- A second possibility is that the protons are chemically identical and thus electronically equivalent. If so, the same product would be formed regardless of which H is substituted by X . In butane, for instance, the six $-\mathrm{CH}_{3}$ hydrogens on C 1 and C 4 are identical, would give the identical structure on substitution by X , and would show an identical NMR absorption. Such protons are said to be homotopic.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0422.jpg?height=310&width=830&top_left_y=189&top_left_x=691)
- The third possibility is a bit more subtle. Although they might at first seem homotopic, the two $-\mathrm{CH}_{2}-$ hydrogens on C 2 in butane (and the two $-\mathrm{CH}_{2}$ - hydrogens on C 3 ) are in fact not identical. Substitution by X of a hydrogen at C2 (or C3) would form a new chirality center, so different enantiomers (Section 5.1) would result, depending on whether the pro- $R$ or pro- $S$ hydrogen had been substituted (Section 5.11). Such hydrogens, whose substitution by X would lead to different enantiomers, are said to be enantiotopic. Enantiotopic hydrogens, even though not identical, are nevertheless electronically equivalent and thus have the same NMR absorption.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0422.jpg?height=232&width=513&top_left_y=800&top_left_x=562)
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13.7 ${ }^{1} \mathrm{H}$ NMR Spectroscopy and Proton Equivalence -

The two hydrogens on C2 (and
The two possible substitution
products are enantiomers.
on C3) are enantiotopic and have the same NMR absorption.


- The fourth possibility arises in chiral molecules, such as ( $R$ )-2-butanol. The two $-\mathrm{CH}_{2}$ - hydrogens at C 3 are neither homotopic nor enantiotopic. Because substitution of a hydrogen at C3 would form a second chirality center, different diastereomers (Section 5.6) would result, depending on whether the pro- $R$ or pro- $S$ hydrogen had been substituted. Such hydrogens, whose substitution 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.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0422.jpg?height=223&width=1085&top_left_y=1425&top_left_x=585)


The two hydrogens on C3 are diastereotopic and have different NMR absorptions.


The two possible substitution products are diastereomers.


PROBLEM Identify the indicated sets of protons as unrelated, homotopic, enantiotopic, or diastereotopic:
13-12 (a)


PROBLEM How many kinds of electronically nonequivalent protons are present in each of the following
13-13 compounds, and thus how many NMR absorptions might you expect in each?
(a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}$
(b) $\mathrm{CH}_{3} \mathrm{OCH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}$
(c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NO}_{2}$
(d) Methylbenzene
(e) 2-Methyl-1-butene (f) cis-3-Hexene


PROBLEM How many absorptions would you expect ( $S$ )-malate, an intermediate in carbohydrate metabolism, 13-14 to have in its ${ }^{1} \mathrm{H}$ NMR spectrum? Explain.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0423.jpg?height=267&width=367&top_left_y=303&top_left_x=413)


(S)-Malate -


(S)-Malate - 13.8 More Complex Spin-Spin Splitting Patterns

In the ${ }^{1} \mathrm{H}$ NMR spectra we've seen so far, the chemical shifts of different protons have been distinct and the spin-spin splitting patterns have been straightforward. It often happens, however, that different kinds of hydrogens in a molecule have accidentally overlapping signals. The spectrum of toluene (methylbenzene) in FIGURE 13.13, for example, shows that the five aromatic ring protons give a complex, overlapping pattern, even though they aren't all equivalent.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0423.jpg?height=486&width=1389&top_left_y=901&top_left_x=365)

FIGURE 13.13 The ${ }^{1}$ H NMR spectrum of toluene, showing the accidental overlap of the five nonequivalent aromatic ring protons.
Yet another complication in ${ }^{1} \mathrm{H}$ NMR spectroscopy arises when a signal is split by two or more nonequivalent kinds of protons, as is the case with trans-cinnamaldehyde, isolated from oil of cinnamon (FIGURE 13.14). Although the $n+1$ rule predicts splitting caused by equivalent protons, splittings caused by nonequivalent protons are more complex.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0423.jpg?height=494&width=1392&top_left_y=1645&top_left_x=364)

FIGURE 13.14 The ${ }^{\mathbf{1}} \mathbf{H}$ NMR spectrum of trans-cinnamaldehyde. The signal of the proton at C 2 (blue) is split into four peaks-a doublet of doublets-by the two nonequivalent neighboring protons.

To understand the ${ }^{1} \mathrm{H}$ NMR spectrum of trans-cinnamaldehyde, we have to isolate the different parts and look at the signal of each proton individually.


