Symmetry And Chirality In

Proton NMR spectra are considerably simplified by the equivalence of many protons: A group of protons may have exactly the same chemical shift ("chemical equivalence") and/or exactly the same J couplings ("magnetic equivalence"). This can happen in two ways: by molecular symmetry (mirror plane or rotation axis) or by rapid conformational change (bond rotation). The simplest example of bond rotation is a methyl (-CH3) group. If it were stationary, we might expect different chemical shifts for each of the three protons and different J couplings due to differences in dihedral angle. In fact, all methyl groups rotate very rapidly about the bond connecting to the rest of the molecule, making all three protons equivalent. The same can be said of a ierf-butyl group (-C(CH3 )3), which has nine equivalent protons and three equivalent 13C nuclei. Cyclohexane has only one proton chemical shift at room temperature because the chair conformation (with axial and equatorial protons) rapidly interchanges with the other chair conformation, exchanging the roles of axial and equatorial so rapidly that all protons experience a single, average chemical shift.

Another way to achieve equivalence is by symmetry. For flexible molecules, we always arrange the molecule in the most symmetric conformation to examine its symmetry properties. Diethyl ether (CH3-CH2-O-CH2-CH3) has only two proton chemical shifts (Fig. 2.12): The four CH2 protons are equivalent and the six CH3 protons are equivalent due to symmetry. Each of the methyl groups contains three equivalent protons due to rotation of the CH3-CH2 bond, and the mirror plane in the center (perpendicular to the plane of the paper) reflects the Hf methyl group into the He methyl group, making them equivalent. The mirror plane also converts Ha (coming out of the paper) into Hc (also coming out of the paper), making them equivalent, and Hb (going into the paper) into Hd. Finally, there is another mirror plane in the plane of the paper that converts Ha into Hb and Hc into Hd. Thus, all four methylene (CH2) protons are equivalent. The spectrum consists of a triplet at about 1.2 ppm (area = 6) and a quartet at about 3.4 ppm (area = 4), with a coupling constant of about 7 Hz (free rotation). Note that protons within an equivalent group do not split each other—we will see why this is when we consider the effect of strong coupling (second-order splitting).

Figure 2.12

In many cases you do not need to talk about formal symmetry elements to see the equivalence of protons. Just look at the world from the point of view of the proton: What kind of environment does it find itself in? If the world looks exactly the same (or is a mirror image) from the point of view of one proton as it does from another, they will be chemically equivalent, that is, they will have the same chemical shift. For example, in 4-bromotoluene (4-bromo-1-methylbenzene), the two protons adjacent to the bromine are chemically equivalent. Imagine sitting at a six-sided table, and you see a bromine seated at your right and a proton to its right, a proton seated to your left and a methyl group to its left, and another proton across from you. Now, if you sit in the other position next to the bromine, you have a bromine to your left and a proton to its left, a proton seated on your right with a methyl group to its right, and a proton across from you. Except for the mirror image relationships, which have no effect on chemical shift, you are in the same environment. If there is a difference, no matter how far away in the molecule, the two protons are not chemically equivalent. If the difference is far enough away, there may be little or no difference in chemical shift, but there is no chemical equivalence in the formal sense.

Chiral molecules do not have mirror planes, but they can have rotation axes as symmetry elements. The molecule shown in Figure 2.13 is chiral in its central oxygen-bridged tricyclic ring system as well as in the two R group substituents. But rotation about the C2 axis by 180° yields the identical molecule, transforming Ha into Hb and Hc into Hd. Even the chiral R groups are interchanged by the rotation, so that there are exactly half the number of unique 1H resonances as one would predict just by counting protons. Without mass spectrometric verification of the molecular weight, we might propose a "monomer" structure rather than the dimer structure shown. Integration of peak areas only gives us the relative number of protons represented by each peak, not the absolute number, so it is often difficult to confirm the presence of symmetrical dimers and higher multimers by NMR alone.

A methyl group always forms an equivalent group of three protons, but saturated methylene (X-CH2-Y) groups are more complicated. In an achiral molecule, such as diethyl ether, they are always a chemically equivalent pair. But if the molecule has a chiral center, it cannot have a mirror plane, and in most cases the two protons of the CH2 group will not be chemically equivalent. Thus, in most of the interesting molecules such as natural products and biological molecules, each CH2 group will give rise to two proton resonances unless they have coincidentally the same chemical shift (a "degenerate" pair). The two

0 0

Post a comment