Ethanol, CH₃CH₂OH, has six hydrogens, yet its proton NMR spectrum shows only three signals: one for the three CH₃ hydrogens, one for the two CH₂ hydrogens and one for the OH. Each signal tells you three things. Its position says what the hydrogens sit near, its size says how many hydrogens produced it, and its shape says how many hydrogens sit on the next carbon.
Proton NMR, written ¹H NMR, is the method that records those signals. NMR stands for nuclear magnetic resonance. IR tells you which functional groups a molecule has; proton NMR shows how its pieces are joined. Read together, the three kinds of information often settle a structure on their own.
What NMR measures
A hydrogen nucleus is a single proton, and it behaves like a tiny bar magnet. Put it in a strong magnetic field, which chemists call B₀, and it lines up either with the field or against it. Lining up against the field costs slightly more energy.
Radio waves of just the right frequency carry exactly that energy difference, so they can flip a proton from the lower state to the higher one. The instrument sends radio waves through the sample and records which frequencies are absorbed. Each absorption shows up as a signal.
The frequency a proton absorbs depends on the field it actually feels, and that is not quite B₀. The electrons around the hydrogen respond to B₀ by setting up a small field of their own that points the opposite way. The nucleus feels B₀ minus that small field, so the electrons are said to shield it.
Compare ethane with fluoromethane, CH₃F. Each hydrogen of ethane sits in a full share of electron density, so it is well shielded. In fluoromethane, the fluorine pulls electron density toward itself and away from the hydrogens. With less density around it, a hydrogen meets a weaker opposing field and feels more of B₀. It is deshielded, and it absorbs at a higher frequency.
Hydrogens in different surroundings absorb at slightly different frequencies. That is why ethanol's three kinds of hydrogen give three separate signals.
Chemical shift: where a signal appears
A signal's position is reported as its chemical shift, δ ("delta"), in parts per million (ppm). The zero point is tetramethylsilane, Si(CH₃)₄, usually called TMS, which is added to the sample as a reference. δ is the signal's distance from TMS, in hertz, divided by the instrument's operating frequency in megahertz. One hertz (Hz) is one cycle per second.
That division makes δ the same on every instrument. On a 300 MHz instrument, where protons absorb near 300 million hertz, ethanol's CH₃ signal lies 360 Hz from TMS, and 360 ÷ 300 = 1.2 ppm. On a 600 MHz instrument the same signal lies 720 Hz from TMS. The gap doubles along with the field, but 720 ÷ 600 is still 1.2 ppm.
TMS makes a good zero point. Its twelve hydrogens are all alike, so together they give one sharp signal. Silicon is less electronegative than carbon, so those hydrogens are more shielded than almost any hydrogen in an organic compound, and nearly every other signal falls on the same side of TMS.
The sample is dissolved in a solvent whose hydrogens have been replaced by deuterium, D, the heavier isotope of hydrogen. The usual choice is CDCl₃. There is much more solvent than sample. Deuterium absorbs at a very different frequency from ordinary hydrogen, though, so the solvent adds no large signal of its own. The trace of ordinary CHCl₃ left in it still gives a small signal at 7.26 ppm.
Spectra are printed with δ increasing from right to left. A deshielded hydrogen has a high δ and appears toward the left, a direction called downfield. A shielded hydrogen has a low δ and appears toward the right, which is upfield. The names come from older instruments, which held the frequency fixed and swept the field: a shielded hydrogen needed a higher field before it absorbed.
Electronegativity sets most shifts. The methyl halides show it in a single series: CH₃I absorbs at 2.2 ppm, CH₃Br at 2.7, CH₃Cl at 3.1 and CH₃F at 4.3. The more electronegative the halogen, the more density it pulls off the hydrogens, and the further downfield they appear. The CH₃ of methanol sits at 3.4, between the chloride and the fluoride, just as oxygen's electronegativity falls between chlorine's and fluorine's. So a C–H next to a halogen can sit anywhere from about 2.2 ppm (iodine) to 4.5 (fluorine). A C–H next to oxygen stays in a narrower band, 3.3–4.5.
