Inequivalent nuclei

15 mT in liquid solution. As in the previous example the protons will give a 1 4 6 4 1 hyperfine pattern. The Pascal triangle method does not apply to nuclei with spins I Vi, see Exercise E3.2 for the construction of a stick diagram for two nuclei with / = 1, to yield a quintet hyperfine pattern in the 1 2 3 2 1 ratio. The two quintets, due to the four equivalent protons, and the two nuclei (/ = 1) are not well separated, see spectrum in Exercise E3.2. 

Even more complex ESR spectra can occur for nitrogen-containing aromatic radicals of the type in Fig. 3.4. A stickplot analysis is not easily performed. At this level of complexity a combination of ESR and ENDOR measurements, simulation of the observed spectra, and theoretical calculations of hyperfine coupling constants is often applied to obtain a reliable assignment. The procedure to obtain the coupling constants from the ENDOR spectrum of the Wurster blue cation is indicated in Exercise E3.3. ENDOR lines due to can be observed more easily than signals due to N, a phenomenon that is quite typical in CW-ENDOR studies. The hyperfine couplings due to N nuclei may therefore have to be deduced from simulation of the ESR spectrum. 

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A great deal of work has been done in measuring chemically equivalent and inequivalent nuclei, using complex and sophisticated pulse techniques, often while rotating the samples (e.g. MAS magic angle spinning, a technique developed ca. 50 years ago). We shall not herein pay attention to the details of the actual instrumental techniques. 

An interesting example is available of inequivalent nuclei becoming equivalent on raising the temperature and going through a phase transition, reversibly. This occurs in squaric acid C4(0)2(0H)2, studied by single-crystal 13C NMR,29 and later (2004) also by 170 NMR. Here, MAS was used to narrow the lines sufficiently to observe the changes in the isotropic parts of the chemical-shift matrices. The phase transition occurs at 373 K. 

P. Tekely, D. Reichert, H. Zimmerman and Z. Luz, Initial conditions for carbon-13 MAS NMR ID exchange involving chemically equivalent and inequivalent nuclei.. Magn. Reson., 2000, 145, 173-183. 

As the number of nuclei increases, the complexity of the spectrum rapidly increases since the spectral density depends on the number of inequivalent nuclei according to ... 

Vo is the nuclear frequency at the applied magnetic field of ca. 3390 G. Group the lines 1-6 due to hyperfine couplings with H (two groups of inequivalent nuclei) and (two equivalent nuclei) in the figure below in pairs v corresponding to the electron spin quantum number nts = /2. 

The data obtained in such experiments can be used to derive kinetic parameters. For a process with first-order kinetics involving two equally intense singlets (i.e. equal numbers of two inequivalent nuclei, with no coupling between them), with frequencies differing by Av, the rate constant can be approximated as... 

Other possible heteroatoms that may be present. Certainly proton and carbon chemical shifts and correlations (or lack thereof) will provide clues to the presence of other nuclei. Also, as previously discussed, NMR is limited to identifying magnetically inequivalent nuclei.Therefore, the NMR spectra of a particular molecule often will be indistinguishable from the corresponding dimer, trimer, etc. Possible structures will therefore include these equivalent structures as well. We need to rely on molecular mass and other complimentary information to make this distinction. This brings us to the secondary interpretation (Figure 36). 

Interpretation of the spectra from solid-state NMR spectroscopy is more complicated than the interpretation of solution NMR spectra [2]. In solution NMR spectroscopy, the nature of the chemically inequivalent nuclei that give rise to resolved resonances must be determined. In the solid state, however, not only must structural assignments of the chemically inequivalent carbons be made, but also whether the chemically inequivalent nuclei are magnetically inequivalent as a result of their solid-state environments [3]. 

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