One distortion, resolved into the species of the group it left

One of the figures on representations: Character tables generated from a molecule's own operations, bases reduced in them, and what a descent in symmetry does to a level.

One essay draws this figure, each at the values its own argument needs rather than at the setting shown above. What each one uses it to show is below, in the words of its own caption.

How far, and along which coordinate

An arbitrary displacement of benzene resolved into the twelve species of D6h. The weights sum to 1.000000, which is the check that the projectors resolve the whole of it: the largest is E2g at 35.0 per cent and the totally symmetric part is 3.4. Two of the twelve species carry nothing, and that is a fact about the molecule rather than about this displacement.

The split: the part of a displacement that translates and rotates the molecule against the part that changes its shape. Six directions out of thirty-six, and a percentage that has nothing to do with the chemistry and everything to do with the frame the coordinates were written in.

Each of benzene’s twelve species applied on its own, with the group of the distorted structure found by the same coordinate search used for every other point group. The totally symmetric species leaves D6h intact; the others leave C6h, D3d, C2h, C6v, D3h, Cs and C2. Two species describe no displacement of twelve atoms at all.