NMR Spectroscopy

How NMR works

Most atomic nuclei carry a property called spin, an intrinsic quantum mechanical angular momentum. In the absence of a magnetic field, spins point every which way and average to nothing. Drop the sample into a superconducting magnet — typically 7 to 23 tesla, hundreds of thousands of times Earth's field — and the spins find two preferred orientations: aligned with the field (lower energy) or against it (higher energy). The energy gap ΔE between those states is set by the Larmor equation:

ΔE = γ ℏ B₀
ν₀ = γ B₀ / (2π)     (Larmor frequency, in Hz)

Here γ is the gyromagnetic ratio — a fixed property of each nuclide — and B₀ is the field strength. For protons in a 11.7-tesla magnet, ν₀ ≈ 500 MHz, smack in the FM radio band. The instrument zaps the sample with a calibrated radiofrequency pulse; the spins absorb, then re-emit as they relax, and an antenna captures the decaying signal. Fourier transform that decay and you get a spectrum — peaks at the resonance frequencies of every chemically distinct nucleus.

The whole game hinges on the word distinct. A bare proton would resonate at exactly ν₀, but real protons are surrounded by electrons that orbit them and screen part of the external field. The local field a nucleus actually feels is B = B₀(1 − σ), where σ is the shielding constant. Protons in different environments — methyl vs methylene vs aromatic vs aldehyde — feel different effective fields and so resonate at different frequencies. That tiny offset, normalised by the spectrometer frequency to make it field-independent, is the chemical shift.

The three observables

An NMR spectrum hands you three numbers per peak, and together they triangulate structure.

• Chemical shift (δ, in ppm). Where on the horizontal axis the peak sits. It tells you the electronic environment: shielded (low δ, upfield) for protons next to electron-donors, deshielded (high δ, downfield) for protons next to electron-withdrawers like oxygen, halogens, or aromatic rings.
• Multiplicity (splitting pattern). The shape of the peak — singlet, doublet, triplet, quartet, multiplet. Caused by J-coupling between non-equivalent nuclei separated by 1, 2 or 3 bonds. Reveals connectivity: what's next to what.
• Integration (area under the peak). Proportional to the number of equivalent nuclei contributing to that peak. A 3:2:1 integration in ¹H NMR reads as 3H : 2H : 1H — the relative count of protons in each environment.

Most introductory structure-elucidation problems are solved by laying these three columns next to each other in a table, walking down them, and asking: what arrangement of atoms could produce exactly this pattern?

Chemical shift cheat sheet

The single most useful piece of furniture in an organic chemist's brain is the ¹H chemical-shift table. A working set:

Proton type	δ (ppm)	Notes
R−CH₃ (alkyl)	0.7 – 1.3	Most shielded; sets your low-end anchor.
R−CH₂−R	1.2 – 1.5	Slightly deshielded vs CH₃ by neighbours.
R−CH₂−C=O	2.0 – 2.5	α-protons next to a carbonyl.
R−CH₂−Cl, R−CH₂−Br	3.0 – 4.0	Halogens pull electron density.
R−O−CH₃, R−O−CH₂−R	3.3 – 4.0	Methoxy and methylene ethers.
=CH−R (vinyl)	4.5 – 6.5	sp² carbon, alkene.
Aromatic H	6.5 – 8.5	Ring-current deshielding.
R−CHO (aldehyde)	9.5 – 10.0	Diagnostic singlet (or doublet if α-H).
R−COOH (carboxylic acid)	10 – 13	Broad; concentration-dependent.

Memorising the anchors — alkyl ~1, α-to-carbonyl ~2, next-to-O ~3.5, vinyl ~5, aromatic ~7, aldehyde ~9.7, acid ~12 — gets you 80% of the way through any first-pass spectrum.

