  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 the
first-order Jahn-Teller distortion. Determination of Van Vleck modes of an
octahedron is complicated by the presence of angular distortion of octahedra
however. 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 code for
doing this, VanVleckCalculator, is introduced, and some examples of its use are
given. Finally, we show that octahedral shear and angular distortion are often,
but not always, correlated, and propose a parameter as the shear fraction,
$\eta$. We demonstrate that $\eta$ can be used to predict whether the values
will be correlated when varying a tuning parameter such as temperature or
pressure.
