It is common in both NMR textbooks and journal articles to loosely describe certain ABX spin systems as AA′X spin systems (1)(2)(3)(4)(5). For purposes of illustration, consider the 13 CH 2 spin system of maleic anhydride shown in Figure 1. One of the AB pair of hydrogen atoms is attached to a 13 C atom, the X-nucleus in the spin system, but the other is attached to a 12 C atom, the NMR-inactive isotopomer of the Xnucleus, and so the symmetry of the molecule is broken. Rigorously, the different isotopes split the chemical shifts of the "false" AA′ pair, and the properly designated AB hydrogen atoms are chemically as well as magnetically inequivalent.In practice, however, the chemical shifts normally are indistinguishable, and many of those same textbooks and journal articles point out that while rigorously the system is ABX, for all practical purposes it can be analyzed as AA′X (1,6). The danger of all of this is that when the chemical shifts are not the same, one may fail to recognize that fact owing to the assumption that the isotopomer shift is always insignificant.
Results and Discussion
P ExamplesA number of authors have noted that diphosphines and transition metal complexes with two phosphine ligands represent interesting test cases of such false AA′X systems (6-8), as shown for diphos (1) in Figure 2. Here the AA′ nuclei are the 31 P atoms, and the X-nucleus is the lone 13 C atom anywhere in this molecule. Detailed descriptions of the expected appearance of AA′X systems have been published (3,4,6), and except for the few cases to be described below, the AA′X description suffices for diphosphorus compounds (2, 6, 7). Representative multiplets from 1 and 2 are shown in Figure 3 for illustration. A common feature of AA′X spectra is that each exhibits a peak at the center of a 3-or 5-line multiplet (for J AA′ ≠ 0); the relative heights of the lines are dependent on the relative values of J AA′ , J AX , and J A′X . The separation of lines 1 and 3 (Fig. 3a,b) or 2 and 4 ( Fig. 3c) is equal to |J PC + J P′C |. The coupling constant J PP′ (if relatively large) can be obtained from the outer "wings" at approximately ± J PP from the central peak (Fig. 3c), or (if relatively small) from matching the height of the central line with that in simulations of the observed spectrum (Fig. 3a). These multiplets are examples of "virtual coupling" (9), because even though the longer range coupling constant J P′C ≈ 0, lines due to the second phosphorus atom are present in the 13 C NMR spectrum caused by the strong coupling of the phosphorus atoms-hence the second phosphorus is "virtually" coupled to carbon. It is important to recognize, especially in the case of the deceptively simple "triplet", that the coupling constants cannot be extracted on the basis of familiar first-order analyses.In contrast to the AA′X patterns seen above, the multiplets due to the ipso and bridging carbon atoms of diphos exhibit split central lines in the 100.6 MHz 13 C NMR spectrum (Figure 4a,b). The spectra are readily modeled if one drops the AA′X ...