¹H vs ¹³C vs ¹⁹F vs ³¹P NMR

Nucleus	Natural abundance	Sensitivity vs ¹H	Typical shift range	What it tells you
¹H (proton)	99.985 %	1.00	0 – 12 ppm	Hydrogen environments, connectivity via splitting.
¹³C (carbon)	1.07 %	1.7 × 10⁻⁴	0 – 220 ppm	Carbon skeleton; a single peak per unique C.
¹⁹F (fluorine)	100 %	0.83	−300 to +400 ppm	Fluorine environments; vital for fluorinated drugs.
³¹P (phosphorus)	100 %	0.066	−200 to +250 ppm	Nucleotides, phosphate metabolism, ligands.
¹⁵N (nitrogen)	0.37 %	3.9 × 10⁻⁶	0 – 900 ppm	Protein backbones; needs ¹⁵N-labelled samples.
²H (deuterium)	0.015 %	1.1 × 10⁻⁶	0 – 12 ppm	Used as field-lock signal in solvents.

Three patterns to take away. Sensitivity tracks γ³ × abundance, so fluorine and phosphorus — both 100% naturally abundant with healthy γ — give clean spectra in minutes. Carbon needs a few thousand scans because of its 1.1% abundance; nitrogen is hopeless without isotopic enrichment. Shift ranges roughly mirror the diversity of bonding environments — fluorine spans 700 ppm because tiny electronic perturbations move ¹⁹F a lot, while protons all huddle within 12 ppm because they sit at the periphery and feel weaker shielding effects.

Splitting and the n+1 rule

Two non-equivalent nuclei separated by up to three bonds couple magnetically. Each "feels" the spin state of the other through the bonding electrons, and that coupling splits the peaks. The simplest case is the n+1 rule: a nucleus with n equivalent neighbours gives n+1 lines, with intensities following Pascal's triangle.

n = 0  singlet     1
n = 1  doublet     1 1
n = 2  triplet     1 2 1
n = 3  quartet     1 3 3 1
n = 4  pentet      1 4 6 4 1

The classic textbook spectrum is ethanol, CH₃−CH₂−OH:

• The CH₃ group sees two equivalent CH₂ neighbours: 2+1 = triplet at δ ~1.2 ppm, integration 3H.
• The CH₂ group sees three equivalent CH₃ neighbours: 3+1 = quartet at δ ~3.7 ppm, integration 2H.
• The OH proton exchanges fast with traces of water, doesn't couple cleanly: broad singlet at δ ~2.5 ppm, integration 1H.

Spacing between lines is the coupling constant J, measured in Hz, and is field-independent. Typical values: J(¹H–¹H) vicinal ~7 Hz in saturated chains, ~12–18 Hz for trans alkenes, ~6–12 Hz for cis alkenes. Mismatched J values (n+1 fails) signal magnetic non-equivalence — diastereotopic CH₂ protons next to a stereocentre, for instance.

Two-dimensional NMR

For molecules bigger than ~20 carbons, 1D spectra get crowded and 2D NMR takes over. The principle: encode chemical shift along two orthogonal axes and let cross-peaks reveal correlations between nuclei.

• COSY (¹H–¹H Correlation Spectroscopy). Cross-peaks at (δ_A, δ_B) wherever protons A and B are J-coupled. Walks you around the proton skeleton bond by bond.
• HSQC (Heteronuclear Single-Quantum Coherence). One-bond ¹H–¹³C correlations: every cross-peak says "this proton sits on this carbon". Great for assignment.
• HMBC (Heteronuclear Multiple-Bond Correlation). Two- and three-bond ¹H–¹³C correlations. Connects fragments across quaternary carbons that have no protons of their own.
• NOESY (Nuclear Overhauser Effect Spectroscopy). Through-space cross-peaks for protons within ~5 Å. Reveals 3D conformation and distinguishes stereoisomers.

A modern protein structure-determination pipeline runs HSQC, HSQC-TOCSY, HNCA and HNCACB in succession, working through all 4,000+ correlations of a 100-residue ¹⁵N/¹³C-labelled protein over the course of a few weeks of magnet time.

