Analysis of an ABX Spectrum

The analysis of an ABX spectrum to extract the magnitudes of the three chemical shifts and the three coupling constants is in principle straightforward, but in practice some care must be exercised to avoid ambiguities. As we have indicated, the values of D+, D, and j o( + /bx I are readily determined from the spectrum. To simplify notation, we define positive quantities M and N by the relations 

Because D+, D, and have been determined, both M and N are known experimentally. Mathematically, the following four solutions result from the possible choices of sign in Eq. B.8 and B.9  

Because M and N are both positive, solution gives (vK — vB) 1/2(JAX Jbx) From Eq. B.3, this means that cos 26- 0, so 0 0 n/2. Solution gives (vK vB) ViUax - Jbx) and tt/2 0 tt. The two solutions usually give significantly different ratios for the intensities of the X lines, only one of which is compatible with the observed spectrum. 

Identify the two ab quartets on the basis of frequency and intensity relations. Note the value ofTab- 

Find the value of Tax + Tbx I from the separation of the centers of the two ab quartets. 

---

Table B.2 summarizes the procedure suggested in the foregoing paragraphs for a manual analysis of an ABX spectrum. Often, such analyses are carried out by computer simulation, but it is important to recognize that the ambiguities discussed are present in such a calculation, which generally relies only on frequencies, not intensities, of lines.

---