Proton NMR - Spin-spin Couplings

Spin-spin Couplings

The chemical shift is not the only indicator used to assign a molecule. Because nuclei themselves possess a small magnetic field, they influence each other, changing the energy and hence frequency of nearby nuclei as they resonate—this is known as spin-spin coupling. The most important type in basic NMR is scalar coupling. This interaction between two nuclei occurs through chemical bonds, and can typically be seen up to three bonds away.

The effect of scalar coupling can be understood by examination of a proton which has a signal at 1ppm. This proton is in a hypothetical molecule where three bonds away exists another proton (in a CH-CH group for instance), the neighbouring group (a magnetic field) causes the signal at 1 ppm to split into two, with one peak being a few hertz higher than 1 ppm and the other peak being the same number of hertz lower than 1 ppm. These peaks each have half the area of the former singlet peak. The magnitude of this splitting (difference in frequency between peaks) is known as the coupling constant. A typical coupling constant value would be 7 Hz.

The coupling constant is independent of magnetic field strength because it is caused by the magnetic field of another nucleus, not the spectrometer magnet. Therefore it is quoted in hertz (frequency) and not ppm (chemical shift).

In another molecule a proton resonates at 2.5 ppm and that proton would also be split into two by the proton at 1 ppm. Because the magnitude of interaction is the same the splitting would have the same coupling constant 7 Hz apart. The spectrum would have two signals, each being a doublet. Each doublet will have the same area because both doublets are produced by one proton each.

The two doublets at 1 ppm and 2.5 ppm from the fictional molecule CH-CH are now changed into CH₂-CH:

• The total area of the 1 ppm CH₂ peak will be twice that of the 2.5 ppm CH peak.
• The CH₂ peak will be split into a doublet by the CH peak—with one peak at 1 ppm + 3.5 Hz and one at 1 ppm - 3.5 Hz (total splitting or coupling constant is 7 Hz).

In consequence the CH peak at 2.5 ppm will be split twice by each proton from the CH₂. The first proton will split the peak into two equal intensities and will go from one peak at 2.5 ppm to two peaks, one at 2.5 ppm + 3.5 Hz and the other at 2.5 ppm - 3.5 Hz—each having equal intensities. However these will be split again by the second proton. The frequencies will change accordingly:

• The 2.5 ppm + 3.5 Hz signal will be split into 2.5 ppm + 7 Hz and 2.5 ppm
• The 2.5 ppm - 3.5 Hz signal will be split into 2.5 ppm and 2.5 ppm - 7 Hz

The net result is not a signal consisting of 4 peaks but three: one signal at 7 Hz above 2.5 ppm, two signals occur at 2.5 ppm, and a final one at 7 Hz below 2.5 ppm. The ratio of height between them is 1:2:1. This is known as a triplet and is an indicator that the proton is three-bonds from a CH₂ group.

This can be extended to any CH_n group. When the CH₂-CH group is changed to CH₃-CH₂, keeping the chemical shift and coupling constants identical, the following changes are observed:

• The relative areas between the CH₃ and CH₂ subunits will be 3:2.
• The CH₃ is coupled to two protons into a 1:2:1 triplet around 1 ppm.
• The CH₂ is coupled to three protons.

Something split by three identical protons takes a shape known as a quartet, each peak having relative intensities of 1:3:3:1.

A peak is split by n identical protons into components whose sizes are in the ratio of the nth row of Pascal's triangle:

n 0 singlet 1 1 doublet 1 1 2 triplet 1 2 1 3 quartet 1 3 3 1 4 quintet 1 4 6 4 1 5 sextet 1 5 10 10 5 1 6 septet 1 6 15 20 15 6 1 7 octet 1 7 21 35 35 21 7 1 8 nonet 1 8 28 56 70 56 28 8 1

Because the nth row has n+1 components, this type of splitting is said to follow the "n+1 rule": a proton with n neighbors appears as a cluster of n+1 peaks.

With 2-methylpropane, (CH₃)₃CH, as another example: the CH proton is attached to three identical methyl groups containing a total of 9 identical protons. The C-H signal in the spectrum would be split into ten peaks according to the (n + 1) rule of multiplicity. Below are NMR signals corresponding to several simple multiplets of this type. Note that the outer lines of the nonet (which are only 1/8 as high as those of the second peak) can barely be seen, giving a superficial resemblance to a septet.

When a proton is coupled to two different protons, then the coupling constants are likely to be different, and instead of a triplet, a doublet of doublets will be seen. Similarly, if a proton is coupled to two other protons of one type, and a third of another type with a different, smaller coupling constant, then a triplet of doublets is seen. In the example below, the triplet coupling constant is larger than the doublet one. By convention the pattern created by the largest coupling constant is indicated first and the splitting patterns of smaller constants are named in turn. In the case below it would be erroneous to refer to the quartet of triplets as a triplet of quartets. The analysis of such multiplets (which can be much more complicated than the ones shown here) provides important clues to the structure of the molecule being studied.

The simple rules for the spin-spin splitting of NMR signals described above apply only if the chemical shifts of the coupling partners are substantially larger than the coupling constant between them. Otherwise there may be more peaks, and the intensities of the individual peaks will be distorted (second-order effects).