The pull adds up, and it fades with distance. CH₂Cl₂ absorbs at 5.3 ppm and CHCl₃ at 7.3, because each extra chlorine removes more density. In 1-chloropropane, CH₃CH₂CH₂Cl, the CH₂ bonded to chlorine is at 3.5 ppm and the next CH₂ is at 1.8. The CH₃ at the far end is at 1.0, almost where it would be in propane.
A carbonyl group or a C=C on the next carbon deshields a hydrogen too, though less than an oxygen or a halogen does. The table collects the ranges worth knowing.
| Environment | ppm |
|---|---|
| alkyl C–H | 0.9–1.5 |
| C–H next to C=C or aryl | 1.6–2.5 |
| C–H alpha to a carbonyl | 2.0–2.5 |
| C–H next to N | 2.3–3.0 |
| C–H next to O | 3.3–4.5 |
| C–H next to a halogen | 2.2–4.5 (I lowest, F highest) |
| ≡C–H (terminal alkyne) | 1.8–3.0 |
| vinyl C–H | 4.5–6.5 |
| aromatic C–H | 6.5–8.5 |
| aldehyde C–H | 9–10 |
| carboxylic acid O–H | 10–13 |
Pi bonds: when geometry sets the shift
Three rows of the table break the electronegativity pattern outright, and a fourth, the aldehyde, is pushed further than electronegativity alone explains. Benzene's hydrogens absorb at 7.3 ppm, although no electronegative atom is anywhere near them. Vinyl hydrogens, the ones on the carbons of a C=C, absorb at 4.5–6.5. And the hydrogen of a terminal alkyne, ≡C–H, absorbs at only 1.8–3.0. That is upfield of a vinyl hydrogen, even though an sp carbon is more electronegative than an sp² one.
Pi electrons explain all four. In the applied field, the π electrons of a ring or a multiple bond circulate, and moving electrons create a field of their own. Like any magnetic field, it runs in closed loops. Where the loops run against B₀, a nearby hydrogen is shielded; where they run with B₀, it is deshielded. So the shift depends on where the hydrogen sits relative to the π system, not only on what it is bonded to. This dependence on direction is called magnetic anisotropy, since "anisotropic" means different in different directions.
In benzene, the π electrons circulate around the ring, a flow called the ring current. Inside the ring, its field opposes B₀. The ring hydrogens stick out past the edge of the ring, where the field loops back and adds to B₀, so they are strongly deshielded and appear at 6.5–8.5 ppm. A signal in that range is good evidence of an aromatic ring.
An alkene shows the same effect on a smaller scale. Its vinyl hydrogens sit out to the sides of the C=C, where the induced field adds to B₀, and they appear at 4.5–6.5. An aldehyde hydrogen is deshielded in two ways at once. It sits beside the π bond of the C=O in the same kind of region, and its carbon also carries an electronegative oxygen, so it appears at 9–10.
The alkyne is the case where anisotropy wins. Its π electrons form a cylinder around the C≡C axis and circulate around that axis. Along the axis itself the induced field runs against B₀, and the ≡C–H sits right on the axis. So the hydrogen is shielded, and it lands at 1.8–3.0 ppm despite the electronegative carbon it is bonded to. Molecules tumble in solution, but the circulation is strongest when the axis lines up with B₀, and it is this orientation that decides the overall effect.
A carboxylic acid O–H is the most deshielded hydrogen in the table, at 10–13 ppm. Its oxygen shares a lone pair with the neighboring C=O, and that sharing draws density away from the O–H hydrogen. Acid molecules also pair up through two hydrogen bonds, and hydrogen bonding deshields an O–H further.
Integration: how many hydrogens
Look again at ethanol. Its CH₃ signal has three times the area of its OH signal, and its CH₂ signal has twice the area of the OH signal. The area under a signal is proportional to the number of hydrogens that produce it, and measuring those areas is called integration. The instrument draws the result as a stepped line over the spectrum. At each signal the line climbs by an amount proportional to that signal's area.
Integration gives a ratio, not a count. Butane, CH₃CH₂CH₂CH₃, gives two signals in a 3 : 2 ratio, but it has six CH₃ hydrogens and four CH₂ hydrogens. To turn a ratio into counts, scale it to the molecular formula. The parts add to 3 + 2 = 5, butane has ten hydrogens, so each part stands for two hydrogens, and the signals are 6H and 4H.
