Nmr  (Page 5/6)

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 ${\text{CH}}_3{\text{CH}}_2^{-}$ 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…

***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.***

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 ${\text{CH}}_3$ group (the coupling constant) will be the same as the distance between the peaks of the ${\text{CH}}_2$ group. Also note that the total intensity of the peaks due to the ${\text{CH}}_3$ group is 1.5 times the size of the total intensity for the peaks of the ${\text{CH}}_2$ group.