- The five aromatic proton signals (black in FIGURE 13.14) overlap into a complex pattern with a large peak at $7.42 \delta$ and a broad absorption at $7.57 \delta$.
- The aldehyde proton signal at C1 (red) appears in the normal downfield position at $9.69 \delta$ and is split into a doublet with $J=6 \mathrm{~Hz}$ by the adjacent proton at C 2 .
- The vinylic proton at C3 (green) is next to the aromatic ring and is therefore shifted downfield from the normal vinylic region. This C3 proton signal appears as a doublet centered at $7.49 \delta$. Because it has one neighbor proton at C 2 , its signal is split into a doublet, with $J=12 \mathrm{~Hz}$.
- The C2 vinylic proton signal (blue) appears at $6.73 \delta$ and shows an interesting, four-line absorption pattern. It is coupled to the two nonequivalent protons at C 1 and C 3 with two different coupling constants: $J_{1-2}=6$ Hz and $J_{2-3}=12 \mathrm{~Hz}$.


A good way to understand the effect of multiple coupling, such as that occurring for the C2 proton of trans-cinnamaldehyde, is to draw a tree diagram, like that in FIGURE 13.15. The diagram shows the individual effect of each coupling constant on the overall pattern. Coupling with the C3 proton splits the signal of the C2 proton in trans-cinnamaldehyde into a doublet with $J=12 \mathrm{~Hz}$. Further coupling with the aldehyde proton then splits each peak of the doublet into new doublets with $J=6 \mathrm{~Hz}$, and we therefore observe a four-line spectrum for the C 2 proton.
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$6.73 \delta$


FIGURE 13.15 A tree diagram for the C2 proton of trans-cinnamaldehyde shows how it is coupled to the C1 and C3 protons with different coupling constants.


One further trait evident in the cinnamaldehyde spectrum is that the four peaks of the C 2 proton signal are not all the same size. The two left-hand peaks are somewhat larger than the two right-hand peaks. Such a size difference occurs whenever coupled nuclei have similar chemical shifts-in this case, $7.49 \delta$ for the C3 proton and $6.73 \delta$ for the C 2 proton. The peaks nearer the signal of the coupled partner are always larger, and the peaks farther from the signal of the coupled partner are always smaller. Thus, the left-hand peaks of the C2 proton multiplet at $6.73 \delta$ are closer to the C3 proton absorption at $7.49 \delta$ and are larger than the right-hand peaks. At the same time, the right-hand peak of the C3 proton doublet at $7.49 \delta$ is larger than the left-hand peak because it is closer to the C 2 proton multiplet at $6.73 \delta$. This skewing effect on multiplets can often be useful because it tells where to look in the spectrum to find the coupled partner: look in the direction of the larger peaks.


PROBLEM 3-Bromo-1-phenyl-1-propene shows a complex NMR spectrum in which the vinylic proton at C2 is
13-15 coupled with both the C 1 vinylic proton $(J=16 \mathrm{~Hz}$ ) and the C 3 methylene protons ( $J=8 \mathrm{~Hz}$ ). Draw a tree diagram for the C 2 proton signal, and account for the fact that a five-line multiplet is observed.
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3-Bromo-1-phenyl-1-propene -


3-Bromo-1-phenyl-1-propene - 13.9 Uses of ${ }^{1} \mathrm{H}$ NMR Spectroscopy

NMR is used to help identify the product of nearly every reaction run in the laboratory. For example, we said in Section 8.5 that hydroboration-oxidation of alkenes occurs with non-Markovnikov regiochemistry to yield the less highly substituted alcohol. With the help of NMR, we can now prove this statement.
Does hydroboration-oxidation of methylenecyclohexane yield cyclohexylmethanol or 1-methylcyclohexanol?
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0425.jpg?height=169&width=1017&top_left_y=192&top_left_x=581)


Methylenecyclohexane
Cyclohexylmethanol 1-Methylcyclohexanol
The ${ }^{1} \mathrm{H}$ NMR spectrum of the reaction product is shown in FIGURE 13.16a. The spectrum shows a two-proton peak at $3.40 \delta$, indicating that the product has a $-\mathrm{CH}_{2}$ - group bonded to an electronegative oxygen atom $\left(-\mathrm{CH}_{2} \mathrm{OH}\right)$. Furthermore, the spectrum shows no large three-proton singlet absorption near $1 \delta$, where we would expect the signal of a quaternary $-\mathrm{CH}_{3}$ group to appear. (FIGURE 13.16b) gives the spectrum of 1-methylcyclohexanol, the alternative product.) Thus, it's clear that cyclohexylmethanol is the reaction product.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0425.jpg?height=1058&width=1408&top_left_y=647&top_left_x=353)

FIGURE 13.16 (a) The ${ }^{\mathbf{1}} \mathrm{H}$ NMR spectrum of cyclohexylmethanol, the product from hydroboration-oxidation of methylenecyclohexane, and (b) the ${ }^{1} H$ NMR spectrum of 1-methylcyclohexanol, the possible alternative reaction product.