Equivalent hydrogens: how many signals
Butane has ten hydrogens but only two signals. Hydrogens that are chemically equivalent, meaning they sit in identical surroundings, absorb at the same frequency and share one signal. Two things make hydrogens equivalent.
The first is rotation. A methyl group turns about its C–C bond far faster than the instrument can follow, so each of its three hydrogens spends equal time in each position. The three always give one signal together.
The second is symmetry. Take p-xylene (1,4-dimethylbenzene). Give the molecule a half turn about the line through both methyl carbons, and the left-hand ring hydrogens swap with the right-hand ones. Flip it end over end, and the two methyls swap, along with the upper and lower ring hydrogens. Between them, all four ring hydrogens are alike, and so are the two methyls. Its ten hydrogens give just two signals: 4H at 7.0 ppm and 6H at 2.3. When a spectrum has fewer signals than the formula suggests, the molecule has symmetry.
The two hydrogens of a CH₂ group need more care, because they are not automatically equivalent. The substitution test from Prochirality settles the question. Replace one hydrogen with a label such as D, then replace the other one instead, and compare the two products. If the products are the same compound, or are enantiomers, the two hydrogens share one signal in an ordinary solvent. If the products are diastereomers, the hydrogens are diastereotopic, and they can have different shifts.
C3 of 2-bromobutane shows how this happens, and Prochirality works it through in full. C2 is already a stereocenter, so replacing either C3 hydrogen gives a product with two stereocenters. The two products match at C2 and differ at C3, which makes them diastereomers. The C3 CH₂ of 2-bromobutane can therefore give two signals, not one.
Splitting: which hydrogens are next door
Look closely at ethanol's CH₃ signal and you see three evenly spaced lines, with the middle one twice as tall as the outer two. The CH₂ signal has four lines (the OH hydrogen does not count as a neighbor; the box after the ethanol example says why). This is splitting, and it reports on the hydrogens on the neighboring carbon.
Each neighboring hydrogen is a tiny magnet too, lined up with B₀ or against it, with almost equal odds. Lined up with the field, it adds a little to the field the observed hydrogen feels; lined up against it, it takes a little away. The CH₃ of ethanol has two neighbors, the CH₂ hydrogens. Both can point with the field, both can point against it, or one can point each way, and "one each way" can happen in two ways. So the CH₃ signal becomes three lines in the ratio 1 : 2 : 1.
Counting this way for any number of neighbors gives the n + 1 rule: a hydrogen with n equivalent neighboring hydrogens gives a signal of n + 1 lines. No neighbors gives a single line, a singlet (s). One neighbor gives a doublet (d), 1 : 1. Two give a triplet (t), 1 : 2 : 1. Three give a quartet (q), 1 : 3 : 3 : 1, which is why ethanol's CH₂, next to a CH₃, is a quartet.
The intensity ratios are the rows of Pascal's triangle, in which each number is the sum of the two numbers above it. Starting from 1 1, the rows run 1 2 1, then 1 3 3 1, then 1 4 6 4 1 for four neighbors, and so on.
Only neighbors that are not equivalent to the observed hydrogen split it. Equivalent hydrogens do not split each other. All four hydrogens of ClCH₂CH₂Cl are alike, so its spectrum is a single singlet at 3.7 ppm, even though each CH₂ sits next to another CH₂.
The spacing between the lines of a split signal is the coupling constant, J, measured in hertz. Two sets of hydrogens that split each other are said to be coupled, and both signals show the same J. Matching J values confirm that two signals come from neighbors, rather than just happening to look alike.
Coupling travels through the bonding electrons, not through space, and it weakens quickly with each bond. Hydrogens on adjacent carbons are three bonds apart (H–C–C–H). Their coupling is called vicinal coupling. It is the coupling the n + 1 rule describes, and it runs about 6–8 Hz in a freely rotating chain. Hydrogens four or more bonds apart usually couple too weakly to see, which is why you only look at the carbon next door. Meta hydrogens on a benzene ring, below, are the main exception.
