Three Coupled Nuclei AX2, AMX, ABX, ABC, AB2 Systems

In the AX2 system, the two X nuclei will afford a two-proton doublet while the A proton will afford a 1 2 1 triplet. The chemical shifts and coupling constants are measured directly. 

In an AMX system, three nuclei with fairly different chemical shifts are coupled with each other with their three respective coupling constants. Since the AS/J ratio is large, the spectrum is essentially first order and each of the three nuclei will give a four-line pattern. Thus A will first be split by M into a doublet, and each of the peaks of the doublet will then be split by X into a double doublet. 

Conventionally, one pseudoquartet is numbered 1, 3, 5, and 7 while the other pseudoquartet is numbered 2,4,6, and 8. The recognition of the lines in each pseudoquartet is facilitated by noting that the following relations apply in the peak positions V3 - = V4 - V2 = V7 - V5 = Vg — so that J b 

A useful procedure for analyzing ABX spectra and other more complex systems is that of subspectral analysis. This is based on the fact that many complex spectra can be seen to contain one or more simpler subspectra which readily lend themselves to separate analysis. Thus the AB part of the ABX spectrum can be divided into two AB-type subspectra. 

Line no. Assignment Energy (i.e., frequency) Relative intensity 

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