PROBLEM How could you use ${ }^{1} \mathrm{H}$ NMR to determine the regiochemistry of electrophilic addition to alkenes?
13-16 For example, does addition of HCl to 1-methylcyclohexene yield 1-chloro-1-methylcyclohexane or 1-chloro-2-methylcyclohexane?


$13.10{ }^{13} \mathrm{C}$ NMR Spectroscopy: Signal Averaging and FT-NMR -

In some ways, it's surprising that carbon NMR is even possible. After all, ${ }^{12} \mathrm{C}$, the most abundant carbon isotope, has no nuclear spin and can't be seen by NMR. Carbon-13 is the only naturally occurring carbon isotope with a nuclear spin, but its natural abundance is only $1.1 \%$. Thus, only about 1 of every 100 carbon atoms in an organic sample can be observed by NMR. The problem of low abundance has been overcome, however, by the use of signal averaging and Fourier-transform NMR (FT-NMR). Signal averaging increases instrument sensitivity, and FT-NMR increases instrument speed.


The low natural abundance of ${ }^{13} \mathrm{C}$ means that any individual NMR spectrum is extremely "noisy." That is, the signals are so weak that they are cluttered with random background electronic noise, as shown in FIGURE 13.17a. If, however, hundreds or thousands of individual runs are added together by a computer and then averaged, a greatly improved spectrum results (FIGURE 13.17b). Background noise, because of its random nature, increases very slowly as the runs are added, while the nonzero signals stand out clearly. Unfortunately,
the value of signal averaging is limited when using the method of NMR spectrometer operation described in Section 13.2, because it takes about 5 to 10 minutes to obtain a single spectrum. Thus, a faster way to obtain spectra is needed if signal averaging is to be used.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0426.jpg?height=1063&width=1403&top_left_y=344&top_left_x=361)


FIGURE 13.17 Carbon-13 NMR spectra of 1-pentanol, $\mathbf{C H}_{\mathbf{3}} \mathbf{C H}_{\mathbf{2}} \mathbf{C H}_{\mathbf{2}} \mathbf{C H}_{\mathbf{2}} \mathbf{C H}_{\mathbf{2}} \mathbf{O H}$. Spectrum (a) is a single run, showing the large amount of background noise. Spectrum (b) is an average of 200 runs.


In the method of NMR spectrometer operation described in Section 13.2, the rf frequency is held constant while the strength of the magnetic field is varied so that all signals in the spectrum are recorded sequentially. In the FT-NMR technique used by modern spectrometers, however, all the signals are recorded simultaneously. A sample is placed in a magnetic field of constant strength and is irradiated with a short pulse of rf energy that covers the entire range of useful frequencies. All ${ }^{1} \mathrm{H}$ or ${ }^{13} \mathrm{C}$ nuclei in the sample resonate at once, giving a complex, composite signal that is mathematically manipulated using so-called Fourier transforms and then displayed in the usual way. Because all resonance signals are collected at once, it takes only a few seconds rather than a few minutes to record an entire spectrum.


Combining the speed of FT-NMR with the sensitivity enhancement of signal averaging is what gives modern NMR spectrometers their power. Literally thousands of spectra can be taken and averaged in a few hours, resulting in sensitivity so high that a ${ }^{13} \mathrm{C}$ NMR spectrum can be obtained from less than 0.1 mg of sample and a ${ }^{1} \mathrm{H}$ spectrum can be recorded from only a few micrograms.


One further question needs to be answered before moving forward with our discussion of ${ }^{13} \mathrm{C}$ NMR. Why is spin-spin splitting seen only for ${ }^{1} \mathrm{H}$ NMR? Why is there no splitting of carbon signals into multiplets in ${ }^{13} \mathrm{C}$ NMR? After all, you might expect that the spin of a given ${ }^{13} \mathrm{C}$ nucleus would couple with the spin of an adjacent magnetic nucleus, either ${ }^{13} \mathrm{C}$ or ${ }^{1} \mathrm{H}$.


