Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section E / 45 / e / Solution

The idealized cage is chiral, with point group $O$, rather than $O_h$. The eight iron tris-chelate units have the same helicity within one cage; the two enantiomers are all-$\Delta$ and all-$\Lambda$. The fourfold axes pass through opposite Pd face centres, and the threefold axes pass through opposite Fe corners. There are also proper twofold rotations through opposite cube-edge midpoints. These proper rotations preserve the local handedness. Mirror planes, inversion and improper rotations would reverse each Fe propeller and are absent from an individual homochiral cage. The proper cubic group has 24 operations: $E$, $8C_3$, $6C_4$, $3C_2$ along the face axes and $6C_2$ along edge axes. Real conformations and crystal packing can lower this idealized molecular symmetry.