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

Abstract

<jats:p>Bond-length distributions are examined for 63 transition metal ions bonded to O<jats:sup>2−</jats: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<jats:sup>2−</jats:sup>. <jats:italic>A priori</jats:italic> 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<jats:sub>topol</jats:sub> and Δ<jats:sub>cryst</jats: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<jats:sub>topol</jats:sub> and Δ<jats:sub>cryst</jats: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 (<jats:italic>e.g.</jats:italic> the pseudo Jahn–Teller effect, PJTE); resolution of the origins of multiple-bond formation follows calculation of the Δ<jats:sub>topol</jats:sub> and Δ<jats:sub>cryst</jats: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 <jats:italic>a priori</jats:italic> 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 <jats:italic>a priori</jats:italic> 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 <jats:italic>not</jats:italic> 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 <jats:italic>d</jats:italic> <jats:sup>0</jats:sup> transition metal oxyanions: Os<jats:sup>8+</jats:sup> &gt; Mo<jats:sup>6+</jats:sup> &gt; W<jats:sup>6+</jats:sup> &gt;&gt; V<jats:sup>5+</jats:sup> &gt; Nb<jats:sup>5+</jats:sup> &gt; Ti<jats:sup>4+</jats:sup> &gt; Ta<jats:sup>5+</jats:sup> &gt; Hf<jats:sup>4+</jats:sup> &gt; Zr<jats:sup>4+</jats:sup> &gt; Re<jats:sup>7+</jats:sup> &gt;&gt; Y<jats:sup>3+</jats:sup> &gt; Sc<jats:sup>3+</jats:sup>. Such ranking varies by coordination number; for [4] it is Re<jats:sup>7+</jats:sup> &gt; Ti<jats:sup>4+</jats:sup> &gt; V<jats:sup>5+</jats:sup> &gt; W<jats:sup>6+</jats:sup> &gt; Mo<jats:sup>6+</jats:sup> &gt; Cr<jats:sup>6+</jats:sup> &gt; Os<jats:sup>8+</jats:sup> &gt;&gt; Mn<jats:sup>7+</jats:sup>; for [5] it is Os<jats:sup>8+</jats:sup> &gt; Re<jats:sup>7+</jats:sup> &gt; Mo<jats:sup>6+</jats:sup> &gt; Ti<jats:sup>4+</jats:sup> &gt; W<jats:sup>6+</jats:sup> &gt; V<jats:sup>5+</jats:sup> &gt; Nb<jats:sup>5+</jats:sup>. It is concluded that non-octahedral coordinations of <jats:italic>d</jats:italic> <jats:sup>0</jats: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-<jats:italic>d</jats:italic> <jats:sup>0</jats:sup> transition metal oxyanions.</jats:p>

(NH4)Mg(HSO4)(SO4)(H2O)2and NaSc(CrO4)2(H2O)2, two crystal structures comprising kröhnkite-type chains, and the temperature-induced phase transition (NH4)Mg(HSO4)(SO4)(H2O)2\rightleftharpoons (NH4)MgH(SO4)2(H2O)2

“…The other two O atoms (O3 and O4) have considerably shorter Cr-O bonds ('1.62 Å ) and are the acceptor atoms for two nearly linear hydrogen bonds of medium-strong nature involving both water H atoms (Table 8). Again, the mean Cr-O bond length of 1.651 Å is in very good agreement with the literature value of 1.65 (6) Å (Gagné & Hawthorne, 2020). The Na I cation shows a [6 + 2] coordination with the six closer O atoms defining a distorted octahedron (O1, O2 and their symmetry-related counterparts in equatorial sites, and O3 and its symmetry-related counterpart in axial sites), with the two remote O4 atoms capping two faces of the octahedron (Table 7).…”

“…In the [ScO 4 (OH 2 ) 2 ] octahedron, the longest bond [2.1222 (14) Å ] is that to the axially bound O5 atom of the water molecule, whereas the equatorial O atoms (O3 and O4), which are also part of a CrO 4 tetrahedron, have shorter Sc-O bonds, with a mean of 2.076 Å ( Table 7). The overall mean value for the Sc-O bond lengths is 2.091 Å , which matches very well the literature values of 2.10 (7) and 2.098 (41) Å given by Serezhkin et al (2003) and Gagné & Hawthorne (2020), respectively. In the CrO 4 tetrahedron, the longest Cr-O bonds ('1.69 Å ) are realized for O1 and O2, which are part of the krö hnkite chains.…”

On the crystal chemistry of inorganic nitrides: crystal-chemical parameters, bonding behavior, and opportunities in the exploration of their compositional space

“…This observation is likely due to a combination of the nascent sampling of the compositional space of inorganic nitrides and a focus by experimentalists on simple compositions and structures as a result of the significant challenges associated with synthesizing and growing these compounds. In fact, of the 18 transition metal configurations with bond-length range > 0.75 Å when bonded to O 2− , 58 only three configurations are observed in our dataset for nitrides: [6] Mn 2+ ( n = 6), with bond lengths 2.170–2.417 Å, [6] Cu 2+ ( n = 3), with bond lengths 1.879–2.722 Å, and [6] Nb 5+ ( n = 2), with bond lengths 2.123–2.129 Å; this compares to bond-length ranges of 0.837, 0.893 and 0.777 Å when bonded to O 2− , 58 respectively. Furthermore, the absence of any substantial bond-length variation in many ion configurations bonded to N 3− is a result of their observation in (relatively) highly symmetrical structures with inherently little to no variation in a priori bond lengths, which was recently demonstrated to be the most common cause of bond-length variation in inorganic solids by Gagné & Hawthorne.…”

“…Such pursuits have been eased by the bond-valence model for many classes of inorganic compounds, which is for example used to screen compounds in pymatgen 55 and to infer the oxidation state of redox-active ions 56 under the umbrella of the Materials Project. 57 Most recently, the bond-topological nature of the bond-valence model was featured in showing how bond-length variation (thus polyhedral distortion) is an inherent, predictable and quantifiable by-product of chemical bonding in inorganic solids 58 (polyhedral distortion having crucial implications with regard to the functional properties of various types of materials not limited to ferroelectricity, 59,60 piezoelectricity, 59,61 flexoelectricity, 62 second-order nonlinear optical behavior, 59,63 negative thermal expansion, 64 and photoluminescence 65,66 ). However, the parameterization of the bond-valence model is largely incomplete for cations bonded to N 3− , and the quality of published bond-valence parameters is not established.…”

“…In this work, we use the method of Gagné & Hawthorne 67 to derive new bond-valence parameters for nitrides, provide a scale of Lewis acidity for nitrides, and further outline a baseline statistical knowledge of bond lengths for cations bonded to N 3− ; these data serve as a contribution to our gradual efforts of systematizing chemical bonding behavior in solids, toward modernizing Shannon's set of ionic radii 68 (see ref. 58 and 69–72 for bond-length statistics of cations bonded to O 2− ; in prep for cations bonded to S 2− , Se 2− and/or Te 2− ), and are a useful aid to structure verification and the design of physically realistic crystal structures. In the second part of this work, we explore new venues for the exploratory synthesis of functional inorganic nitrides, using the systematic nature of this dataset to identify plausible ion configurations likely to lead to new and promising functional units to be transposed across various chemical spaces.…”