No coupling of a ${ }^{13} \mathrm{C}$ nucleus with nearby carbons is seen because their low natural abundance makes it unlikely that two ${ }^{13} \mathrm{C}$ nuclei will be adjacent. No coupling of a ${ }^{13} \mathrm{C}$ nucleus with nearby hydrogens is seen because ${ }^{13} \mathrm{C}$ spectra are normally recorded using broadband decoupling. At the same time that the sample is irradiated with a pulse of rf energy to cover the carbon resonance frequencies, it is also irradiated by a second band of rf energy covering all the hydrogen resonance frequencies. This second irradiation makes the hydrogens spin-flip so rapidly that their local magnetic fields average to zero and no coupling with carbon spins occurs.


$13.10{ }^{13} \mathrm{C}$ NMR Spectroscopy: Signal Averaging and FT-NMR - 13.11 Characteristics of ${ }^{13}$ C NMR Spectroscopy

At its simplest, ${ }^{13} \mathrm{C}$ NMR makes it possible to count the number of different carbon atoms in a molecule. Look at the ${ }^{13} \mathrm{C}$ NMR spectra of methyl acetate and 1-pentanol shown previously in FIGURE 13.4b and FIGURE 13.17b. In each case, a single sharp resonance line is observed for each different carbon atom.
Most ${ }^{13} \mathrm{C}$ resonances are between 0 and 220 ppm downfield from the TMS reference line, with the exact chemical shift of each ${ }^{13} \mathrm{C}$ resonance dependent on that carbon's electronic environment within the molecule. FIGURE 13.18 shows the correlation of chemical shift with environment.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0427.jpg?height=537&width=1519&top_left_y=561&top_left_x=298)


The factors that determine chemical shifts are complex, but it's possible to make some generalizations from the data in FIGURE 13.18. One trend is that a carbon atom's chemical shift is affected by the electronegativity of nearby atoms. Carbons bonded to oxygen, nitrogen, or halogen absorb downfield (to the left) of typical alkane carbons. Because electronegative atoms attract electrons, they pull electrons away from neighboring carbon atoms, causing those carbons to be deshielded and to come into resonance at a lower field.


Another trend is that $s p^{3}$-hybridized carbons generally absorb from 0 to $90 \delta$, while $s p^{2}$ carbons absorb from 110 to 220 . Carbonyl carbons ( $\mathrm{C}=0$ ) are particularly distinct in ${ }^{13} \mathrm{C}$ NMR and are always found at the lowfield end of the spectrum, from 160 to $220 \delta$. FIGURE 13.19 shows the ${ }^{13} \mathrm{C}$ NMR spectra of 2 -butanone and para-bromoacetophenone and indicates the peak assignments. Note that the $\mathrm{C}=\mathrm{O}$ carbons are at the left edge of the spectrum in each case.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0428.jpg?height=1093&width=1418&top_left_y=169&top_left_x=348)


FIGURE 13.19 Carbon-13 NMR spectra of (a) 2-butanone and (b) para-bromoacetophenone.
The ${ }^{13} \mathrm{C}$ NMR spectrum of para-bromoacetophenone is interesting in several ways. Note particularly that only six carbon absorptions are observed, even though the molecule contains eight carbons. para-bromoacetophenone has a symmetry plane that makes ring carbons 4 and $4^{\prime}$, and ring carbons 5 and $5^{\prime}$ equivalent. (Remember from Section 2.4 that aromatic rings have two resonance forms.) Thus, the six ring carbons show only four absorptions in the range 128 to $137 \delta$.
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para-Bromoacetophenone
A second interesting point about both spectra in FIGURE 13.19 is that the peaks aren't uniform in size. Some peaks are larger than others even though they are one-carbon resonances (except for the two 2-carbon peaks of para-bromoacetophenone). This difference in peak size is a general feature of broadband-decoupled ${ }^{13} \mathrm{C}$ NMR spectra, and explains why we can't integrate ${ }^{13} \mathrm{C}$ NMR spectra in the same way we integrate the resonances in a ${ }^{1} \mathrm{H}$ NMR spectrum. The local environment of each carbon atom determines not only its chemical shift but also the time it takes for the nuclei to return to their equilibrium state after receiving a pulse of rf radiation and flipping their spins. Quaternary carbons, regardless of their hybridization state or substituents, typically give smaller resonances than primary, secondary, or tertiary carbons.


