NMR Absorptions

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

The bracketed term in Eq. (4-60b) describes a Lorentzian line shape for the NMR absorption band. The maximum in the band occurs at the resonance frequency, wq. Expressed in units of X0W0T2/2, the maximum value of x" s 1 at one-half this maximum peak height we find, by substitution, that (wq — w) = IIT. Using w = 2 ttv to convert to frequency (in Hz) gives (vq — v) = 3-7 T 2. However, the peak width is twice this, or... 

Figure 4-8. NMR absorption by a hypothetical two-identical site system with chemical exchange (/I) Slow exchange limit. (B) Moderately slow exchange. (D) Coalescence. (F) Fast exchange limit.

From the description thus far, you might expect all 1H nuclei in a molecule to absorb energy at the same frequency and all 13C nuclei to absorb at the same frequency. If so, we would observe only a single NMR absorption band in the H or 13C spectrum of a molecule, a situation that would be of little use. In fact, the absorption frequency is not the same for all 4H or all 13C nuclei. 

By using a system of measurement in which NMR absorptions are expressed in relative terms (parts per million relative to spectrometer frequency) rather than absolute terms (Hz), it s possible to compare spectra obtained on different instruments. The chemical shift of an NMR absorption in 8 units is constant, regardless of the operating frequency of the spectrometer. A H nucleus that absorbs at 2.0 8 on a 200 MHz instrument also absorbs at 2.0 8 on a 500 MHz instrument. 

At what approximate positions would you expect H2C=CHC02CH2CH3, to show l3C NMR absorptions ... 

For relatively small molecules, a quick look at a structure is often enough to decide how many kinds of protons are present and thus how many NMR absorptions might appear. If in doubt, though, the equivalence or nonequiva-lence of two protons can be determined by comparing the structures that would be formed if each hydrogen were replaced by an X group. There are four possibilities. 

I One possibility is that the protons are chemically unrelated and thus nonequivalent. If so, the products formed on replacement of Ii by X would be different constitutional isomers. In butane, for instance, the -CH3 protons are different from the -CH2- protons, would give different products on replacement by X, and would likely show different NMR absorptions. 

B The fourth possibility arises in chiral molecules, such as (R)-2-butanol. The two — CH2- hydrogens at C3 are neither homotopic nor enantiotopic. Since replacement of a hydrogen at C3 would form a second chirality center, different diastereomers (Section 9.6) would result depending on whether the pro-R or pro-S hydrogen were replaced. Such hydrogens, whose replacement by X leads to different diastereomers, are said to be diastereotopic. Diastereotopic hydrogens are neither chemically nor electronically equivalent. They are completely different and would likely show different NMR absorptions. 

How many kinds of electronically nonequivalent protons are present in each of [ the following compounds, and thus how many NMR absorptions might you expect in each ... 

The following NMR absorptions were obtained on a spectrometer operating at 200 MHz and are given in hertz downfield from the TMS standard. Convert the absorptions to 5 units. 

How many 13C NMR absorptions would you expect for c/s-1,3-dimethyl-cyclohexane For fra/is-l,3-dimethylcyclohexane Explain. 

Figure 15.16 Some, 3C NMR absorptions of aromatic compounds (8 units).

Phenols, like all aromatic compounds, show H NMR absorptions near 7 to 8 6, the expected position for aromatic-ring protons (Section 15.8). In addition, phenol O—H protons absorb at 3 to 8 5. In neither case are these... 

Hydrogens on carbon next to an ether oxygen are shifted downfield from the normal alkane resonance and show U-f NMR absorptions in the region 3.4 to 4.5 8. This downfield shift is clearly seen in the spectrum of dipropyl ether shown in Figure 18.4. 

The carbonyl-group carbon atoms of aldehydes and ketones have characteristic 13C NMR resonances in the range 190 to 215 8. Since no other kinds of carbons absorb in this range, the presence of an NMR absorption near 200 8 is clear evidence for a carbonyl group. Saturated aldehyde or ketone carbons usually absorb in the region from 200 to 215 8, while aromatic and a,p-unsaturated carbonyl carbons absorb in the 190 to 200 5 region. 

Doublet (Section 13.11) A two-line NMR absorption caused by spin-spin splitting when the spin of the nucleus under observation couples with the spin of a neighboring magnetic nucleus. 

Homotopic (Section 13.8) Hydrogens that give the identical structure on replacement by X and thus show identical NMR absorptions. 

Chlorobenzene, electrostatic potential map of, 565 13C NMR absorptions of, 536 phenol from, 575 p-Chlorobenzoic acid, pKa of, 760... 

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