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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

submitted on 14.01.2020 and posted on 17.01.2020 by Olivier Charles GagnΓ©, Frank Christopher Hawthorne
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, Ξ”π‘‘π‘œπ‘π‘œπ‘™ and Ξ”π‘π‘Ÿπ‘¦π‘ π‘‘, 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 Ξ”π‘‘π‘œπ‘π‘œπ‘™ and Ξ”π‘π‘Ÿπ‘¦π‘ π‘‘ 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 Ξ”π‘‘π‘œπ‘π‘œπ‘™ and Ξ”π‘π‘Ÿπ‘¦π‘ π‘‘ 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 Ο€-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+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5], it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > 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.


Banting post-doctoral fellowship, NSERC

PGS-D3 scholarship, NSERC

Carnegie post-doctoral fellowship, Carnegie Institution for Science

Discovery Grant, NSERC

a Canada Research Chair in Crystallography and Mineralogy, NSERC


Email Address of Submitting Author


Carnegie Institution for Science


United States

ORCID For Submitting Author


Declaration of Conflict of Interest

No conflict of interest