WORKED EXAMPLE 13.3 -


Predicting Chemical Shifts in ${ }^{13} \mathrm{C}$ NMR Spectra -

At what approximate positions would you expect ethyl acrylate, $\mathrm{H}_{2} \mathrm{C}=\mathrm{CHCO}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}$, to show ${ }^{13} \mathrm{C}$ NMR absorptions?


Strategy -

Identify the distinct carbons in the molecule, and note whether each is alkyl, vinylic, aromatic, or in a carbonyl group. Then predict where each absorbs, using FIGURE 13.18 as necessary.


Solution -

Ethyl acrylate has five chemically distinct carbons: two different $\mathrm{C}=\mathrm{C}$, one $\mathrm{C}=\mathrm{O}$, one $\mathrm{O}-\mathrm{C}$, and one alkyl C . From FIGURE 13.18, the likely absorptions are
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0429.jpg?height=245&width=519&top_left_y=517&top_left_x=803)


Solution -

The actual absorptions are at $14.1,60.5,128.5,130.3$, and $166.0 \delta$.


Solution -

PROBLEM Predict the number of carbon resonance lines you would expect in the ${ }^{13}$ C NMR spectra of the 13-17 following compounds:
(a) Methylcyclopentane (b) 1-Methylcyclohexene (c) 1,2-Dimethylbenzene
(d) 2-Methyl-2-butene
(e)
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Solution -

PROBLEM Propose structures for compounds that fit the following descriptions:
13-18 (a) A hydrocarbon with seven lines in its ${ }^{13} \mathrm{C}$ NMR spectrum
(b) A six-carbon compound with only five lines in its ${ }^{13} \mathrm{C}$ NMR spectrum
(c) A four-carbon compound with three lines in its ${ }^{13} \mathrm{C}$ NMR spectrum


Solution -

PROBLEM Classify the resonances in the ${ }^{13} \mathrm{C}$ NMR spectrum of methyl propanoate, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{CH}_{3}$ (Figure 13-19 13.20).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0429.jpg?height=505&width=1389&top_left_y=1536&top_left_x=455)

FIGURE $13.20{ }^{13} \mathrm{C}$ NMR spectrum of methyl propanoate, Problem 19.


Solution - 13.12 DEPT ${ }^{13} \mathrm{C}$ NMR Spectroscopy

Numerous techniques developed in recent years have made it possible to obtain enormous amounts of information from ${ }^{13} \mathrm{C}$ NMR spectra. Among these techniques is one called DEPT-NMR, for distortionless enhancement by polarization transfer, which makes it possible to distinguish between signals due to $\mathrm{CH}_{3}, \mathrm{CH}_{2}$, CH , and quaternary carbons. That is, the number of hydrogens attached to each carbon in a molecule can be determined.

A DEPT experiment is usually done in three stages, as shown in FIGURE 13.21 for 6-methyl-5-hepten-2-ol. The first stage is to run an ordinary spectrum (called a broadband-decoupled spectrum) to locate the chemical shifts
of all carbons. Next, a second spectrum called a DEPT-90 is run, using special conditions under which only signals due to CH carbons appear. Signals due to $\mathrm{CH}_{3}, \mathrm{CH}_{2}$, and quaternary carbons are absent. Finally, a third spectrum called a DEPT-135 is run, using conditions under which $\mathrm{CH}_{3}$ and CH resonances appear as positive signals, $\mathrm{CH}_{2}$ resonances appear as negative signals-that is, as peaks below the baseline-and quaternary carbons are again absent.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0430.jpg?height=1606&width=1407&top_left_y=430&top_left_x=359)

FIGURE 13.21 DEPT-NMR spectra for 6-methyl-5-hepten-2-ol. Part (a) is an ordinary broadband-decoupled spectrum, which shows signals for all eight carbons. Part (b) is a DEPT-90 spectrum, which shows only signals for the two CH carbons. Part (c) is a DEPT-135 spectrum, which shows positive signals for the two CH and three $\mathrm{CH}_{3}$ carbons and negative signals for the two $\mathrm{CH}_{2}$ carbons.

