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 O2- in 147 configurations, for 7522 coordination polyhedra and 41,488 bond distances, providing baseline statistical knowledge of bond lengths for transi-tion metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination poly-hedra for 85 transition-metal ion configurations with anomalous bond-length distributions. Two new indices, Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡, 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] multi-ple-bond formation; crystallographic mechanisms are [3] electronic effects (with inherent focus on coupled electronic-vibra-tional degeneracy in this work), and [4] crystal-structure effects. The Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the dis-torting 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 variations may be optimized in a given crystal structure (and inform how optimization may be achieved), and more. We find the observation of multiple bonds to be primarily driven by the bond-topological requirements of crystal structures in solids. However, we sometimes observe multiple bonds to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect); resolution of the origins of multiple-bond formation follows calculation of the Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 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 pseudo Jahn-Teller effect (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 a priori 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 asym-metry, comparable to those resulting from the strong JTE, and less than those induced by π-bond formation. From a compar-ison of a priori 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 Jahn-Teller effect is found not to have a symbiotic relation with the bond-topo-logical requirements of crystal structures. The magnitude of bond-length variations caused by the PJTE decreases in the fol-lowing order for octahedrally coordinated d0 transition metals oxyanions: Os8+ &gt; Mo6+ &gt; W6+ &gt;&gt; V5+ &gt; Nb5+ &gt; Ti4+ &gt; Ta5+ &gt; Hf4+ &gt; Zr4+ &gt; Re7+ &gt;&gt; Y3+ &gt; Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ &gt; Ti4+ &gt; V5+ &gt; W6+ &gt; Mo6+ &gt; Cr6+ &gt; Os8+ &gt;&gt; Mn7+; for [5], it is Os8+ &gt; Re7+ &gt; Mo6+ &gt; Ti4+ &gt; W6+ &gt; V5+ &gt; Nb5+. We conclude that non-octahedral coordinations of d0 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-d0 transition-metal oxyanions.&lt;br&gt;</jats:p>

On the Crystal Chemistry of Inorganic Nitrides: Crystal-Chemical Parameters and Opportunities in the Exploration of Their Compositional Space

“…For the three Cu 2+ N6 octahedra, the observed bond lengths are 4 × 2.061 and 2 × 2.612 Å for Cu(NH3)4)(Ag(SCN)3 (10065), 134 135 and 2 × 1.879, 2 × 1.965 and 2 × 2.722 Å for K2CuFe(CN)6 (99499). 136 The surprisingly large range of bond-length observed for the latter structure, 0.843 Å, appears to support the case for higher distortion magnitude in inorganic nitrides; of 365 polyhedra observed bonding to O 2-by Gagné & Hawthorne, 50 only one is observed with a larger range of bond lengths, 0.870 Å, for mrázekite Bi 3+ 2Cu 2+ 3(OH)2O2(PO4)2(H2O)2 (71934). 137 To verify that the large variation of bond lengths is not due (or partly due) to non-local bond-topological asymmetry in K2CuFe(CN)6, we calculate values of ∆ and ∆ for the Cu 2+ N6 octahedron using the method of Gagné & Hawthorne; 50 ∆ is calculated as the mean (absolute) weighted deviation between the bond valences of a given polyhedron and that of its regular variety with equidistant bond lengths, i.e.…”

“…In this work, we use the method of Gagné & Hawthorne 59 to derive new bondvalence 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-as a contribution to our gradual effort toward modernizing Shannon's set of ionic radii 60 (see refs. 50,[61][62][63][64] for bondlength statistics of cations bonded to O 2-; in prep for cations bonded to S 2-, Se 2-and/or Te 2-). Later in this work, we explore new and interesting venues for the exploratory synthesis of functional inorganic nitrides from a crystal-chemical perspective.…”

“…3c gives such an example for [3] C 4+ bonded to N 3-). Gagné & Hawthorne state that deviations from such shape are the result of bond-topological, electronic and/or crystal-structure effects, 50 which they go on to describe for all cations of the periodic table observed bonding to O 2-in inorganic structures. 50,[61][62][63][64] Notable examples of anomalous bond-length distributions include a tri-modal distribution for [4] P 5+ -O 2bonds, 62 caused by varying bond-valence requirements as a function of the degree of polymerization of the [PO4] 3-oxyanion (i.e.…”

“…Gagné & Hawthorne state that deviations from such shape are the result of bond-topological, electronic and/or crystal-structure effects, 50 which they go on to describe for all cations of the periodic table observed bonding to O 2-in inorganic structures. 50,[61][62][63][64] Notable examples of anomalous bond-length distributions include a tri-modal distribution for [4] P 5+ -O 2bonds, 62 caused by varying bond-valence requirements as a function of the degree of polymerization of the [PO4] 3-oxyanion (i.e. bond-topological effects), a tri-modal distribution for [6] Mo 6+ -O 2-bonds, 50 arising from a combination of pseudo Jahn-Teller and bond-topological effects, and anomalously long tails at longer bond lengths for penta-coordinated ion configurations of Cr 2+ , Co 2+ and Cu 2+ , also caused by pseudo Jahn-Teller and bond-topological effects.…”

“…In light of the recent extensive review of the crystal chemistry of oxides and oxysalts by Gagné & Hawthorne,50,[61][62][63][64] we investigate our dataset of inorganic nitride structures for the occurrence of bond topological, electronic and/or crystal-structure effects, placing emphasis on the functional properties resulting from these effects. Compositional and structural divergences are expected between the compounds making up these two datasets.…”