Symmetry coordinates of a linear XYX molecule

As its suffix implies, (s leaves the symmetry of the molecule unchanged, but motion along any of the other three vibrational symmetry coordinates reduces the symmetry of the molecule to the subgroup that is the kernel of its representation. Thus  

The symmetry coordinates of the non-linear molecule, relabelled with the aid of Table 2.3, are shown in Fig. 4.3. It has been produced by bending the linear 

For the tetraatomic system HXXH, representing both the linear acetylene and the non-linear hydrogen peroxide, we expect to be able to construct twelve symmetry coordinates. Three of them are translational, whereas two of the remaining nine in the linear conformation and three in the non-linear one are reserved for rotations. Linear tetraatomics thus have seven vibrational coordinates, motion along which changes the potential energy, whereas their nonlinear counterparts have six. Those of the linear HXXH molecule are shown in Fig. 4.4 with the subgroup into which each is taken, if only momentarily, by the displacement. 

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Figure 4.2. Symmetry coordinates of a linear XYX molecule (D2/1). (Consult Table 3.1 to obtain the Doo/i labels)...

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