13.3 ¹H and ¹³C NMR: Chemical Shift, Spin–Spin Coupling and Coupling Constants

13.3.1 How NMR works ★★

¹H and ¹³C have spin I = ½. In a field B₀ the two spin states (m = +½, aligned; −½, opposed) split by ΔE; radio waves of exactly that energy flip the spin (resonance). The nuclei feel not B₀ but a slightly smaller local field, because the electrons round them circulate and oppose B₀: they are shielded.

• A 9.4 T magnet makes ¹H resonate near 400 MHz and ¹³C near 100 MHz (γ of ¹³C is a quarter of ¹H). “A 400 MHz spectrometer” names the field.SN
• Population difference is tiny (a few in 10⁵), so NMR is insensitive; ¹³C is 1.1 % abundant and weaker still. Spectra are run in CDCl₃ with TMS, Si(CH₃)₄, as the zero: 12 equivalent, strongly shielded H and inert.

13.3.2 Chemical shift ★★★

• δ does not depend on the field; Hz does. δ 3.0 at 100 MHz is 300 Hz from TMS; at 500 MHz it is 1500 Hz, still δ 3.0. J (4.5 Hz) is the same at both fields CSE 2025 Q5(e) 10m. Two signals at δ 4.3 and 5.7 on a 400 MHz instrument: Δν = 1.4 × 400 = 560 Hz IFoS 2023 Q7(g) 5m.SN
• Electronegativity deshields: CH₃–X: Si 0, C 0.9, N 2.2, Cl 3.0, O 3.4, F 4.3. Each extra halogen adds ≈ 2 ppm (CH₂Cl₂ 5.3, CHCl₃ 7.3).SN
• Hybridisation and anisotropy (13.3.3) decide the alkene (4.5–6.5), arene (6.5–8.5), aldehyde (9.5–10) and alkyne (≈ 2.5) values.
• Resonance moves alkene H: in an enol ether (CH₂=CH–OMe) the O lone pair (+M) pushes density to the β-carbon: Hβ ≈ 4.0–4.2; in an enone (CH₂=CH–COMe) C=O pulls it away (−M): Hβ ≈ 6.1–6.3. Ethene is 5.3 CSE 2025 Q8(a)(ii) 5m.SN
• Para-substituted benzenes: all three groups withdraw, so all are downfield of benzene (7.27): CF₃ (−I only, ≈ 7.8) < COOH (−M, −I, ≈ 8.1) < NO₂ (strongest −M, −I, ≈ 8.4) Geo 2022 Q6(g) 4m. Ordering lettered protons by δ CSE 2023 Q6(c)(ii) 10m CSE 2024 Q5(e) 10m.

13.3.3 Diamagnetic anisotropy ★★

• Benzene: the ring current's induced field adds to B₀ at the ring H (δ 7.3) and opposes it inside and above the ring. In anthracene H-9,10 (beside two rings) δ 8.42 > H-1 8.00 > H-2 7.45 CSE 2024 Q5(e).SN
• Inside the ring current: the internal CH₃ groups of trans-15,16-dimethyldihydropyrene sit over the centre of an aromatic 14π periphery and come at δ −4.2, below TMS; the outer H are at 8–8.7 IFoS 2021 Q3(a)(ii) 5m. [18]Annulene: inner H −3, outer H 9.3.SN
• Alkyne: the cylinder of π electrons, with its axis along B₀, shields the ≡C–H: δ ≈ 2.5 (not 5–6). In 4-methylpent-1-yne ≡C–H 2.5 (s; the 2–3 Hz coupling to CH₂ is often unresolved), CH₂ 2.0 (d), CH 1.7 (m), (CH₃)₂ 1.0 (d) Geo 2025 Q6(j) 4m.
• C=O and C=C: H in the plane are deshielded: aldehyde H 9.5–10; the vinyl H cis to C=O in an acrylate is the most downfield (6.4).

13.3.4 Equivalence: how many signals ★★★

Chemically equivalent (isochronous) protons are interchanged by a symmetry operation (C_n axis: homotopic; mirror plane: enantiotopic) or by fast rotation: one signal. Diastereotopic protons (replace each in turn by D: diastereomers result) are anisochronous: two signals. Magnetically equivalent needs, in addition, the same J to every other nucleus.SN

• 2-Chlorobutane: 5 signals (two CH₃, CHCl and the two diastereotopic CH₂ H). 1,6-Dimethylcyclohexa-1,4-diene, one stereocentre and no symmetry: 8 signals CSE 2025 Q8(a)(iii) 5m.SN
• Styrene: the two terminal =CH₂ protons are neither chemically nor magnetically equivalent (one cis, one trans to the internal H; different δ and different J). Ortho H-2/H-6 share a δ but couple differently to H-3, so they are chemically but not magnetically equivalent IFoS 2023 Q5(f) 5m.
• A p-disubstituted ring with an =CH₂ on one side: the two vinylic H are diastereotopic, two aromatic sets, seven signals in all; trans-1,2-dimethylcyclopropane (C₂ axis) 3 signals, cis (mirror plane only, its CH₂ protons differ) 4 CSE 2023 Q5(a) 10m.
• Anthracene (D₂h), cyclohexa-1,3-diene (C₂) and norbornadiene (C₂v): three signals each. Norbornadiene vinyl H 6.75 (strained C=C), bridgehead 3.58, CH₂ 1.95 CSE 2024 Q5(e).