Spin-Spin Splitting: The Effect of Nonequivalent Neighboring Hydrogens

From what we have learned about ¹H NMR spectra so far, we might predict that the spectrum of bromoethane, CH₃CH₂Br, would consist of two peaks—one, at about 1.0-2.0 d, caused by the methyl group (shifted downfield because of the presence of the electronegative bromine atom in the molecule), and one, at 3.0-4.0 d caused by the methylene ( CH₂ ) group attached to a bromine atom. However, when we look at Figure 1.13 (Organic Chemistry, 8th ed., p. 477), we see a spectrum which appears to be much more complex. True, we see absorptions in the regions we predicted, but these absorptions appear as a group of four peaks (a quartet) in the 3-4 d region and a group of three peaks (a triplet) in the 1-2 d region. This complication, which may be disturbing to the student who longs for the simple life, is in fact very useful to the organic chemist, and adds greatly to the power of NMR spectroscopy as a tool for the elucidation of chemical structures. The split peaks (multiplets) arise because the magnetic field experienced by the protons of one group is influenced by the spin arrangements of the protons in an adjacent group. For example, the field experienced by the methylene (-CH₂-) group in bromoethane is modified by the fields generated by the nuclear spins of the hydrogen atoms in the neighboring methyl group. Each of these nuclei (which you will recall are just protons) can spin either with the applied field, or against the applied field. Thus, there are four possibilities (see Figure 1.1, below) and the methylene protons can therefore experience four slightly different fields. These four fields give rise to the quartet which we observe in the ¹H NMR spectrum.

Figure 1.1: Possible spin orientations for the protons of a methyl group placed in an applied magnetic field

Notice that there are three possible ways in which the spins can be arranged so that two of them are aligned with the applied field and one is aligned against. Similarly, there are three ways of obtaining an arrangement in which one spin is aligned against the field and two are aligned with it. Of course there is only one way of aligning all three spins with the field, and only one way of aligning all three spins against the field. Thus, these last two arrangements are both three times less likely than either of the first two, and this probability accounts for the fact that the four peaks in the quartet are not of equal height (or area). In fact, the ratio of the peak areas is, as you might expect, 1 : 3 : 3 : 1. Just as the signal from the methylene (-CH₂-) group is split into a quartet by the neighboring methyl group, so the signal from the methyl (CH₃-) group is split into a triplet by the neighboring methylene group. You might wish to analyze this situation using the approach described above, and satisfy yourself that the areas of the triplet peaks should be in a ratio of 1 : 2 : 1. Spin-spin coupling is often one of the more challenging topics for organic chemistry students to master.