Learn · NMR
Build the Spectrum
A molecule, and an empty spectrum. Slide each hydrogen's peak to where it belongs, then grow its splitting one neighbour at a time.
What you do
Most NMR teaching hands you a spectrum and asks which molecule made it. This runs the other way. You are given the molecule, with every hydrogen drawn, and you build its spectrum yourself.
For each set of hydrogens there are two moves.
- Place the peak. Slide it along the axis. Beside the molecule is a close-up of one hydrogen sitting in the magnet. As you slide left, its electron cloud thins and its spin quickens. That is all a chemical shift is.
- Split it. Add neighbouring hydrogens one at a time and watch the tree grow. Each neighbour is spin up or spin down, and each one splits every line in two.
Lock in an answer and the real peak appears, in the colour of the hydrogens that made it, with the reason.
Seven molecules, from acetone to benzaldehyde.
What you find out
- Why a hydrogen near an oxygen sits further left than one in a plain chain.
- Why the hydrogens on a benzene ring feel more of the magnet, not less.
- Where the 1 : 3 : 3 : 1 of a quartet comes from.
- Why acetone’s six hydrogens give a single line.
- Why an alcohol’s OH is broad, splits nothing, and will not stay put.
- What a quartet beside a triplet is telling you.
The real calculation
The cloud is not a figure of speech. Its effect is a number, the shielding σ: the fraction of the magnet’s field that the electrons cancel at the nucleus. Press on after the last molecule and the game walks through it.
How fast a hydrogen spins in a magnet of strength B:
ν = (γ / 2π) · B · (1 − σ)
Where its peak sits, measured against a reference compound:
δ = (σreference − σ) × 106
For a single atom, σ can be worked by hand. The magnet sets the whole cloud circulating, and the circulation makes a small field of its own that opposes the magnet at the nucleus. Lamb’s formula turns the cloud’s average closeness to the nucleus into σ:
σ = (μ0 e2 / 12π me) · ⟨1/r⟩
For a lone hydrogen atom the average of 1/r is one over the Bohr radius, and everything collapses to a single constant of nature:
σ = α2 / 3 = 17.75 ppm
Measured values for real substances sit a little above that: 25.69 ppm for liquid water, 26.29 ppm for hydrogen gas. A whole proton spectrum is a window about 13 ppm wide on this scale.
A molecule has two parts. The cloud as it stands always shields, which is Lamb’s part. But the magnet also mixes in a trace of the molecule’s excited states, which lets electrons circulate the other way and takes shielding off. That is Ramsey’s part, and it needs the quantum mechanics of the whole molecule.
So a computer first solves for the electrons. Then it asks how the molecule’s energy changes when the magnet and the nucleus’s own tiny magnet are both switched on. That double change is σ. Do the same for the reference compound, subtract, and you have the position of the peak.
The quick sum
Nobody does that at the bench. There is a rule of thumb that needs only addition. Start from methane and add a fixed amount for each group on the carbon:
δ ≈ 0.23 + (the sum of the amounts for each group)
| Group on the carbon | Amount (ppm) |
|---|---|
| a carbon | 0.47 |
| C(=O)O | 1.55 |
| C=O | 1.70 |
| a benzene ring | 1.83 |
| O–R | 2.36 |
| Cl | 2.53 |
| OH | 2.56 |
| an ester O | 3.13 |
In the game, press S while placing a peak and the sum is written out for that carbon, with a mark on the axis. Against the measured peaks:
| Hydrogens | The sum | Predicted | Measured |
|---|---|---|---|
| Acetone CH3 | 0.23 + 1.70 | 1.93 | 2.17 |
| Toluene CH3 | 0.23 + 1.83 | 2.06 | 2.35 |
| Ethanol CH3 | 0.23 + 0.47 | 0.70 | 1.22 |
| Ethanol CH2 | 0.23 + 0.47 + 2.56 | 3.26 | 3.69 |
| Ethyl acetate O–CH2 | 0.23 + 0.47 + 3.13 | 3.83 | 4.12 |
| Isopropanol CH | 0.23 + 0.47 + 0.47 + 2.56 | 3.73 | 4.02 |
The rule was made for a CH2 carrying two groups, and is stretched here to CH3 and CH. It sees only what is on the carbon itself, which is why ethanol’s CH3, with an oxygen one carbon away, comes out furthest off. For these molecules it runs 0.2 to 0.6 ppm short every time. That is near enough to choose the region, and no substitute for the measurement.
What is drawn falsely, on purpose
Two things, and the game says so on screen.
The difference in spin rate between two hydrogens is a few parts in a million. The close-up exaggerates it about a million times, or there would be nothing to see.
A real splitting is roughly a hundredth of a ppm. The spectrum draws it far wider, so the lines can be counted.
Where the science comes from
The peak positions were checked against the table every synthetic chemist keeps to hand, Fulmer and colleagues’ chemical shifts of common impurities (Organometallics, 2010), and sit within 0.03 ppm of it. The explanations, shielding, ring current, the n + 1 rule and exchange, were checked against the OpenStax organic chemistry text.
The quick sum is Shoolery’s rule, with the amounts as tabulated from Schaller, Arnold and Pretsch (1995). The hydrogen atom’s 17.75 ppm is arithmetic from the fine-structure constant. The water and hydrogen gas values are measurements reported by Neronov and Seregin (2013).
The splitting is first-order only, which is why the crowded ring hydrogens are shown and not asked. The alcohol OH is not asked either, because its position depends on how much alcohol is in the tube.