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.
Notice that in both conformations all the bonds to the substituents on one carbon are staggered with respect to those on the adjacent carbons. Despite this, the structure on the right has higher potential energy than the one on the left. Before we look at why this is so, we need to expand our vocabulary: There are two types of hydrogens in cyclohexane, axial and equatorial. If you imagine the six carbon atoms of the ring to define the "equator" of the ring, those hydrogens that lie more or less along the "equator" are called equatorial, while those which are oriented vertically are called axial . Notice in Figure 4 that there are 6 axial hydrogens; 3 point up while the other 3 point down. Similarly, there are 6 equatorial hydrogens; 3 angle upwards, while the other 3 angle downwards. Click here for a demonstration on how to draw cyclohexane rings. Now back to methylcyclohexane.
The conformation of methylcyclohexane in which the methyl group is axial is less stable than its equatorial partner because of a phenomenon called 1,3-diaxial interactions. Basically, the axial methyl group is too close to the other two axial hydrogen atoms that are on the same side of the "equator". This causes increased electron-electron repulsions. To demonstrate this, diplay both models in the space filling format: select the Space Filling sub-menu from the Display Models menu. Notice the distance between the axial hydrogen atoms in the left-hand conformation. Compare that to the distance between one of the hydrogen atoms on the axial methyl group and one of the axial hydrogens on the ring of the right-hand model. The implication of "1,3" in the term 1,3-diaxial interactions is that the interactions occur between axial groups attached to every other atom, not between groups on adjacent atoms. In the right-hand model of methylcyclohexane there is a 1,3-diaxial interaction between the axial methyl group and both of the axial hydrogens.
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.
An organic chemist would view D-glucose as a molecule of cyclohexane in which one of the ring CH2 groups has been replaced by an oxygen atom. In addition, five of the equatorial hydrogens have been replaced by OH groups, while the sixth has been replaced by a CH2OH group. Note that all of the substituents on the ring which are larger than hydrogen occupy equatorial positions.
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