2.8.4: Spin-Spin Coupling

The ¹H-NMR spectra that we have seen so far (of methyl acetate and 1,4-dimethylbenzene) are somewhat unusual in the sense that in both of these molecules, each set of protons generates a single NMR signal. In fact, the ¹H-NMR spectra of most molecules contain signals that are 'split' into two or more sub-peaks. Rather than being a complication, however, this splitting behavior is actually very useful because it provides us with more information about our sample molecule.

Consider the spectrum for 1,1,2-trichloroethane. In this and in many spectra to follow, we show enlargements of individual signals so that the signal splitting patterns are recognizable.

The signal at 3.96 ppm, corresponding to the two H_a protons, is split into two subpeaks of equal height (and area) – this is referred to as a doublet. The H_b signal at 5.76 ppm, on the other hand, is split into three sub-peaks, with the middle peak higher than the two outside peaks - if we were to integrate each subpeak, we would see that the area under the middle peak is twice that of each of the outside peaks. This is called a triplet.

The source of signal splitting is a phenomenon called spin-spin coupling, a term that describes the magnetic interactions between neighboring, non-equivalent NMR-active nuclei. (The terms 'splitting' and 'coupling' are often used interchangeably when discussing NMR.) In our 1,1,2 trichloromethane example, the H_a and H_b protons are spin-coupled to each other. Here's how it works, looking first at the H_a signal: in addition to being shielded by nearby valence electrons, each of the H_a protons is also influenced by the small magnetic field generated by H_b next door (remember, each spinning proton is like a tiny magnet). The magnetic moment of H_b will be aligned with B₀ in slightly more than half of the molecules in the sample, while in the remaining molecules it will be opposed to B₀. The B_eff ‘felt’ by H_a is a slightly weaker if H_b is aligned against B₀, or slightly stronger if H_b is aligned with B₀. In other words, in half of the molecules H_a is shielded by H_b (thus the NMR signal is shifted slightly upfield) and in the other half H_a is deshielded by H_b (and the NMR signal shifted slightly downfield). What would otherwise be a single H_a peak has been split into two sub-peaks (a doublet), one upfield and one downfield of the original signal. These ideas an be illustrated by a splitting diagram, as shown below.

Now, let's think about the H_b signal. The magnetic environment experienced by H_b is influenced by the fields of both neighboring H_a protons, which we will call H_a1 and H_a2. There are four possibilities here, each of which is equally probable. First, the magnetic fields of both H_a1 and H_a2 could be aligned with B₀, which would deshield H_b, shifting its NMR signal slightly downfield. Second, both the H_a1 and H_a2 magnetic fields could be aligned opposed to B₀, which would shield H_b, shifting its resonance signal slightly upfield. Third and fourth, H_a1 could be with B₀ and H_a2 opposed, or H_a1 opposed to B₀ and H_a2 with B₀. In each of the last two cases, the shielding effect of one H_a proton would cancel the deshielding effect of the other, and the chemical shift of H_b would be unchanged.

So in the end, the signal for H_b is a triplet, with the middle peak twice as large as the two outer peaks because there are two ways that H_a1 and H_a2 can cancel each other out.

While this coupling most often occurs between the same nuclei as seen in the proton spectrum above, nuclei of different atoms will couple if they are in close enough proximity. For example, if the ¹³C NMR spectrum of 1,1,2-trichloroethane were obtained, there would be two signals. Since the carbon atoms are not equivalent, they would couple each other. In practice this is not typically a concern due to the low natural abundance of ¹³C. The carbon signals would also couple with the protons making for a very complex signal. As many molecules contain multiple protons, we often seek to eliminate this complication. In this case, the ¹³C{¹H} NMR spectrum would be obtained. The {¹H} indicates proton decoupling which means irradiating the sample with a frequency such that the protons become 'invisible' and no coupling to them is seen. Running decoupled spectra is very common for non-hydrogen nuclei.

Video tutorials: proton NMR spectroscopy

Video of an actual NMR experiment

Contributors

• Organic Chemistry With a Biological Emphasis by Tim Soderberg (University of Minnesota, Morris)