Putting together the information from all three spectra makes it possible to tell the number of hydrogens attached to each carbon. The CH carbons are identified in the DEPT- 90 spectrum, the $\mathrm{CH}_{2}$ carbons are identified as negative peaks in the DEPT- 135 spectrum, the $\mathrm{CH}_{3}$ carbons are identified by subtracting the CH peaks from the positive peaks in the DEPT-135 spectrum, and quaternary carbons are identified by subtracting all peaks in the DEPT-135 spectrum from the peaks in the broadband-decoupled spectrum.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0431.jpg?height=218&width=933&top_left_y=192&top_left_x=599)
c Subtract DEPT-135 from broadband-decoupled spectrum
CH DEPT-90
$\mathrm{CH}_{2}$ Negative DEPT-135
$\mathrm{CH}_{3}$ Subtract DEPT-90 from positive DEPT-135


WORKED EXAMPLE 13.4 -


Assigning a Chemical Structure from a ${ }^{13}$ C NMR Spectrum -

Propose a structure for an alcohol, $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}$, that has the following ${ }^{13} \mathrm{C}$ NMR spectral data:
Broadband decoupled ${ }^{13}$ C NMR: 19.0, 31.7, 69.5 ס;
DEPT-90: 31.7 ס;
DEPT-135: positive peak at $19.0 \delta$, negative peak at $69.5 \delta$.


Strategy -

As noted in Section 7.2, it usually helps with compounds of known formula but unknown structure to calculate the compound's degree of unsaturation. In the present instance, a formula of $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}$ corresponds to a saturated, open-chain molecule.


Strategy -

To gain information from the ${ }^{13} \mathrm{C}$ data, let's begin by noting that the unknown alcohol has four carbon atoms, yet has only three NMR absorptions, which implies that two of the carbons must be equivalent. Looking at chemical shifts, two of the absorptions are in the typical alkane region (19.0 and $31.7 \delta$ ), while one is in the region of a carbon bonded to an electronegative atom ( $69.5 \delta$ )-oxygen in this instance. The DEPT-90 spectrum tells us that the alkyl carbon at $31.7 \delta$ is tertiary (CH); the DEPT- 135 spectrum tells us that the alkyl carbon at $19.0 \delta$ is a methyl $\left(\mathrm{CH}_{3}\right)$ and that the carbon bonded to oxygen ( $69.5 \delta$ ) is secondary $\left(\mathrm{CH}_{2}\right)$. The two equivalent carbons are probably both methyls bonded to the same tertiary carbon, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-$. We can now put the pieces together to propose a structure: 2-methyl-1-propanol.


Solution -


Solution -

PROBLEM Assign a chemical shift to each carbon in 6-methyl-5-hepten-2-ol (Figure 13.21).


13-20 -

PROBLEM Estimate the chemical shift of each carbon in the following molecule. Predict which carbons will 13-21 appear in the DEPT-90 spectrum, which will give positive peaks in the DEPT-135 spectrum, and which will give negative peaks in the DEPT-135 spectrum.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0432.jpg?height=353&width=470&top_left_y=187&top_left_x=407)


13-20 -

PROBLEM Propose a structure for an aromatic hydrocarbon, $\mathrm{C}_{11} \mathrm{H}_{16}$, that has the following ${ }^{13} \mathrm{C}$ NMR spectral 13-22 data:


13-20 -

Broadband decoupled: 29.5, 31.8, 50.2, 125.5, 127.5, 130.3, $139.8 \delta$
DEPT-90: 125.5, 127.5, $130.3 \delta$
DEPT-135: positive peaks at $29.5,125.5,127.5,130.3 \delta$; negative peak at $50.2 \delta$


13-20 - 13.13 Uses of ${ }^{13} \mathrm{C}$ NMR Spectroscopy

The information derived from ${ }^{13} \mathrm{C}$ NMR spectroscopy is extraordinarily useful for structure determination. Not only can we count the number of nonequivalent carbon atoms in a molecule, we can also get information about the electronic environment of each carbon and find how many protons are attached to each. As a result, we can address many structural questions that go unanswered by IR spectroscopy or mass spectrometry.


Here's an example: how do we know that the E2 reaction of an alkyl halide follows Zaitsev's rule (Section 11.7)? Does treatment of 1-chloro-1-methylcyclohexane with a strong base give predominantly the trisubstituted alkene 1-methylcyclohexene or the disubstituted alkene methylenecyclohexane?
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0432.jpg?height=315&width=1004&top_left_y=1225&top_left_x=558)


1-Methylcyclohexene will have five $s p^{3}$-carbon resonances in the 20 to $50 \delta$ range and two $s p^{2}$-carbon resonances in the 100 to $150 \delta$ range. Methylenecyclohexane, however, because of its symmetry, will have only three $s p^{3}$-carbon resonance peaks and two $s p^{2}$-carbon peaks. The spectrum of the actual reaction product, shown in FIGURE 13.22, clearly identifies 1-methylcyclohexene as the product of this E2 reaction.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0432.jpg?height=571&width=1536&top_left_y=1720&top_left_x=346) 1-chloro-1-methylcyclohexane with base.


