Patterns of coupling
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
526-527
2025-12-10
43
Patterns of coupling
We have seen that in an AX system, spin–spin coupling will result in four lines in the NMR spectrum. Instead of a single line from A, we get a doublet of lines separated by J and centred on the chemical shift characteristic of A. The same splitting occurs in the X resonance: instead of a single line, the resonance is a doublet with splitting J (the same value as for the splitting of A) centred on the chemical shift characteristic of X. These features are summarized in Fig. 15.13. A subtle point is that the X resonance in an AXn species (such as an AX2 or AX3 species) is also a doublet with splitting J. As we shall explain below, a group of equivalent nuclei resonates like a single nucleus. The only difference for the X resonance of an AX nspecies is that the intensity is n times as great as that of an AX species (Fig. 15.14). The A resonance in an AXn species, though, is quite different from the A resonance in an AX species. For example, consider an AX2 species with two equivalent X nuclei. The resonance of A is split into a doublet of separation J by one X, and each line of that doublet is split again by the same amount by the second X (Fig. 15.15). This splitting results in three lines in the intensity ratio 1:2:1 (because the central frequency can be obtained in two ways). The A resonance of an AnX2 species would also be a 1:2:1 triplet of splitting J, the only difference being that the intensity of the A resonance would be n times as great as that of AX2.
Three equivalent X nuclei (an AX3 species) split the resonance of A into four lines of intensity ratio 1:3:3:1 and separation J (Fig. 15.16). The X resonance, though, is still a doublet of separation J. In general, n equivalent spin-1–2 nuclei split the resonance of a nearby spin or group of equivalent spins into n + 1 lines with an intensity distribution given by ‘Pascal’s triangle’ in which each entry is the sum of the two entries immediately above (4). The easiest way of constructing the pattern of fine structure is to draw a diagram in which successive rows show the splitting of a subsequent proton. The procedure is illustrated in Fig. 15.17 and was used in Figs. 15.15 and 15.16. It is easily extended to molecules containing nuclei with I > 
(Fig. 15.18).
Fig. 15.14 The X resonance of an AX2 species is also a doublet, because the two equivalent X nuclei behave like a single nucleus; however, the overall absorption is twice as intense as that of an AX species.
Fig. 15.15 The origin of the 1:2:1 triplet in the A resonance of an AX2 species. The resonance of A is split into two by coupling with one X nucleus (as shown in the inset), and then each of those two lines is split into two by coupling to the second X nucleus. Because each X nucleus causes the same splitting, the two central transitions are coincident and give rise to an absorption line of double the intensity of the outer lines.
Fig. 15.16 The origin of the 1:3:3:1 quartet in the A resonance of an AX3 species. The third X nucleus splits each of the lines shown in Fig. 15.15 for an AX2 species into a doublet, and the intensity distribution reflects the number of transitions that have the same energy.
Fig. 15.17 The intensity distribution of the A resonance of an AXn resonance can be constructed by considering the splitting caused by 1, 2,...n protons, as in Figs. 15.15 and 15.16. The resulting intensity distribution has a binomial distribution and is given by the integers in the corresponding row of Pascal’s triangle. Note that, although the lines have been drawn side-by-side for clarity, the members of each group are coincident. Four protons, in AX4, split the A resonance into a 1:4:6:4:1 quintet.
Fig. 15.18 The intensity distribution arising from spin–spin interaction with nuclei with I = 1 can be constructed similarly, but each successive nucleus splits the lines into three equal intensity components. Two equivalent spin-1 nuclei give rise to a 1:2:3:2:1 quintet.
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