond-length distributions. Two new indices, Δ<sub>topol</sub> and Δ<sub>cryst</sub>, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are (1) non-local bond-topological asymmetry and (2) multiple-bond formation; crystallographic mechanisms are (3) electronic effects (with an inherent focus on coupled electronic vibrational degeneracy in this work) and (4) crystal-structure effects. The indices Δ<sub>topol</sub> and Δ<sub>cryst</sub> allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the distorting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variation may be optimized in a given crystal structure (and inform how optimization may be achieved) and more. These indices further provide an equal footing for comparing bond-length variation and the distorting power of ions across ligand types, including resolution for heteroligand polyhedra. The observation of multiple bonds is found to be primarily driven by the bond-topological requirements of crystal structures in solids. However, sometimes multiple bonds are observed to form as a result of electronic effects (<i>e.g.</i> the pseudo Jahn-Teller effect, PJTE); resolution of the origins of multiple-bond formation follows calculation of the Δ<sub>topol</sub> and Δ<sub>cryst</sub> indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition metal oxides and oxysalts, followed closely by the PJTE. Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no <i>a priori</i> limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asymmetry, comparable with those resulting from the strong JTE, and less than those induced by π-bond formation. From a comparison of <i>a priori</i> and observed bond valences for ∼150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the JTE is found <i>not</i> to have a cooperative relation with the bond-topological requirements of crystal structures. The magnitude of bond-length variation caused by the PJTE decreases in the following order for octahedrally coordinated <i>d</i> <sup>0</sup> transition metal oxyanions: Os<sup>8+</sup> > Mo<sup>6+</sup> > W<sup>6+</sup> >> V<sup>5+</sup> > Nb<sup>5+</sup> > Ti<sup>4+</sup> > Ta<sup>5+</sup> > Hf<sup>4+</sup> > Zr<sup>4+</sup> > Re<sup>7+</sup> >> Y<sup>3+</sup> > Sc<sup>3+</sup>. Such ranking varies by coordination number; for [4] it is Re<sup>7+</sup> > Ti<sup>4+</sup> > V<sup>5+</sup> > W<sup>6+</sup> > Mo<sup>6+</sup> > Cr<sup>6+</sup> > Os<sup>8+</sup> >> Mn<sup>7+</sup>; for [5] it is Os<sup>8+</sup> > Re<sup>7+</sup> > Mo<sup>6+</sup> > Ti<sup>4+</sup> > W<sup>6+</sup> > V<sup>5+</sup> > Nb<sup>5+</sup>. It is concluded that non-octahedral coordinations of <i>d</i> <sup>0</sup> ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-<i>d</i> <sup>0</sup> transition metal oxyanions. Bond length ; Transition metal ; Ion ; Bond ; Chemistry ; Oxygen ; Variation (astronomy) ; Inorganic chemistry ; Materials science ; Chemical physics ; Crystallography ; Nanotechnology ; Organic chemistry ; Catalysis ; Crystal structure ; Physics ; Business Solid-state spectroscopy and crystallography ; Crystal Structures and Properties ; X-ray Diffraction in Crystallography