PROBLEM We saw in Section 9.3 that addition of HBr to a terminal alkyne leads to the Markovnikov addition
13-23 product, with the Br bonding to the more highly substituted carbon. How could you use ${ }^{13} \mathrm{C}$ NMR to identify the product of the addition of 1 equivalent of HBr to 1-hexyne?


Magnetic Resonance Imaging (MRI) -

As practiced by organic chemists, NMR spectroscopy is a powerful method of structure determination. A small amount of sample, typically a few milligrams or less, is dissolved in a small amount of solvent, the solution is placed in a thin glass tube, and the tube is placed into the narrow ( $1-2 \mathrm{~cm}$ ) gap between the poles of a strong magnet. Imagine, though, that a much larger NMR instrument were available. Instead of a few milligrams, the sample size could be tens of kilograms; instead of a narrow gap between magnet poles, the gap could be large enough for a whole person to climb into so that an NMR spectrum of body parts could be obtained. That large instrument is exactly what's used for magnetic resonance imaging (MRI), a diagnostic technique of enormous value to the medical community.


Magnetic Resonance Imaging (MRI) -

Like NMR spectroscopy, MRI takes advantage of the magnetic properties of certain nuclei, typically hydrogen, and of the signals emitted when those nuclei are stimulated by radiofrequency energy. Unlike what happens in NMR spectroscopy, though, MRI instruments use data manipulation techniques to look at the threedimensional location of magnetic nuclei in the body rather than at the chemical nature of the nuclei. As noted, most MRI instruments currently look at hydrogen, present in abundance wherever there is water or fat in the body.


Magnetic Resonance Imaging (MRI) -

The signals detected by MRI vary with the density of hydrogen atoms and with the nature of their surroundings, allowing identification of different types of tissue and even allowing the visualization of motion. For example, the volume of blood leaving the heart in a single stroke can be measured, and heart motion can be observed. Soft tissues that don't show up well on X-ray images can be seen clearly, allowing diagnosis of brain tumors, strokes, and other conditions. This technique is also valuable in diagnosing damage to knees or other joints and is a noninvasive alternative to surgical explorations.


Magnetic Resonance Imaging (MRI) -

Several types of atoms in addition to hydrogen can be detected by MRI, and the applications of images based on
${ }^{31} \mathrm{P}$ atoms are being explored. This approach holds great promise for studies of metabolism.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0433.jpg?height=828&width=825&top_left_y=1489&top_left_x=647)


Magnetic Resonance Imaging (MRI) -

FIGURE 13.23 If you're a runner, you really don't want this to happen to you. The MRI of this left knee shows bone formation in the tissue in a patient with osteochondroma. (credit: "Osteochondroma MRI" by Michael R Carmont, Sian Davies, Daniel Gey van Pittius and Robin Rees/ Wikimedia Commons, CC BY 2.0)


Key Terms -

```
• chemical shift • homotopic
- coupling
- integration
- coupling constant (J)
- multiplet
- delta (\delta) scale
- n+1 rule
- DEPT-NMR
- nuclear magnetic resonance (NMR) spectroscopy
- diastereotopic
- shielding
- downfield
- spin-spin splitting
- enantiotopic
- upfield
- FT-NMR
```


Key Terms -


Summary -

Nuclear magnetic resonance spectroscopy, or NMR, is the most valuable of the numerous spectroscopic techniques used for structure determination. Although we focused in this chapter on NMR applications with small molecules, more advanced NMR techniques are also used in biological chemistry to study protein structure and folding.


Summary -

When magnetic nuclei, such as ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$, are placed in a strong magnetic field, their spins orient either with or against the field. On irradiation with radiofrequency (rf) waves, energy is absorbed and the nuclei "spin-flip" from the lower energy state to the higher energy state. This absorption of rf energy is detected, amplified, and displayed as an NMR spectrum.


Summary -

Each electronically distinct ${ }^{1} \mathrm{H}$ or ${ }^{13} \mathrm{C}$ nucleus in a molecule comes into resonance at a slightly different value of the applied field, thereby producing a unique absorption signal. The exact position of each peak is called the chemical shift. Chemical shifts are caused by electrons setting up tiny local magnetic fields that shield a nearby nucleus from the applied field.