Two hydrogens on the same carbon are only two bonds apart, and their coupling is called geminal coupling. When the two hydrogens are equivalent, as in a CH₃ group, it has no visible effect. When they are diastereotopic, as at C3 of 2-bromobutane, they have different shifts and do split each other.
The n + 1 rule has a condition that is easy to miss: the n neighbors must be equivalent to each other. A hydrogen with two different sets of neighbors is split by each set in turn. In CH₃–CH₂–CHBr–CH₃, the CHBr hydrogen has three neighbors on the CH₃ and two on the CH₂. It is not simply "five neighbors, so a sextet". The CH₃ splits its signal into a quartet, and the CH₂ then splits each of those four lines into a triplet. The result is a quartet of triplets, twelve lines in all.
In 2-bromobutane the two J values happen to be almost equal, so many of the twelve lines land on the same positions and the pattern looks like a sextet. When the J values differ, the lines stay apart. Styrene, C₆H₅–CH=CH₂, shows this. The hydrogen on the ring-side carbon couples to the trans hydrogen of the CH₂ with J = 17.6 Hz and to the cis one with J = 10.9 Hz. It gives four lines of equal height, a doublet of doublets, a pattern the n + 1 rule cannot produce. The n + 1 rule is the special case in which every J is equal. That holds well in freely rotating chains and fails for most vinyl hydrogens. The safe habit is to build any pattern one coupling at a time, as a tree, and only then ask what it looks like.
J values carry structural information of their own. On a C=C, two hydrogens on opposite sides (trans) couple with J = 12–18 Hz, and two on the same side (cis) with J = 6–12 Hz. For an alkene RCH=CHR′, trans is E and cis is Z, so J tells the two apart. On a benzene ring, hydrogens on neighboring carbons (ortho) couple with J = 7–10 Hz, and hydrogens one carbon further apart (meta) with J = 2–3 Hz, which helps place the substituents.
1.2 ppm, 3H, triplet. Three hydrogens suggest a CH₃. A triplet means two neighboring hydrogens, so it sits next to a CH₂. At 1.2 ppm, nothing electronegative is close. This is the CH₃.
3.6 ppm, 2H, quartet. Two hydrogens with three neighbors make a CH₂ next to the CH₃. The signal sits well downfield, so this CH₂ is bonded to the oxygen.
1H, broad singlet, usually between 2 and 5 ppm. This is the OH. It has a CH₂ next door, yet it is not split, for the reason given in the box below. Its position also moves from sample to sample.
Working a spectrum
A reliable order of work:
- Count the signals. That is the number of different hydrogen environments. A small number compared with the formula means symmetry.
- Read the integrations as a ratio, and scale it to the formula.
- Use the shifts to say what each set of hydrogens is attached to or near.
- Use the splitting to work out which sets sit next to which.
- Assemble the pieces into a structure that fits the formula and its degrees of unsaturation.
Some groups leave patterns you learn to spot. A 3H triplet with a 2H quartet is an ethyl group, CH₃CH₂–. A 6H doublet with a 1H septet (seven lines) is an isopropyl group, (CH₃)₂CH–. A 9H singlet is a tert-butyl group, (CH₃)₃C–. And two 2H signals in the aromatic region that each look like a doublet mark a para-disubstituted ring.
Data: 1.3 ppm (3H, t), 2.0 ppm (3H, s), 4.1 ppm (2H, q). The IR spectrum shows a strong peak at 1735 cm⁻¹.
Degrees of unsaturation = (2 × 4 + 2 − 8) ÷ 2 = 1. The 1735 cm⁻¹ IR band says that this one degree is an ester C=O.
The triplet and quartet together are an ethyl group, and the quartet at 4.1 puts that CH₂ on an oxygen, so the piece is –OCH₂CH₃. The 3H singlet at 2.0 is a methyl with no neighboring hydrogens, at a shift typical of a CH₃ on a carbonyl carbon.
Put the pieces together: CH₃–CO–O–CH₂CH₃, ethyl acetate. Every signal is accounted for.
What carries forward
Proton NMR does its best work alongside the other methods. IR names the functional groups. Mass spectrometry, from the same earlier chapter, measures the mass of the molecule and so helps fix its formula. Then ¹³C NMR, the next section, counts the carbon environments using the same idea of chemical shift.