Analysis of Second-Order, Three- and Four-Spin Systems by Inspection

Analysis of Second-Order, Three- and Four-Spin Systems by Inspection 

The chemical shift of the B proton occurs at the average of the fifth and seventh peaks, or 

The next level of spectral complexity is the case in which all three nuclei have different chemical shifts, but one of the resonances is well removed from the other two (ABX). This spectrum is determined by six parameters ua,ub Bx- The X resonance 

X part, the individual values for y x Ax calculated. Two solutions, however, are 

If the arithmetic for a particular ABX spectrum is followed through, the exact values of X ( a Ob) 7ab obtained, but two sets of 7ax Ax e produced, with ei- 

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The analysis of the second-order, two-spin (AB) system by inspection is given in Section 4-7 and is explained in Appendix 3. A few other second-order systems may be analyzed without recourse to computer methods. Analyzing a three-spin systems ranges from the trivial (AX2, AMX) to the impossible (many ABC systems). As the AX chemical-shift difference in the AX2 system decreases, degeneracies are lifted, intensities change, and a new peak can appear (Figure A4-1). In the AB2 extreme, a total of nine peaks can be observed. Four of these peaks result from spin flips of A protons, four from spin flips of B protons, and one from simultaneous spin flips of both A and B protons. The ninth peak, called a combination line, is forbidden in the first-order case (AX2) and is rarely observed even in the AB2 extreme. The combination line is seen only in the most closely coupled case at the top, as a very low intensity peak at the far right. 

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