Summary -

The NMR chart is calibrated in delta units ( $\boldsymbol{\delta}$ ), where $1 \delta=1 \mathrm{ppm}$ of spectrometer frequency. Tetramethylsilane (TMS) is used as a reference point because it shows both ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ absorptions at unusually high values of applied magnetic field. The TMS absorption occurs on the right-hand (upfield) side of the chart and is arbitrarily assigned a value of $0 \delta$.
${ }^{13} \mathrm{C}$ spectra are run on Fourier-transform NMR (FT-NMR) spectrometers using broadband decoupling of proton spins so that each chemically distinct carbon shows a single unsplit resonance line. As with ${ }^{1} \mathrm{H}$ NMR, the chemical shift of each ${ }^{13} \mathrm{C}$ signal provides information about a carbon's chemical environment in the sample. In addition, the number of protons attached to each carbon can be determined using the DEPT-NMR technique.


Summary -

In ${ }^{1} H$ NMR spectra, the area under each absorption peak can be electronically integrated to determine the relative number of hydrogens responsible for each peak. In addition, neighboring nuclear spins can couple, causing the spin-spin splitting of NMR peaks into multiplets. The NMR signal of a hydrogen neighbored by $n$ equivalent adjacent hydrogens splits into $n+1$ peaks (the $\boldsymbol{n}+\mathbf{1}$ rule) with coupling constant $\boldsymbol{J}$.


Additional Problems -


Visualizing Chemistry -

PROBLEM Into how many peaks would you expect the ${ }^{1} \mathrm{H}$ NMR signals of the indicated protons to be split? 13-24 $($ Green $=\mathrm{Cl}$.)
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=296&width=443&top_left_y=226&top_left_x=489)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=394&width=576&top_left_y=204&top_left_x=1013)


Visualizing Chemistry -

PROBLEM How many absorptions would you expect the following compound to have in its ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ NMR 13-25 spectra?
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=378&width=359&top_left_y=749&top_left_x=417)

PROBLEM Sketch what you might expect the ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ NMR spectra of the following compound to look like 13-26 (green $=\mathrm{Cl}$ ):
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=262&width=432&top_left_y=1273&top_left_x=429)


Visualizing Chemistry -

PROBLEM How many electronically nonequivalent kinds of protons and how many kinds of carbons are 13-27 present in the following compound? Don't forget that cyclohexane rings can ring-flip.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=329&width=481&top_left_y=1668&top_left_x=421)


Visualizing Chemistry -

PROBLEM Identify the indicated protons in the following molecules as unrelated, homotopic, enantiotopic, or 13-28 diastereotopic.
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=346&width=430&top_left_y=2112&top_left_x=482)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0435.jpg?height=288&width=345&top_left_y=2130&top_left_x=993)
Cysteine


Chemical Shifts and NMR Spectroscopy -

PROBLEM The following ${ }^{1} \mathrm{H}$ NMR absorptions were obtained on a spectrometer operating at 200 MHz and are 13-29 given in hertz downfield from the TMS standard. Convert the absorptions to $\delta$ units.
(a) 436 Hz
(b) 956 Hz
(c) 1504 Hz

PROBLEM The following ${ }^{1} \mathrm{H}$ NMR absorptions were obtained on a spectrometer operating at 300 MHz . Convert 13-30 the chemical shifts from $\delta$ units to hertz downfield from TMS.
(a) $2.1 \mathrm{\delta}$
(b) $3.45 \delta$
(c) $6.30 \delta$
(d) $7.70 \delta$


Chemical Shifts and NMR Spectroscopy -

PROBLEM When measured on a spectrometer operating at 200 MHz , chloroform $\left(\mathrm{CHCl}_{3}\right)$ shows a single sharp 13-31 absorption at $7.3 \delta$.
(a) How many parts per million downfield from TMS does chloroform absorb?
(b) How many hertz downfield from TMS would chloroform absorb if the measurement were carried out on a spectrometer operating at 360 MHz ?
(c) What would be the position of the chloroform absorption in $\delta$ units when measured on a 360 MHz spectrometer?
PROBLEM Why do you suppose accidental overlap of signals is much more common in ${ }^{1} \mathrm{H}$ NMR than in ${ }^{13} \mathrm{C}$ 13-32 NMR?


Chemical Shifts and NMR Spectroscopy -

PROBLEM Is a nucleus that absorbs at $6.50 \delta$ more shielded or less shielded than a nucleus that absorbs at 13-33 3.20 $\delta$ ? Does the nucleus that absorbs at $6.50 \delta$ require a stronger applied field or a weaker applied field to come into resonance than the one that absorbs at $3.20 \delta$ ?


${ }^{\mathbf{1}} \mathrm{H}$ NMR Spectroscopy -