The ABX System

We discussed the ABX system briefly in Section 6.13. Here we provide additional details on the form of the matrix elements, the factoring of the secular equation, and the expressions for transition frequencies and intensities. In addition, we describe in some detail the use of the resultant algebraic expressions to analyze an experimental ABX spectrum. Although such analysis for a specific case can be carried out by computer spectral simulation, it is instructive to see the steps used in the general algebraic procedure, which is analogous to that used in Section 6.8 but is more tedious. 

---

The complexity of this spectrum does not end there however as two key features of this spectrum must now be addressed. First, the X part of the ABX system we have just discussed consists of far more than the normal four lines and second, the four-line multiplets centred at 2.88 and 2.73 ppm are clearly A and B parts of a second ABX system These features are linked in that the COSY spectrum clearly shows that the complex X part (4.05-3.98 ppm) is in fact coupled to both the A and B parts of the second ABX system. Therefore, we can deduce that... 

The configurational stability of primary organolithiums, while of no synthetic consequence, has been determined by NMR methods. Analysis of the line shape of the AA BB system of 1713 or of the ABX system of 1814 gave half-lives for inversion of about 0.01 s for 17 or 18 in ether at 30 °C, increasing (for 17) to about 0.1 s at 0 °C and 1 s at -18 °C. The rate of inversion was decreased by a factor of 8 in pentane or 10 in toluene, but the addition of 1 equiv. TMEDA to pentane restored a rate of inversion more or less equal to that in pentane. 

MORE ABOUT THE ABX SYSTEM DECEPTIVE SIMPLICITY AND VIRTUAL COUPLING... 

A second variant of the ABC system occurs when the chemical shift of one nucleus differs substantially from that of the other two — an ABX system. The presence of one nucleus only weakly coupled to the others permits factoring of the secular equation so that algebraic solutions are possible. The basis functions for the ABX system are just those shown in Table 6.3 for the general three-spin system. However, because (vA — vx) and (vB — vx) are much larger than Jax and /BX, we can define an Fz for the AB nuclei separately from Fz for the... 

The ABX system also provides a convenient framework for exploring the consequences of strong coupling from a slighdy different perspective. Consider the ABX system in the molecular fragment VI. 

Treatment with acidic ethanol simply makes the diethyl acetal from the aldehyde group Since A1 and A2 are in equilibrium, all A2 is eventually converted into B via Al. Compou.-v 1 again chiral so the ABX system reappears with further coupling of H to the acetal proton. T v xir now four triplets and quartets for the four OEt groups. 

The nitrogen atom of the ethanamine bridge may be attached to carbon atom 5, 9, 10, or 14. Carbon atom 8 is excluded by the intolerable strain that such an attachment would cause. Carbon atom 5 is easily ruled out because all of the compounds 1-8 have a sharp singlet at S 5.0 + 0.2 characteristic of the C-5-H (S). Attachment of the bridge at carbon atom 14 is rendered unlikely by the observation that the spectrum of cancentrine methine 4 shows the presence of two olefinic protons constituting the A and B parts of the ABX system C-9-H, C-IO-H, C-14-H. 

Spectra of benzylpenilloic acids (see Figure 5.36) are more complex than those of the penicilloic acids as a result of the non-equivalence of the methylene protons produced at C-6 after decarboxylation. Full analysis is possible, however, from a 400 MHz spectrum, which reveals four 2-methyl resonances and duplicate 3-H, PhCH2, 5-H and fi-Hj signals, all evidence of the isomeric nature of the product (Figure 5.36). The 6-Hj signals are both composed of 8 lines as required by the ABX system (CH2CH), while the 5-H resonances appear as triplets. 

The compound A1 fits the formula for A and the H NMR spectrum of the compound with the low field signal (assigned to the CHO proton). This structure would also show an ABX system in its H NMR spectrum. But what is the other compound (A2) It is obviously in equiUbrium with A1 and it lacks both the aldehyde proton and the ABX system and it sounds like an enol. Compound A1 is chiral so the CH2 group appears as an ABX system but A2 is not chiral so the CH2 group is a singlet. Here are the structures with their NMR assignments. In both cases the 3H triplets and 2H quartets are ethyl groups. 

If the chemical shift differences between two of the three nuclei (A and B) are small as compared to their coupling constants (i.e., AS/J is small for H and Hb), while the difference between the chemical shifts of these nuclei and the third nucleus (X) is large as compared to the coupling constants between nucleus X and nuclei A and B, then one gets an ABX spectrum in which the AB portion of the spectrum can contain up to eight lines while the X portion can contain six lines. Figure 2.28 shows that the ABX system is an intermediate... 

On the basis of first-order arguments, one can draw the coupling tree for the ABX system shown in Figure 2.30. This would afford four lines for the X part which would be of equal intensity, and eight lines for the A and B protons. Note that the line separation is not necessarily equal to the coupling constant—hence S (separation) has been used to indicate the distances between the lines, rather than J values. 

In practice, due to second-order perturbation effects, the X proton may give rise to six lines, and the pseudoquartets from the A and B protons may partly overlap. The ABX patterns obtained are dependent on the signs of the coupling constants, J x and Jbx but are unaffected by the sign of The AB component of the ABX system may give rise to any of the three patterns shown in Figure 2.31. 

---