In Molecular Motions I we saw that free rotation was a property of sigma bonds. We also learned that the adjective "free" has a qualified meaning, implying a potential energy barrier that is small compared to the amount of energy available at room temperature. We're now going to look at situations where structural features raise that barrier, thereby restricting free rotation.
Consider the color-coded structure and 1H-NMR spectrum of N,N-dimethylacetamide shown in Figure 1.
You don't have to know much about NMR to realize that the presence of three signals of equal intensity suggests that the three methyl groups in N,N-dimethylacetamide are different. If the formula in the inset represented the true structure of N,N-dimethylacetamide, you should expect free rotation around the sigma bond between the nitrogen atom and the carbonyl carbon. This rotation would make the two methyl groups attached to the nitrogen atom identical. In that case, the 1H-NMR spectrum of N,N-dimethylacetamide should contain two signals, one for the methyl group attached to the carbonyl carbon, and a second for the two methyl groups attached to the nitrogen. The intensity of the second signal should be twice that of the first. Clearly that is not the case. Something must be restricting the rotation around the C-N bond.
In our discussion of resonance theory, we learned that one of the structural features required for resonance involved a non-bonded pair of electrons adjacent to a pi bond. This situation occurs in amides, where the lone pair of electrons on the nitrogen atom interacts with the pi bond of the carbonyl group. This interaction is shown in Figure 2 for N,N-dimethylacetamide.
Structure C in Figure 2 represents the resonance hybrid that is formed by mixing structures A and B. The partial double bond in the hybrid structure C implies a barrier to rotation around the bond between the nitrogen atom and the carbonyl carbon atom. If that barrier is great enough, the two methyl groups attached to the nitrogen atom would be non-identical; one of them would always be adjacent to the methyl group attached to the carbonyl carbon, while the other would be next to the carbonyl oxygen atom. Then the 1H-NMR spectrum of N,N-dimethylacetamide should contain three signals, one for the methyl group attached to the carbonyl carbon, and one for each methyl group attached to the nitrogen. The intensities of the three signals should be the same. Clearly that's the case.
The restricted rotation observed in N,N-dimethylacetamide is characteristic of amides found proteins, i.e. polypeptides. Figure 3 presents a common representation of the "backbone" of a protein chain with the peptide bond shown in red. Notice how the N-H bond is always pointing in the opposite direction from the C-O double bond. This structural regularity is a direct result of restricted rotation about the peptide bond.
Now let's turn our attention to a situation that does not involve resonance, but where rotation is nonetheless restricted.
Figure 4 presents an interactive model of cyclohexane. Take a look along each of the C-C bonds. Notice that the three substituents attached to each carbon are in a staggered conformation with respect to the substituents on the adjacent carbons. This is the most stable overall confomation of the molecule. It is called the chair conformation.
Since each carbon is connected, either directly or indirectly, to every other carbon in the ring, the effect of the movement of one carbon atom will be transmitted to all the other carbon atoms in the ring. You can see this by shift-clicking two adjacent carbon atoms, holding down the control key, and selecting the Spin Torsional Angles from the sub-menu of the Movies menu. Clearly this rotation distorts the ring, raising its potential energy. This restricts rotation.
An interesting situation arises when the cyclohexane ring bears a substituent such as a methyl group or a chlorine atom, i.e. a group that is larger than a hydrogen atom. In these cases, there are two chair conformations possible. One can be converted into the other by rotation around the C-C bonds in the ring, but the two conformations do not have the same energy. Figure 5 shows the two chair conformations of methylcyclohexane.
The study of substituted cyclohexanes has provided tremendous insight into the nature of conformational changes in simple molecules. The value of that insight lies in its application to more complex systems. For example, our understanding of a lot of the chemistry of D-glucose is derived from conformational analysis of substituted cyclohexanes. A model of one conformation of D-glucose is shown in Figure 6.