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Van Vleck analysis of angularly distorted octahedra using VanVleckCalculator.

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Van Vleck modes describe all possible displacements of octahedrally coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for first-order Jahn-Teller distortions, but determination of the Van Vleck modes of an octahedron is complicated by the presence of angular distortion of the octahedron. This problem is most commonly resolved by calculating the bond distortion modes (Q 2, Q 3) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes (Q 4, Q 5 and Q 6) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the Van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python package for doing this, VanVleckCalculator, is introduced and some examples of its use are given. Finally, it is shown that octahedral shear and angular distortion are often, but not always, correlated, and a parameter η is proposed as the shear fraction. It is demonstrated that η can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.



Jahn–Teller distortion, crystal structure, crystallographic software, octahedral distortion, octahedral tilting

Journal Title

J Appl Crystallogr

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Volume Title


International Union of Crystallography
Engineering and Physical Sciences Research Council (2275821)