Hydrogen peroxide molecule, symmetry

We provide here a short analysis of the three different concepts for symmetry breaking, because often they are not carefully distinguished from each other, and we refer the reader to [5,15-23] for a more complete discussion. If we consider the example of the chiral hydrogen peroxide molecule H2O2 (Fig. 3.3), we can represent the stereomutation as a one-dimensional torsion about the angle r ( q below) and represent it with one potential function with two minima corresponding to the two enantiomers and a low potential barrier in the planar trans conformation [30]. 

In Section 4.2.1 it will be pointed out that hydrogen peroxide (Figure 4.1 la) has only one symmetry element, a C2 axis, and is therefore a chiral molecule although the enantiomers have never been separated. The complex ion [Co(ethylenediamine)3], discussed in Section 4.2.4 and shown in Figure 4.11(f), is also chiral, having only a C3 axis and three C2 axes. 

The structure of this molecule was initially determined assuming >3 symmetry. The calculated STO-3G 0—0 bond length (1.405 A) is similar to the corresponding value for hydrogen peroxide (1.396 A). However, it is likely that both these values underestimate the actual 0—0 bond lengths in these molecules (see Table 4). At the STO-3G level, distortions from this >3 structure obtained by lowering the symmetry to C2 lead to an increase in calculated energy. 

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. 

Determine the number of IR-active vibrations for the following molecules. You may have to determine their symmetry first, (a) Hydrogen peroxide, HjOj (b) Oxalic acid. 

Figure 3.8 Example molecules from the point group, (a) The O—H bonds of hydrogen peroxide are not coplanar the only symmetry operations for this molecule are E and Cj. (b) (IS,2S)-1,2-Dimethylcyclopropane. Three-dimensional models of each molecule are shown to the right of the chemical drawings.

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