The source of spin-spin coupling

The ¹H-NMR spectra that we have seen so far (of methyl acetate and para-xylene) 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 organic  molecules contain proton signals that are ‘split’ into two or more sub-peaks.  Rather than being a complication, however, this splitting behavior actually 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. 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 half of the 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_bsignal.  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_a1opposed 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.

Now, consider the spectrum for ethyl acetate:

We see an unsplit ‘singlet’ peak at 1.833 ppm that corresponds to the acetyl (H_a) hydrogens – this is similar to the signal for the acetate hydrogens in methyl acetate that we considered earlier.  This signal is unsplit because there are no adjacent hydrogens on the molecule.  The signal at 1.055 ppm for the H_c hydrogens is split into a triplet by the two H_b hydrogens next door.  The explanation here is the same as the explanation for the triplet peak we saw previously for 1,1,2-trichloroethane.

The H_bhydrogens give rise to a quartet signal at 3.915 ppm – notice that the two middle peaks are taller then the two outside peaks.  This splitting pattern results from the spin-coupling effect of the three H_c hydrogens next door, and can be explained by an analysis similar to that which we used to explain the doublet and triplet patterns.

By now, you probably have recognized the pattern which is usually referred to as the n + 1 rule: if a set of hydrogens has n neighboring, non-equivalent hydrogens, it will be split into n + 1 subpeaks. Thus the two H_b hydrogens in ethyl acetate split the H_c signal into a triplet, and the three H_c hydrogens split the H_b signal into a quartet.  This is very useful information if we are trying to determine the structure of an unknown molecule: if we see a triplet signal, we know that the corresponding hydrogen or set of hydrogens has two `neighbors`.  When we begin to determine structures of unknown compounds using ¹H-NMR spectral data, it will become more apparent how this kind of information can be used.

Three important points need to be emphasized here.  First, signal splitting only occurs between non-equivalent hydrogens – in other words, H_a1 in 1,1,2-trichloroethane is not split by H_a2, and vice-versa.

Second, splitting occurs primarily between hydrogens that are separated by three bonds.  This is why the H_a hydrogens in ethyl acetate form a singlet– the nearest hydrogen neighbors are five bonds away, too far for coupling to occur.

Occasionally we will see four-bond and even 5-bond splitting, but in these cases the magnetic influence of one set of hydrogens on the other set is much more subtle than what we typically see in three-bond splitting (more details about how we quantify coupling interactions is provided in section 5.5B). Finally, splitting is most noticeable with hydrogens bonded to carbon.  Hydrogens that are bonded to heteroatoms (alcohol or amino hydrogens, for example) are coupled weakly – or not at all – to their neighbors.  This has to do with the fact that these protons exchange rapidly with solvent or other sample molecules.

Below are a few more examples of chemical shift and splitting pattern information for some relatively simple organic molecules.

Multiplicity in Proton NMR

The number of lines in a peak is always one more (n+1) than the number of hydrogens on the neighboring carbon.  This table summarizes coupling patterns that arise when protons have different numbers of neighbors.