The Carbon-13 Nucleus

Carbon-12, the most abundant isotope of carbon, is NMR inactive since it has a spin of zero (see Section 3.1). Carbon-13, or C, however, has odd mass and does have nuclear spin, with / =. Unfortunately, the resonances of C nuclei are more difficult to observe than those of protons ( H). They are about 6000 times weaker than proton resonances, for two major reasons. 

the natural abundance of carbon-13 is very low only 1.08% of aQ carbon atoms in nature are C atoms. If the total number of carbons in a molecule is low, it is very likely that a majority of the molecules in a sample will have no C nuclei at all. In molecules containing a C isotope, it is unlikely that a second atom in the same molecule will be a C atom. Therefore, when we observe a C spectram, we are observing a spectrum buUt up from a collection of molecules, where each molecule supphes no more than a single resonance. No single molecule supphes a complete spectrum. 

Second, since the magnetogyric ratio of a nucleus is smaller than that of hydrogen (Table 3.2), nuclei always have resonance at a frequency lower than protons. Recall that at lower frequencies, the population of excess nuclei is reduced (Table 3.3) this, in turn, reduces the sensitivity of NMR detection procedures. 

Through the use of modem Fourier transform instrumentation (Section 3.7B), it is possible to obtain NMR spectra of organic compounds even though detection of carbon signals is difficult compared to detection of proton spectra. To compensate for the low natural abundance of carbon, a greater number of individual seans of the speetrum must be accumulated than is common for a proton spectmm. 

For a given magnetic field strength, the resonance frequency of a nucleus is about one-fourth the frequency required to observe proton resonances (see Table 3.2). For example, in a 7.05-Tesla applied magnetic field, protons are observed at 300 MHz while nuclei are observed at about 75 MHz. With modem instmmentation, it is a simple matter to switch the transmitter frequency from the value required to observe proton resonances to the value required for resonances. 

For a given magnetic field strength, the resonance frequency of a nucleus is about one-fourth 

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178 Nuclear Magnetic Resonance Spectroscopy Part Two Carbon-13 Spectra 

Chapter 3 Structure of Charged Particle Tracks in Condensed Media 

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In contrast, the curve for V3 in Figure 6.38(b) is symmetrical about the centre. It is approximately parabolic but shows steeper sides corresponding to the reluctance of an oxygen nucleus to approach the carbon nucleus at either extreme of the vibrational motion. 

The lowest energy molecular orbital of singlet methylene looks like a Is atomic orbital on carbon. The electrons occupying this orbital restrict their motion to the immediate region of the carbon nucleus and do not significantly affect bonding. Because of this restriction, and because the orbital s energy is very low (-11 au), this orbital is referred to as a core orbital and its electrons are referred to as core electrons. 

Figure 8.5 A comparison of alkyl, vinylic, and acetylide anions. The acetylide anion, with sp hybridization, has more s character and is more stable. Electrostatic potential maps show that placing the negative charge closer to the carbon nucleus makes carbon appear less negative (red).

The structure of 65 was determined via a detailed mono- and bidimen-sional NMR study. In C NMR a signal at 20.3 ppm corresponds to the methyl groups and the carbon nucleus = C2 - H carbon appeared at 142.3 ppm. The gem-dimethylcyclopropene structure of 65 was consistent with an analysis of the HMBC spectrum. 

Figure 6.13 Relief map of the electron density for methanal (formaldehyde) in the molecular plane. There is a bond critical point between the carbon and the oxygen nuclei, as well as between the carbon nucleus and each hydrogen nucleus. No gradient path or bond critical point can be seen between the two hydrogen nuclei because there is no point at which the gradient of the electron density vanishes. There is no bond between the hydrogen atoms consistent with the conventional picture of the bonding in this molecule.

Now we focus on the gradient paths, which do not terminate at a nucleus, but rather link two nuclei. For example, the bond critical point between C and H in Figure 6.14 is the origin of two gradient paths. One gradient path terminates at the hydrogen nucleus, the other at the carbon nucleus. This pair of gradient paths is called an atomic interaction line. It is found... 

