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Coupling in H-NMR

So far the H-NMR 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 1,1-dichloroethane shown below.

H-NMR spectrum of 1,1-dichloroethane
Before we look at the coupling, lets review the assignment of the peaks first: Now, what about the coupling patterns ?

 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 -CH3.
Magnetic origin of coupling CH with CH3 in CH3CHCl2 The methine -CH can adopt two alignments with respect to the applied field. As a result, the signal for the adjacent methyl -CH3 is split in two lines, of equal intensity, a doublet.
Now consider the effect of the -CH3 group has on the adjacent -CH .
Magnetic origin of coupling CH3 with CH in CH3CHCl2 The methyl -CH3 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.

Now we can do more a complete analysis, including the application of the "n+1" rule to 1,1-dichloroethane: Coupling Constant, J
 
coupling constant, J 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, Ha-C-C-Hbthen the coupling of Ha with Hb, Jab
MUST BE EQUAL to the coupling of Hb with Ha, Jba, therefore Jab = Jba
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 H-NMR spectra of 1,1-dichloroethane (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 H-NMR 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.
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organic chemistry © Dr. Ian Hunt, Department of Chemistry University of Calgary