Chapter 13: Spectroscopy 
Coupling in HNMR
So far the HNMR spectra that we have looked at have all had different types of protons that are seen as singlets in the spectra. This is not the normal case.... spectra usually have peaks that appear as groups of peaks due to coupling with neighbouring protons, for example, see the spectra of 1,1dichloroethane shown below.
Coupling arises because the magnetic field of vicinal (adjacent) protons influences the field that the proton experiences.
To understand the implications of this we should first consider the effect the CH group has on the adjacent CH_{3}.  
The methine CH can adopt two alignments with respect to the applied field. As a result, the signal for the adjacent methyl CH_{3} is split in two lines, of equal intensity, a doublet.  
Now consider the effect of the CH_{3} group has on the adjacent CH .  
The methyl CH_{3} protons give rise to 8 possible combinations with respect to the applied field. However, some combinations are equivalent and there are four magnetically different effects. As a result, the signal for the adjacent methine CH is split into four lines, of intensity ratio 1:3:3:1, a quartet. 
The coupling constant, J (usually in frequency units, Hz) is a measure
of the interaction between a pair of protons. In a vicinal system of the general type, H_{a}CCH_{b}then the coupling of H_{a} with H_{b}, J_{ab}, MUST BE EQUAL to the coupling of H_{b} with H_{a}, J_{ba}, therefore J_{ab} = J_{ba}. The implications are that the spacing between the lines in the coupling patterns are the same as can be seen in the coupling patterns from the HNMR spectra of 1,1dichloroethane (see left). 
Pascal's Triangle
The relative intensitites of the lines in a coupling pattern is given
by a binomial expansion or more conviently by Pascal's triangle.
To derive Pascal's triangle, start at the apex, and generate each lower row by creating each number by adding the two numbers above and to either side in the row above together. The first six rows are shown to the right. So for HNMR a proton with zero neighbours, n = 0, appears as a single line, a proton with one neighbours, n =1 as two lines of equal intensity, a proton with two neighbours, n = 2, as three lines of intensities 1 : 2 : 1, etc. 
Summary
© Dr. Ian Hunt, Department of Chemistry, University
of Calgary