The use of solid state NMR for the investigation of polymorphism is easily understood based on the following model. If a compound exists in two, true polymorphic forms, labeled as A and B, each crystalline form is conformationally different. This means for instance, that a carbon nucleus in form A may be situated in a slightly different molecular geometry compared with the same carbon nucleus in form B. Although the connectivity of the carbon nucleus is the same in each form, the local environment may be different. Since the local environment may be different, this leads to a different chemical shift interaction for each carbon, and ultimately, a different isotropic chemical shift for the same carbon atom in the two different polymorphic forms. If one is able to obtain pure material for the two forms, analysis and spectral assignment of the solid state NMR spectra of the two forms can lead to the origin of the conformational differences in the two polymorphs. Solid state NMR is thus an important tool in conjunction with thermal analysis, optical microscopy, infrared (IR) spectroscopy, and powder... 

Fig. 7.2. Energy levels involved in helium fusion. The existence of an energy level of the carbon nucleus at 7.65 MeV above the ground state is particularly welcome. It considerably increases the probability of carbon synthesis in red giants.

It is easy to perceive that since the factor 26.05 corresponds only to certain definite initial and final stages of the electron, whenever a substance is burned which contains some electrons displaced from that position, the calculated value should either be smaller or larger than the experimental value, depending upon whether the electrons are nearer or farther from the carbon nucleus than those of CH4... 

As the size of an atom increases, its outer electrons move further away from the attractive force of the nucleus. The electrons are held less tightly and are said to be more polarizable. Fluoride is a nucleophile having hard or low polarizability, with its electrons held close to the nucleus, and it must approach the carbon nucleus closely before orbital overlap can occur. The outer shell of the soft iodide has loosely held electrons, and these can easily shift and overlap with the carbon atom at a relatively long distance. 

Diazoalkane carbon shifts behave similiarly to those of the isoelectronic ketenimines [357, 358], The contribution of resonance formulae with carbanionic carbons predominates, as indicated by a considerable shielding of the carbon nucleus a to the diazonium residue. 

Fig. 5.17. Carbon-13 signal assignment of aflatoxin B, [603] by two-dimensional carbon-proton shift correlation (30 mg in 0.4 mL of hexadeuteriodimethyl sulfoxide, 30 C, 100.576 MHz for 13C, 400.133 MHz for H full and strong contours correlations via one-bond couplings empty and weaker contours correlations via two- and Lhree-bond couplings). Boldface printed substructures in Lhe formula can be directly derived from this figure the carbon nucleus at 91.4 ppm, for example, is correlated with the proton at 6.72 ppm via one-bond coupling this proton is additionally correlated with the adjacent carbon nuclei at 165.1, 161.4, 107.2, and 103.5 ppm as indicated by correlation signals via two- and three-bond couplings.

On the average the s electrons are closer to the carbon nucleus than are p electrons. Therefore, the more s character there is to the C—H bond, the closer the electrons of the bond are, on the average, to the carbon nucleus. This makes it easier to remove the hydrogens as protons. This displacement of the electrons is clearly shown by the GVB orbitals (see Section 6-6) for the hydrogenbonding orbitals of ethane and ethyne (Figure 11-4). 

A sigma (a) bond is formed between atoms by the overlap of two atomic orbitals along the line that connects the atoms. Carbon uses sp hybridized orbitals to form four such bonds. These bonds are directed from the carbon nucleus toward the corners of a tetrahedron. In methane, for example, the carbon is at the center and the four hydrogens are at the corners of a regular tetrahedron with H-C-H bond angles of 109.5°. 

Faced with a choice during the early development of nuclear magnetic resonance spectrometry, most organic chemists would certainly have selected the carbon nucleus over the hydrogen nucleus for immediate investigation. After all, the carbon skeletons of rings and chains are central to organic chemistry. The problem, of course, is that the carbon skeleton consists almost completely of the 12C nucleus, which is not accessible to NMR spectrometry. The spectrometrist is left to cope with the very small amount of the 13C nucleus. 

By comparison, a saturated methine carbon (C-H) has a CSA of only 25 ppm because the mobility of electrons around the carbon nucleus is much less in an sp3-hybridized carbon and depends much less on the orientation of the C-H bond with respect to B0. In solution-state NMR we only see the isotropic chemical shift, < iso, and the fixed-position chemical shifts and the CSA value are obtained from solid-state NMR measurements. Although CSA does not affect chemical shifts in solution, it does contribute to NMR relaxation and can be exploited to sharpen peaks of large molecules such as proteins in solution. For large molecules, such as proteins, nucleic acids, and polymers, or in viscous solutions, molecular tumbling is slow and CSA broadens NMR lines due to incomplete averaging of the three principle chemical shift values on the NMR timescale. Like isotropic chemical shifts, CSA in parts per million is independent of magnetic field strength B0 but is proportional to B0 when expressed in hertz. Because linewidths are measured in... 

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