NMR spectroscopy

How NMR works

Some nuclei, including ¹H and ¹³C (but not ¹²C or ¹⁶O), behave like tiny magnets because they have a property called spin. In a strong external magnetic field they line up either with the field (lower energy) or against it (higher energy). Radio-frequency radiation with an energy equal to the gap, $\Delta E = hf$, is absorbed and flips nuclei to the higher state. This absorption is resonance.

The key to NMR is that $\Delta E$ depends slightly on the electrons around each nucleus. Electrons create a small magnetic field that opposes the external one, shielding the nucleus. A nearby electronegative atom (O, N, Cl) or a C=O group pulls electron density away, deshielding the nucleus so it absorbs at a higher frequency. Nuclei in different chemical environments therefore give separate signals.

Modern NMR spectrometers use superconducting magnets cooled by liquid helium, with fields of about 9–23 tesla. They are described by the frequency at which ¹H resonates: research instruments of 400–800 MHz are standard and the largest exceed 1 GHz. (Older textbooks describe 60–300 MHz instruments, which are now mainly used for teaching.) The sample is dissolved in a solvent with no ordinary hydrogen atoms, such as CDCl₃, so the solvent doesn't swamp the spectrum.

Chemical shift

Signals are plotted against chemical shift, $\delta$, in parts per million (ppm), measured from the signal of a reference compound, tetramethylsilane (TMS, Si(CH₃)₄), which is set to 0. TMS is used because its 12 identical hydrogens and 4 identical carbons give one strong signal, it is unreactive, and its nuclei are more shielded than almost any in an organic molecule. Because $\delta$ is a ratio, the same compound gives the same shifts on any instrument. The scale runs from right (0) to left (larger $\delta$, more deshielded).

Carbon-13 NMR

Only about 1.1% of carbon atoms are ¹³C, so ¹³C spectra are weaker and are usually recorded so that each carbon environment gives a single line. A ¹³C spectrum tells you two things:

• The number of signals = the number of different carbon environments. Carbons related by the molecule's symmetry are equivalent and give one signal.
• The chemical shift of each signal shows what the carbon is bonded to. Typical values (use the data sheet ranges in exams): CH₃ or CH₂ in a chain 5–45 ppm; C bonded to O 50–90 ppm; C=C 110–150 ppm; C=O of acids and esters 160–185 ppm; C=O of aldehydes and ketones 190–220 ppm.

Signal heights in a routine ¹³C spectrum are not proportional to the number of carbons, so you can't count atoms from them.

Proton (¹H) NMR

A ¹H spectrum gives four pieces of information:

1. Number of signals: the number of different hydrogen environments.
2. Chemical shift: the type of environment. Typical values: H on a carbon in a chain 0.9–1.7 ppm; H on a carbon next to C=O 2.0–2.7 ppm; H on a carbon bonded to O 3.3–4.8 ppm; H on C=C 4.5–7 ppm; aldehyde H 9.4–10 ppm; carboxylic acid H 10–13 ppm; alcohol O–H anywhere from 1 to 6 ppm.
3. Relative intensity (integration): the area under each signal is proportional to the number of hydrogens in that environment. Ethanol gives 3 : 2 : 1 for CH₃ : CH₂ : OH.
4. Splitting pattern: how many hydrogens are on the neighbouring carbon atoms.

Splitting: the n + 1 rule

The small magnetic fields of hydrogens on the next carbon add to or subtract from the field felt by a hydrogen, splitting its signal into a cluster of peaks. A signal from H atoms with $n$ equivalent H neighbours on adjacent carbons is split into $n + 1$ peaks:

Three useful rules: equivalent hydrogens don't split each other; O–H hydrogens usually appear as a singlet and don't split their neighbours (they exchange rapidly between molecules); and the classic ethyl group, CH₃CH₂–, always shows as a 3H triplet plus a 2H quartet. A 6H doublet with a 1H septet means an isopropyl group, (CH₃)₂CH–.