Carbon nucleus, spin

Example. The carbon nucleus in an external magnetic field. We consider a single carbon nucleus (spin quantum number Ic = j) in a molecule with non-magnetic other nuclei. 

For 19F Fermi contact shift of fluorine bound to sp2 carbon atoms, spin density on the nucleus arises from spin polarization by as for analogous CC moieties, and from spin polarization by /Op, which occurs via direct delocalization through C—F ji bonding (Fig. 2.18). The hyperfine coupling is therefore... 

Now assume that the carbon nucleus undergoes transition and inverts its spin. The excited state that results from the less-favored ground state (seen at the top of part b) turns out to have a lower energy than the one resulting from the favored ground state (top of part a) because aU of its nuclear and electronic spins are paired. Thus, we see two different transitions for the nucleus (spin = -hi), depending on the spin of the attached hydrogen. As a result, in a proton-coupled NMR spectrum a doublet is observed for a methine carbon ( C— H). 

A carbon nucleus does not spin and so does not behave like a bar magnet and is invisible in NMR. That is a blessing, because otherwise even a quite simple organic molecule would give an impossibly complex NMR spectrum. However, carbon atoms can be revealed cautiously by replacing ordinary carbon atoms, carbon-12, with an isotope, carhon-13, which has an extra neutron in its nucleus and is magnetic. Judicious replacement of carbon-12 by carbon-13 can therefore be used to map the locations of carbon atoms too, and the identity and structure of the molecule can then be pinned down unambiguously. 

Samples with natural abundance are the usual case in routine application. For a molecule with N carbon atoms, the NMR spectrum usually appears as a mixture of N different spin systems CHaHiHjn,..., Hr, where the subscripts d, 1, m,. .., r refer to protons directly attached to, or separated by two or more bonds from, the carbon, respectively. Accordingly, the spectrum is a superposition of N subspectra centered at the chemical shift d,- of the carbon nucleus i with N. In case of molec-... 

To insure acquisition of quantitative NMR spectra, the rf Bi field pulses must be sufficiently separated by delay times that insure spin relaxation is realized for all carbon nuclei in the sample (see Fig. 20.5). If the repetition rate of the rf pulses approaches the Tis of some of the C nuclei in the sample, then incorrect relative intensities will be recorded. As a practical mle [12], the delay between rf pulses should be five times the Ti of the slowest relaxing carbon nucleus in the sample. 

Besides infrared spectroscopy the most convenient method for deducing the molecular structure is nuclear magnetic resonance spectroscopy (nmr). The basic principle of this method is the detection of changes in the orientation of the atomic nuclear spin of hydrogen (the spin of a proton) and carbon (the spin of the nucleus of the isotope). 

Table 3.26 shows the results of ab initio calculations of the CH3 hyperfine coupling constants. The correct qualitative results are obtained—a positive spin density at the carbon nucleus and a negative spin density at the hydrogen nuclei. The magnitudes of the spin densities are too large, however. They... 

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