Ethane point groups

Show that [CoCl2(en)2] (en = ethane-1,2-diamine) can be racemic. Determine the symmetry point groups of each isomer and assign suitable stereodescriptors. 

Fig. 2.10. Isometric structures of the ethane molecule, obtained by symmetry operations of the point group Dj and by rotation of one methyl group with respect to the other...

The PE spectra of methane and ethane are rather special cases, because of their high symmetry. The point groups of methane and of ethane, the latter in its staggered conformation, are and D d respectively, with the consequence that some of their valence shell orbitals are degenerate. They are indicated in bold type in the following list ... 

The symmetry elements of the point groups (a) >3, (b) D2d and (c) Dgh- (a) A twisted form of ethane, neither perfectly staggered nor eclipsed, viewed along the C3 axis, (b) Allene, where the planes xz and yz are planes and the C 2 axes lie at 45° to the x and y axes in the xy plane, (c) Benzene. Note that the Cg axis includes C3, C2, Sg and S3 axes. Also shown are the three axes (one of which lies along x) and the three C axes (one of which lies along y). The xy plane is CTh and there are vertical mirror planes including each C 2 and C axis the center of the molecule is an inversion center, i. 

Next, consider staggered ethane, which we have earlier assigned to the Dm point group. Orbital energy levels and sketches of the MOs appear in Fig. 13-14. The character table for the Dm group is given in Table 13-24. 

The missing symmetry operations for ethane in the staggered conformation are improper rotations. Ethane has an order 6 improper rotation axis, S, which is illustrated along with the operation, in Figure 2.7. After describing the operations that the Se axis leads to, we will use them to close the symmetry point group of ethane. 

If a molecule has only an inversion centre present it has Q symmetry. Examples of this point group are less common, but substituted ethanes such as (15,2/ )-l,2-dichloro-1,2-difluoroethane (Figure 3.5a) can take on conformations with C, symmetry, and some bimetallic complexes, such as the general structure shown in Figure 3.5b, also fall into this classification. 

Symmetry operations for ethane in the staggered conformation were covered in Section 2.3.3, including the illustration of example operations in Figure 2.5. It should now be clear that these are just the operations required to classify ethane as belonging to the Dm point group. 

Figure 3.33 S axes present In the point groups for (a) methane, CH4, (b) B(OH)i and (c) the staggered conformation of ethane.

Property 3 ean be confirmed by inspecting any of the character tables in Appendix 12. For example, the Ad point group for molecules such as ethane in the staggered conformation has the headings... 

Center of Symmetry (C,). A center of symmetry exists in a molecule if one half of the molecule is obtained from the other by inversion through the center of symmetry there may or may not be an atom at the center of symmetry. There are a few molecules with a center of symmetry as the sole symmetry element. One such molecule would be a substituted ethane HXYC-CYXH, where each pair of similar atoms is in the trans position. If a line is drawn from one atom to the center of symmetry and continued on, it would intercept a similar atom at the same distance from the center of symmetry as the original atom. The molecule HXYC-CYXH would be described as belonging to the point group C -, since it has only the symmetry element C -. 

By utilizing three models of ethane (C2H6) it is possible to illustrate the three point groups Z>3, 2)3, and Figures 4-22 to 4-24 illustrate these three groups, but the reader may wish to use space models to help him understand the following discussion. 

The types of vibrations (species) of molecules with related symmetry can be correlated and these correlations used to assign vibrations. For example, ethane and its various derivatives have somewhat similar symmetry elements. Ethane belongs to point group while CH3CCI3 has symmetry. The D d groups have... 

---