Simple multiplets

Intensities can be calculated using the rule of binomial coefficients. The relative intensities in a simple multiplet (only one type of coupling neighbour) are as follows ... 

Table 5,9 Relative Line Intensities for Simple Multiplets...

Each chemically distinct nucleus is assigned a letter and a numerical subscript is used to indicate the number of such nuclei. If the chemical shift difference between two sets of nuclei is large compared with the coupling constant between them (3i - S2 > > Jn), letters that are well apart in the alphabet are used A, X, M. Such systems are first order and give rise to simple multiplets in the NMR spectra. On the other hand, if the chemical shift difference is of the same order of magnitude as the coupling constant between the two nuclei ( 1 - 2 J12), then consecutive letters are used A, B, C,. . . , X, Y, Z. The latter systems give rise to second-order spectra with complex multiple patterns. 

As Av/J decreases, the simple multiplets observed in weakly coupled spectra become increasingly distorted new lines can appear and others merge or disappear. Such spectra are termed second-order or strongly coupled spectra. In these cases the chemical shift does not lie in the center of the multiplet and coupling constants are not always obvious. A simple example of such a change is seen... 

In Fig. 5. The structure of the negative parity states is as follows. The low lying 3 and 5 states appear to be rather complicated as their population does not follow the (2J+1) population expected for a simple multiplet. In contrast, the 7 , 9 and 10 appear to have equivalent f7/2 il3/2 strength and thus have rather simple structure. On the %other hand, no evidence is found for the 4 or 8 states and only weak evidence that the state at 3.3 MeV is a 6 state. Configuration mixing is a possible, though not a certain, reason for the absence of these states. In any case, there does not appear to be a simple vf7/2 v13/2 multiplet. 

A complex, first-order multiplet differs from a simple, first-order multiplet in that several different coupling constants are involved in the complex multiplet. The requirement that A vIJ be greater than about 8 still holds, but Pascal s triangle does not hold for the complex multiplet. An example is presented later in Figure 3.37 where it can be seen in the expanded splitting pattern that the multiplet consists of a quartet of doublets the stick pattern is shown in the text and consists of a sequence of two simple multiplets. Some dexterity with stick diagrams will be required throughout. Section 3.5.5 provides a more sophisticated treatment. 

The approximate centers of all simple multiplets, broad peaks, and unresolved multiplets can also usually be correlated with functional groups. The absence of lines in characteristic regions often furnishes important data. 

Abraham and coworkers and by Turner. Occasionally, a particular hydrogen atom is coupled with so many adjacent protons that its signal is too complex for analysis, but it is often possible to remove the unwanted couplings by double resonance, leaving a simple multiplet for analysis. For example, the HI, H2 coupling of ds- and observed after the coupling constants of the methylene protons had been removed by double resonance. 

For simple multiplets, where only one value of J is involved (one coupling), there is little difficulty in measuring the coupling constant. In this case it is a simple matter of determining the spacing (in Hertz) between the successive peaks in the multiplet. This was discussed in Chapter 3, Section 3.17. Also discussed in that section was the method of converting differences in parts per rmlMon (ppm) to Hertz (Hz). Use of the relationship... 

There are some exeeptions to this simple picture, for instance if there is magnetic non-equivalence, or if the chemical shift difference for the nuclei is not much greater than the mutual coupling constant. The spectra will then be second order, and will not be simple multiplets. Methods of analyzing second-order spectra are discussed briefly in Section 4.9.1. For now, we consider only first-order spectra arising from spin-1/2 nuclei. 

This complicates the term scheme considerably. For a triplet system, for instance, we must ima e that all terms in Fig. 1 (except for those with I = 0) become three-fold multiple. With respect to the intensities, we must note that we deal — just os in III — with a spin-free term with the azimuthal quantum number I and a partition z, and so all rules derived in III remain intact. Since, meanwhile, we obtain in the case of a triplet system, for instance, six or seven lines from one, all of which lie very close together, the multiplet fine structure of these bands will be difiicult to analyse. They can be derived easily with the help of theory, if we keep in mind what has been said above, that we obtain a simple multiplet for each of the terms indicated in Fig. 1. In this way we also obtain the formulae for the intensities. 

Before we consider multiplets with more than one distinct coupling relationship, it is helpful to review simple multiplets, those adequately described by the n -i- 1 Rule, and begin to consider them as series of doublets by considering each individual coupling relationship separately. For example, a triplet (t) can be considered a doublet of doublets (dd) where two identical couplings (n = 2) are present (Ji = /2>. The sum of the triplet s line intensities (1 2 1) is equal to 2" where n = 2(l-i-2-i-l) = 2 = 4). Similarly, a quartet can be considered a doublet of doublet of doublets where three identical couplings (n = 3) are present (7i =J2 = J3) and the sum of the quartet s line intensities (1 3 3 1) equals 2" where n = 3(l-i-3-i-3-i-l = 2 =8). This analysis is continued in Table 7.8. 

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