Spin One-Half Nuclei

We start by acknowledging that our goals are modest as we confront such a vast field as multinuclear NMR. In Section 3.7, we have seen the impact of other nuclei that possess a magnetic moment (especially those with spin one-half) on proton spectra. We will briefly examine the NMR spectrometry of four spin one-half nuclei, which were selected for their historic importance in organic chemistry (and related natural products and pharmaceutical fields), biochemistry, and polymer chemistry. These four nuclei, l5N, 19F, 29Si, and 31P, are presented with a few simple examples and a brief consideration of important experimental factors and limitations. 

Consider two spin one-half nuclei with spins I a and Ib in an applied field B = (0 0 B). The free energy expression... 

In the Breit Hamiltonian in (3.2) we have omitted all terms which depend on spin variables of the heavy particle. As a result the corrections to the energy levels in (3.4) do not depend on the relative orientation of the spins of the heavy and light particles (in other words they do not describe hyperfine splitting). Moreover, almost all contributions in (3.4) are independent not only of the mutual orientation of spins of the heavy and light particles but also of the magnitude of the spin of the heavy particle. The only exception is the small contribution proportional to the term Sio, called the Darwin-Foldy contribution. This term arises in the matrix element of the Breit Hamiltonian only for the spin one-half nucleus and should be omitted for spinless or spin one nuclei. This contribution combines naturally with the nuclear size correction, and we postpone its discussion to Subsect. 6.1.2 dealing with the nuclear size contribution. 

The DD relaxation mechanism is combined of both intramolecular and intermolecular processes. A detailed account of the derivation of Ti from the various intermolecular and intramolecular dipole-dipole interactions has been described by Bloembergen et al. (30). The intramolecular relaxation process is governed by the angular reorientation of the vector connecting the spin one-half (5) nuclei—in this case either H or in benzene or perfluorobenzene. The relaxation rate (1/Ti) is... 

Finally, let us consider molecules with identical nuclei that are subject to C (n > 2) rotations. For C2v molecules in which the C2 rotation exchanges two nuclei of half-integer spin, the nuclear statistical weights of the symmetric and antisymmetric rotational levels will be one and three, respectively. For molecules where C2 exchanges two spinless nuclei, one-half of the rotational levels (odd or even J values, depending on the vibrational and electronic states)... 

Fiq. 1. a, Energy level diagram for an electron having no orbital momentum and no interacting magnetic nuclei. 6, As for a but with three equally coupled nuclei with a spin of one-half (e.g. the methyl radical). 

We described the nuclear Overhauser effect (NOE) among protons in Section 3.16 we now discuss the het-eronuclear NOE, which results from broadband proton decoupling in 13C NMR spectra (see Figure 4.1b). The net effect of NOE on 13C spectra is the enhancement of peaks whose carbon atoms have attached protons. This enhancement is due to the reversal of spin populations from the predicted Boltzmann distribution. The total amount of enhancement depends on the theoretical maximum and the mode of relaxation. The maximum possible enhancement is equal to one-half the ratio of the nuclei s magnetogyric ratios (y s) while the... 

The previous three chapters have shown that nuclear magnetic resonance experiments with 1H and 13C nuclei are enormously useful to the chemist working with organic compounds. There is no need, however, to limit ourselves to these two important nuclei. Indeed, there are 120 different nuclei whose spin number, /, is greater than zero and, therefore, theoretically observable in an NMR experiment. Of these 120 nuclei, 31 of them are dipolar, which means that their spin number is one-half (/ = ). 

Nuclei with spin greater than one-half are not covered in this treatment. We note that, with proper consideration of experimental details, we can record a spectrum from a deuterium sample. 

Nuclei can be classified into three types according to their magnetic properties those with no magnetic moment (/ = 0) those with a nuclear spin equal to one half (/ = 1/2) but no quadrupole moment and those with a spin of one or larger (/> 1/2) and a quadrupole moment. 

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