Worked example: an unknown C₄H₈O₂

You receive a colourless liquid with molecular formula C₄H₈O₂ and the following ¹H NMR spectrum (CDCl₃):

δ (ppm)	Multiplicity	Integration
4.10	quartet, J = 7 Hz	2H
2.05	singlet	3H
1.25	triplet, J = 7 Hz	3H

Reasoning. Total integration 8H matches C₄H₈O₂. The triplet at 1.25 ppm + quartet at 4.10 ppm with matched J = 7 Hz is a textbook ethyl group. The 4.10 ppm shift puts that CH₂ next to an electron-withdrawing oxygen — so we have −O−CH₂−CH₃. The lone singlet at 2.05 ppm with 3H integration is an isolated CH₃ with no ¹H neighbours, sitting at a shift typical of α-to-carbonyl. The remaining atoms account for an acetate carbonyl, C(=O)O. Stitch the pieces: CH₃−C(=O)−O−CH₂−CH₃, ethyl acetate. Cross-checked by ¹³C NMR (four peaks: 171, 60, 21, 14 ppm) and IR (1742 cm⁻¹ ester C=O).

Practical considerations

• Sample concentration. 5–20 mg of solute in 0.6 mL of deuterated solvent for routine ¹H. ¹³C wants 30–50 mg or hours of scans.
• Solvent choice. CDCl₃ is the workhorse (residual peak at δ 7.26 ppm). DMSO-d₆ for hydrogen-bonded compounds, D₂O for water-soluble salts, methanol-d₄, acetone-d₆ for niche cases.
• Shimming. The magnetic field must be homogeneous to a few parts per billion across the sample volume. Auto-shim adjusts a stack of correction coils until linewidths drop below ~1 Hz.
• Field-frequency lock. The deuterium signal of the solvent is monitored continuously; its frequency drift drives a feedback loop that keeps the field stable for the hours-long acquisitions of insensitive nuclei.
• Relaxation delays. ¹H usually relaxes in 1–5 s; ¹³C can take 10–60 s. Setting the recycle delay too short under-counts slow-relaxing carbons in quantitative experiments.

Where NMR earns its keep

• Drug discovery. Every new pharmaceutical compound is characterised by ¹H, ¹³C and 2D NMR before it reaches a regulator. Pfizer, Roche and Novartis each run thousands of samples per week through automated 600 MHz queues.
• Protein structure. Solution NMR and solid-state NMR have deposited ~13,000 structures in the Protein Data Bank, complementing X-ray crystallography for proteins under 30 kDa or those that refuse to crystallise.
• Metabolomics. Untargeted ¹H NMR of urine or plasma quantifies dozens of metabolites simultaneously; clinical platforms like the Bruker IVDr profile blood samples in 30 minutes.
• Medical imaging. Magnetic resonance imaging is NMR with spatial encoding; the same physics, dressed in gradient coils.
• Polymer characterisation. Tacticity, end-group analysis, copolymer composition — all routine NMR jobs in industrial labs.
• Petroleum and food. ¹H NMR fingerprints olive oil grades, distinguishes single-malt whiskies, and monitors fuel composition.

Common mistakes and pitfalls

• Trusting the integration on protons that exchange. OH, NH and COOH protons swap with traces of water in the solvent; their integrations can be anything between 0 and the true value, and their multiplicity is usually washed out.
• Forgetting the solvent residual peak. CDCl₃ leaves a peak at δ 7.26 ppm, DMSO-d₆ at 2.50 ppm, D₂O at 4.79 ppm. Mistaking residual solvent for a sample peak is a beginner's classic.
• Assuming all CH₂ groups give triplets. n+1 holds only for first-order spectra (Δν / J > ~6). When chemical-shift difference is comparable to J, "second-order" patterns emerge: roofing, leaning, AB quartets that look weird until you remember the coupling regime.
• Quantifying ¹³C peaks naively. Standard ¹³C uses NOE enhancement and short relaxation delays — peak heights are not proportional to atom counts. Use inverse-gated decoupling and long delays for quantitative ¹³C.
• Ignoring impurities and tautomers. A small extra peak isn't always noise; it might be a regiosomeric impurity, a tautomer, or starting material. Cross-check integration sums against the proposed formula.
• Misreading multiplets in dilute samples. Lock-noise and t₁ noise on weak peaks can disguise a doublet of doublets as a triplet. When in doubt, expand the region and check J in Hz — coupling constants are diagnostic.