Although similar large-scale studies were done for inorganic crystals in the 1970s and 1980s (Shannon, 1976; Brown Altermatt, 1985 ), publication of raw data and their statistics has been lacking.A priori 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, topol and cryst, 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 topol and cryst 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 ( e.g. JahnTeller effect, PJTE); resolution of the origins of multiple-bond formation follows calculation of the topol and cryst indices on a structure-by-structure basis. 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 asymmetry, comparable with those resulting from the strong JTE, and less than those induced by -bond formation. From a comparison 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 JTE is found not 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 d 0 transition metal oxyanions: Os 8 Mo 6 W 6 V 5 Nb 5 Ti 4 Ta 5 Hf 4 Zr 4 Re 7 Y 3 Sc 3. However, smaller bond-length variations are expected from the PJTE for non- d 0 transition metal oxyanions. Keywords: bond-length variation; bond-topological effects; vibronic mixing; pseudo JahnTeller effect; materials design. Similar articles 1. Introduction Transition metals are a unique set of elements whose compounds have an extraordinarily varied range of chemical and physical properties. The behaviour of transition metal compounds is characterized by the metastability of partially filled d orbitals, affording them distinctive electronic, magnetic, vibronic, optical and other properties of fundamental and technological interest. For instance, the wide array of metastable oxidation states characteristic of transition metals facilitates electron-transfer reactions central to catalysis (Fukuzumi, 2001 ), while metastable spin states associated with d -orbital occupancy are used as bistable atomic switches in spin-crossover compounds, controllable via external perturbations (Halcrow, 2013; Guionneau, 2014; Senthil Kumar Ruben, 2017 ), and whose lifetime may be increased by several orders of magnitude via coupled electronic vibrational degeneracy (Garcia-Fernandez Bersuker, 2011 ). As such, deciphering the causal mechanisms underlying bond-length variation, and the extent to which bond lengths vary in solids, has significant implications in the materials sciences. For one thing, systematization of chemical bonding behaviour via large-scale bond-length dispersion analysis facilitates tracing anomalous bonding behaviour to the causal mechanisms underlying material properties, and further facilitates recognition of anomalously bonded coordination units bearing functional properties for their transposition into new chemical spaces. Further resolving the extent to which these mechanisms affect bond-length variation is crucial in order to maximize the harnessing of these effects within the constraints of physically realistic crystal structures. In addition, knowledge derived from large-scale bond-length dispersion analysis facilitates ion identification in crystal-structure refinements (with additional help from the bond-valence model), as the metrics of bonding behaviour are often characteristic of an ion configuration, particularly for transition metals. This information facilitates quantitative resolution of disordered andor mixed-valent site occupancy in crystals, with particular relevance to understanding the mineralogical makeup of Earth and other planetary bodies, and the many geological processes we may infer from them.
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