Ethane symmetry point group

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. 

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. 

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. 

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. 

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 -. 

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... 

If we plot some property of the ethane molecule, say, its potential energy, as a function of the torsion angle, we obtain a curve with threefold periodicity. In crystallographic parlance we have a repeating one-dimensional pattern with the line group pm and periodicity t = 120°. The special positions (fixed points) at a = 0° and 60° (modulo 120°) correspond to structures with special symmetry at 0° the eclipsed conformations with D31, symmetry, at 60° the staggered conformations with >3d symmetry. A general position corresponds to a chiral conformation with Z>3 symmetry only. Note that the order of D3 is half that of or 3d but the number of isometric Dj conformations is double the number of isometric 1)31, or conformations. 

---