Coupling is another very important aspect of NMR spectroscopy that gives a great deal of information about structure. Coupling results in a signal being split into more signals due to neighboring atoms which also have a nuclear spin. This arises frequently between protons on adjacent carbon atoms. One important aspect of this phenomenon is that equivalent nuclei do not couple to each other.
The reason coupling occurs can be described as follows. For example, let us consider the case of a molecule containing two carbon atoms, each with a single proton and other atoms which do not have a nuclear spin coupling to the protons. One such molecule is 1,1-dibromo-2,2-dichloroethane.
The protons in this molecule are not equivalent, so we would expect to see two signals. Additionally, the proton attached to the
CCl2CCl2 size 12{ ital "CCl" rSub { size 8{2} } } {} group will have two different spin states, +1/2 and -1/2. This means that the proton on the
CBr2CBr2 size 12{ ital "CBr" rSub { size 8{2} } } {} group will see two slightly different magnetic fields depending upon whether the proton on the
CCl2CCl2 size 12{ ital "CCl" rSub { size 8{2} } } {} group is in the +1/2 or -1/2 spin state. Since these spin states are not equivalent in the presence of a large external magnetic field, we actually observe two signals for the H atom attached to the
CBr2CBr2 size 12{ ital "CBr" rSub { size 8{2} } } {} group. This is also true for the hydrogen atom attached to the
CCl2CCl2 size 12{ ital "CCl" rSub { size 8{2} } } {} group. In these situations, we say that the proton on the
CCl2CCl2 size 12{ ital "CCl" rSub { size 8{2} } } {} is coupled to the proton on the
CBr2CBr2 size 12{ ital "CBr" rSub { size 8{2} } } {} group. When a peak is split into two equal components by coupling, it is called a doublet. We would expect the proton NMR spectrum of 1,1-dibromo-2,2-dichloroethane to look something like this:
The differences in chemical shift labeled J are known as the coupling constant. If two nuclei are coupled to each other, the coupling constants will be the same. For example, in the case of 1,1-dibromo-2,2-dichloroethane, the two peaks that make up the doublet due to the
CCl2CCl2 size 12{ ital "CCl" rSub { size 8{2} } } {} will be exactly split the same distance as the two peaks that make up the doublet due to the
CBr2CBr2 size 12{ ital "CBr" rSub { size 8{2} } } {} group. In a complex spectrum, this allows us to identify which peaks are coupled to each other. Peaks that are coupled to each other will most likely arise because the H atoms are on adjacent (or nearby) carbon atoms.
We need to consider a couple of other cases in order to have enough information on coupling patterns to understand common problems. There are cases where there is more than one proton on adjacent carbon atoms.
Let us first consider the case where one or more protons on one carbon atom (let's call it Carbon A) "see" two identical protons on a neighboring carbon atom (called Carbon B). What types of magnetic fields will be seen by the protons on Carbon A? To sort this out, we need to consider the different possible spin combinations of the protons on Carbon B. This is done purely by probability. There are four possibilities:
These can be described by the spin numbers: (+1/2, +1/2), (+1/2, -1/2), (-1/2, +1/2), (-1/2, -1/2). It should be easy to see that the energies of the two combinations (+1/2, -1/2) and (-1/2, +1/2) will be equal. We can order these possibilities according to their expected energies in the presence of a strong external field:
The splitting of the protons on Carbon A will be into three signals in a 1:2:1 ratio, the 2 arising because that energy level is twice as probable.
The case for three protons on an adjacent carbon atom is worked out in a similar fashion. Again, the splitting seen by the protons on Carbon A attached to Carbon B (a methyl group) would be as follows:
There are 8 possible combinations of spin states which divide into a 1:3:3:1 ratio. Either all spins are up, two up and one down, two down and one up, or all up. A proton or protons on one carbon atom adjacent to a methyl group will, therefore, split into a quartet with area ratios of 1:3:3:1.
Ethyl
If we have a
CH3CH2−CH3CH2− size 12{ ital "CH" rSub { size 8{3} } ital "CH" rSub { size 8{2} } rSup { size 8{ - {}} } } {} group, as in chloroethane, we would expect to see two peaks in a ratio of 3:2. The methyl group signal will be split into a triplet (with relative areas of 1:2:1) by coupling to the methylene protons. The methylene protons are split into a quartet (with relative areas of 1:3:3:1) by coupling to the methyl protons. Therefore, we expect the spectrum of an ethyl group to look something like…
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Notice that the chemical shift of a peak split by coupling is defined as the center of the peak pattern. As mentioned earlier, the distance between the peaks of the
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} group (the coupling constant) will be the same as the distance between the peaks of the
CH2CH2 size 12{ ital "CH" rSub { size 8{2} } } {} group. Also note that the total intensity of the peaks due to the
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} group is 1.5 times the size of the total intensity for the peaks of the
CH2CH2 size 12{ ital "CH" rSub { size 8{2} } } {} group.
Butane
In the molecule
CH3CH2CH2CH3CH3CH2CH2CH3 size 12{ ital "CH" rSub { size 8{3} } ital "CH" rSub { size 8{2} } ital "CH" rSub { size 8{2} } ital "CH" rSub { size 8{3} } } {}, the methyl groups are equivalent and the methylene groups are equivalent. As described earlier, we would expect to see two signals in a 3:2 ratio. If we now consider coupling, we see that the methyl groups are attached to methylene groups. The
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} protons will thus be split into triplets by the methylene protons. Likewise, the methylene protons will be split into quartets by the protons on the methyl groups. However, notice that because the methylene groups are equivalent, they do not couple to each other. Therefore, we expect to see the same pattern as that predicted for the ethyl group shown above.
More Complex Coupling Patterns
If a hydrogen atom is attached to a carbon atom to which nonequivalent carbon atoms with different numbers of protons are attached, then a more complex pattern is observed. One arrives at the total number of signals expected by multiplying the individual couplings. For example, consider 1,2-dichloropropane with three carbon atoms having different protons attached:
The
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} protons will see one adjacent proton and the signal will be split into a doublet. The
CH2CH2 size 12{ ital "CH" rSub { size 8{2} } } {} group will likewise be split into a doublet by the CH proton. Coupling between the
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} group and the
CH2CH2 size 12{ ital "CH" rSub { size 8{2} } } {} group will generally not be observed. However, the CH group in the middle is adjacent to two different types of carbon atoms with different numbers of protons attached. This CH group will be split into a quartet by the
CH3CH3 size 12{ ital "CH" rSub { size 8{3} } } {} group and into a triplet by the
CH2CH2 size 12{ ital "CH" rSub { size 8{2} } } {} group. The overall pattern will have 4 x 3 lines, or a total of 12, if our instrument is able to resolve all the lines. This pattern would be described as either a triplet of quartets or a quartet of a triplet, depending upon which coupling constant is larger. Often, these complex patterns are not cleanly resolved and a very complex spectrum results. The two limiting possibilities for the CH group would look something like the following. Notice that there are two different coupling constants in each case.
Quartet of triplets
Triplet of quartets