19.5: Carbon-13 NMR

The relatively slow development of instrumentation for ¹³C NMR spectra is the result of its limited sensitivity compared to ¹H NMR. This difference in sensitivity is due to two key differences between the nuclei ¹H and ¹³C: their relative abundances and their relative magnetogyric ratios. While ¹H comprises 99% of all hydrogen, ¹³C accounts for just 1% of all carbon. The strength of an NMR signal also depends on the difference in energy, \(\Delta E\), between the ground state and the excited state, which is a function of the magnetogyric ratio, \(\gamma\)

\[\Delta E = h \nu = \frac{\gamma B_0}{2 \pi} \label{carbon1} \]

The greater the difference in energy, the greater the difference in the population between the ground and the excited states, and the greater the signal. The magnetogyric ratio, \(\gamma\), for ¹H is \(4 \times\) greater than that for ¹³C. As a result of these two factors, ¹H NMR is approximately \(6400 \times\) more senstitive than ¹³C. The development of magnets with higher field strengths and the capabilities of signal averaging (see Chapter 5 on signals and noise) when using Fourier transforms to gather and analyze data, make ¹³C feasible.

Figure \(\PageIndex{1}\) shows ¹³C NMR spectrum for three related molecules: p-nitrophenol, o-nitrophenol, and m-nitrophenol. There are three things to make note of from this figure. First, each spectrum consists of a set of peaks, each of which is a singlet, suggesting that no spin-spin coupling is taking place. Second, the number of peaks in each spectrum is the same as the number of unique types of carbon—four unique carbons for p-nitrophenol and six each for m-nitrophenol and o-nitrophenol—which suggests that chemical shifts in ¹³C provide useful information about the environment of the carbon atoms and, therefore, the molecule's structure. And, third, unlike ¹H, there is no relationship between the intensity of a ¹³C peak and the number of carbon atoms. This is particularly evident when comparing the intensity of the peaks for the carbon bonded to the –NO₂ group and the carbon bonded to the –OH group, which are significantly less intense than the peaks for other carbons. We will consider each of these observations in the remainder of this section.

Figure \(\PageIndex{1}\). ¹³C NMR spectra for three nitrophenols. The original data used to construct these spectra are found here. The spectra were recorded on a 15 MHz instrument (with respect to ¹³C, or 60 MHz with respect to ¹H).

Proton Decoupling

In ¹³C NMR there is no coupling between adjacent carbon atoms because it is unlikely that both are ¹³C, the only isotope of carbon that is NMR active (the odds that two adjacent carbons are both ¹³C is \(0.01 \times 0.01\), or \(0.0001\) or \(0.010\%\)). Coupling does take place between ¹³C and ¹H when the hydrogen atoms are attached to the carbon atom. Such coupling follows the same N+1 rule as in ¹H NMR; thus, a quartenary carbon (R₄C) appears as a singlet, a methine carbon (R₃CH) appears as a doublet, a methylene carbon (R₂CH₂) appears as a triplet, and a methyl carbon (RCH₃) appears as a quartet. Even with the extensive range of ppm values over which ¹³C peaks appear—chemical shifts for ¹³C spectra run from 250 – 0 ppm instead of 14 – 0 ppm for ¹H spectra—a compound with many different types of carbon atoms, each with 1 – 3 hydrogen atoms results in a complex spectrum. For this reason, ¹³C NMR spectra are acquired in a way that prevents coupling between ¹³C and ¹H. This is called proton decoupling.

The most common method of proton decoupling is to use a second RF generator to irradiate the sample with a broad-band of RF signals that spans the range of frequencies for the protons. As described earlier in Section 19.3, the effect is to saturate the proton's ground and excited states, which prevents the protons from absorbing energy and from coupling with each other and with the carbons atoms. The ¹³C spectra in Figure \(\PageIndex{1}\) are examples of decoupled spectra.

Qualitative Applications of ¹³C NMR

Just as with ¹H NMR spectra, tables of chemical shifts for ¹³C peaks aids in determining a molecules structure. Table \(\PageIndex{1}\) provides ranges of chemical shifts for different types of carbon atom. A set of tables is available here.

Table \(\PageIndex{1}\). ¹³C Shifts in ppm

type of carbon atom	example	range of chemical shifts (ppm)
primary alkyl	\(\ce{R-CH3}\)	10 – 30
secondary alkyl	\(\ce{R-CH2–R}\)	15 – 55
tertiary alkyl	\(\ce{R3CH}\)	20 – 60
quaternary alkyl	\(\ce{R4C}\)	30 – 40
alkynl	\(\ce{R–C#C–H}\)	65 – 90
alkenyl	\(\ce{R–C=C–H}\)	100 – 150
aromatic	\(\ce{C6H6}\)	110 – 170
ester	\(\ce{R-C(=O)-O-R}\)	165 – 175
amide	\(\ce{R-C(=O)-N-R2}\)	165 – 175
carboxylic acid	\(\ce{R–C(=O)–OH}\)	175 – 185
aldehyde	\(\ce{R–C(=O)–H}\)	190 – 220
ketone	\(\ce{R-C(=O)-R}\)	205 – 220
attached to iodine	\(\ce{C-I}\)	0 – 40
attached to bromine	\(\ce{C-Br}\)	25 – 65
attached to chlorine	\(\ce{C-Cl}\)	35 – 80
attached to oxygen	\(\ce{C-O}\)	40 – 80
attached to nitrogen	\(\ce{C-N}\)	40 – 60

Nuclear Overhauser Enhancement

The most intense peak in the ¹³C NMR spectrum for m-nitrophenol (see Figure \(\PageIndex{1}\) above) is the carbon in the benzene ring labeled as position 4, with an intensity of 1000 (the intensity scale is normalized here to a maximum value of 1000, but for this section, let's take it as an absolute value). Because the spectrum was acquired with proton decoupling turned on, the peak for this carbon appears as a singlet. If we turn proton decoupling off, then we expect the peak to appear as a doublet as this carbon has one hydrogen attached to it. We might reasonably expect to find that each peak has an intensity of 500, giving a total intensity of 1000. The actual intensities of the peaks for this carbon, however, are smaller than expected. Put another way, when we turn proton decoupling on, the intensity of a ¹³C line increases more than expected and the more hydrogens, the greater the effect. This is called nuclear overhauser enhancement (NOE).

NOE is the result of the relative populations of the ground and excited states. The technical details are more than we will consider here, but the extent of the total enhancement of the peak intensities is proportional to the ratio of the magnetogyric ratios of the irradiated nucleus (¹H) and the observed nucleus (¹³C), which for a ¹H decoupled ¹³C NMR results in a total enhancement of the intensity of approximately 200%. As magnetogyric ratios can be negative, as is the case for ¹⁵N, a decoupled spectrum can result in less intense peaks. One important consequence of NOE, is that integrated peak areas are not proportional to the number of identical carbon atoms, which is a loss of information.

Note

Although our focus in this chapter is on ¹H and ¹³C NMR, other nuclei, such as ³¹P, ¹⁹F, and ¹⁵N are useful for the study of chemically and biochemically important molecules.