Quiz on Point Group Symmetry
(This quiz will test your understanding of point group symmetry; it will not be collected for credit)

In the following it may help to make a model. Break out the models that you were coerced to buy in Sophomore Organic.

1a) Identify all symmetry elements in the eclipsed ethane conformer. List them.


1b) To what point group does this eclipsed conformer belong?


1c)  Now stagger the molecule and identify the symmetry operations.


1d) To what point group does this staggered conformer belong?


2a)  Take a look at the chair form of cyclohexane. Does it have an S symmetry operation? **Did you look for these in the conformers that you considered above?**


2b)  To what point group does the chair of cyclohexane belong?


2c)  Now let's unsaturate cyclohexane to make cyclohexene. This molecule rests in the half chair. If this terminology is unknown to you, look it up. To what point group does cyclohexene belong?

 
2d) Do the same for 1,3-cyclohexadiene, basically flat.


2e) Do the same for 1,4-cyclohexadiene, basically flat.


2f) Do the same for benzene, definitely flat.


3)  Fire a hard, round, fast bullet at a perfect hard wall. It bounces back along the exact same trajectory as it was fired. How are the forward and reverse trajectories of the bullet related symmetrically? What symmetry operation converts one trajectory into the other? Can you understand this statement applied to this example?, This is a proper use of an improper operation.

4) Movement also can have symmetry. In general an object can not increase its symmetry by performing repetitive movements. Oscillations are important in IR spectroscopy.

4a)  For example the carbonyl groups in 2,2-dimethylcyclohexan-1,3-dione should have carbonyl stretches in the IR spectrum. How many do you expect to see? These stretching motions occur in the chair conformation. What is the point group of this molecule in this conformation? Only stretching motions that change the overall dipole moment of the molecule will appear in the IR spectrum.

4b) You may have answered 1 to question 5a because there is a symmetry operation that interconverts the two carbonyl functionalities in the chair conformation. What is that symmetry operation? We say that these two groups in the molecule are symmetry-related. We would expect to see only one ¹³C NMR signal for these two carbonylcarbon atoms because they are symmetry-related.

4c) How many ¹³C NMR signals are there in this molecule?

4d)  I don't expect you to get this. In the case of the IR, the two oscillators will couple. There will be a stretching motion that is symmetric with respect to the molecule and one that is asymmetric. Can you see these in your mind? Can you draw how the molecular dipole moment will change with the symmetric and the asymmetric stretch? Remember that the dipole moment is a vector quantity having direction and magnitude.