Carbon13 13c Nmr Spectroscopy

4.1 SENSITIVITY OF 13C

After XH, the second most important nucleus is13 C because carbon is the building block of all organic molecules, including natural products as well as biopolymers. The 13C nuclear magnet strength is very close to one fourth of that of 1H (yC/yH = 1/4), leading to a sensitivity of 1/64 (y3) of that of 1H. Further bad news is that the natural abundance of 13C on earth is only 1.1%, with nearly all of the remainder being 12C, whose nucleus has no magnetic properties. Thus the overall sensitivity of 13C is about (1/64) x (0.011) = 1.72 x 10-4 relative to that of 1H, a "hit" of nearly four orders of magnitude. To get the same 13C signal-to-noise ratio as a single-scan proton signal would require 33,850,000 scans because S/N is proportional to the square root of the number of scans! In fact, 13C NMR was not practical until pulsed Fourier transform instruments were available. While a 1H spectrum can be obtained in a single scan for samples of organic molecules as small as 1 mg, a "fat" sample of 30 mg might require 1000 scans or more for a 13 C spectrum.

4.2 SPLITTING OF 13C SIGNALS 4.2.1 13C-13C J Coupling

Although the low natural abundance of 13C carries a big sensitivity disadvantage, it also is a big advantage in that13 C is a "dilute" nucleus: the chances of a13 C being right next to another 13C in a molecule are extremely small (0.011 x 0.011 = 1.21 x 10-4). For this reason we never see 13C-13C splitting in 13C spectra of natural-abundance samples. Compared to the complexity and wide "footprint" of 1H signals due to 1H-1H splitting, this is an enormous

NMR Spectroscopy Explained: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology, by Neil E Jacobsen Copyright © 2007 John Wiley & Sons, Inc.

simplification of the spectrum. Of course, this is also a loss of information, but we will make up for that later by using 1H-13C couplings to piece together the carbon skeleton. Thus from the point of view of carbon isotopes, the NMR sample of a pure compound is a complex mixture of isotopomers (molecules of different isotopic composition at specific positions within the molecule). For example, a sample of n-propanol (3 carbons) at a concentration of 1 mM actually has the following components, each giving rise to a resonance in the 13C spectrum:

13CH3-12CH2-12CH2-OH 11 ^M = 0.011 x 1 mM 12CH3-13CH2-12CH2-OH 11 ^M 12CH3-12CH2-13CH2-OH 11 ^M

In addition, there are isotopomers with two 13 C isotopes in one molecule:

13CH3-13CH2-12CH2-OH 121 nM = (0.011)2 x 1mM

12CH3-13CH2-13CH2-OH 121 nM

13CH3-12CH2-13CH2-OH 121 nM

Each of these gives rise to an AB pattern due to 13C-13C splitting (XJCC for the first two and 2JCC for the third species). These additional 13C signals appear as weak satellite peaks (0.55% of the main peak) around the main peaks from the first three species, and because signal-to-noise ratios are typically much less than 200 for 13 C spectra, these signals will be buried in the noise. Finally, there is one isotopomer with three 13C nuclei:

13CH3-13CH2-13CH2-OH 1.33nM = (0.011)3 x 1mM

This species, which can be prepared by uniform isotopic labeling, would give a spectrum even more complex than a 1H spectrum: the CH3 signal, for example, would be split into a double doublet by XJCC (large: ~35 Hz) and 2JCC (small: <5 Hz). The central CH2 signal would be split into a double-doublet or triplet by two large XJCC splittings. In a natural abundance sample we would have to have a signal-to-noise ratio of 33,000:1 to see these signals rising out of the noise!

The remainder of the 1 mM concentration is made up of the predominant isotopomer: the one without any 13 C at all:

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