13.6 Spin–Spin Splitting in 1H NMR Spectra

Spin–Spin Splitting in 1H NMR Spectra

Spin-spin splitting is the reason 1H NMR signals appear as multiplets (doublets, triplets, quartets, etc.) rather than single peaks. These splitting patterns tell you how many non-equivalent protons are on neighboring carbons, which is incredibly useful for piecing together a molecule's connectivity.

Two main tools drive your analysis here: the n+1 rule (which predicts how many peaks you'll see) and coupling constants (which reveal spatial relationships between protons).

Spin-Spin Splitting in 1H NMR Spectra

Spin-spin splitting in NMR spectra

Splitting happens because neighboring non-equivalent protons influence each other's local magnetic fields. Each neighboring proton can exist in one of two spin states: $\alpha$ (aligned with the external field) or $\beta$ (opposed to it). These two states slightly increase or decrease the effective field felt by the proton you're observing, which shifts its resonance frequency and splits the signal.

• The number of peaks in a split signal (a multiplet) depends on how many neighboring non-equivalent protons ($n$) are present, following the n+1 rule
• The intensity ratios within a multiplet follow Pascal's triangle: 1:1 for a doublet, 1:2:1 for a triplet, 1:3:3:1 for a quartet, and so on
• The spacing between peaks in a multiplet is the coupling constant ($J$), measured in Hertz (Hz)

The coupling constant is independent of the spectrometer's magnetic field strength. Its magnitude depends on how many bonds separate the interacting protons and the dihedral angle between them.

Multiplet patterns and the n+1 rule

The n+1 rule is straightforward: the number of peaks in a multiplet equals the number of neighboring non-equivalent protons ($n$) plus one.

1. $n = 0$ (no non-equivalent neighbors) → singlet (1 peak)
2. $n = 1$ (one neighbor) → doublet (2 peaks)
3. $n = 2$ (two neighbors) → triplet (3 peaks)
4. $n = 3$ (three neighbors) → quartet (4 peaks)

For example, in an ethyl group ($-CH_2CH_3$), the $CH_2$ protons have three neighboring $CH_3$ protons, so they appear as a quartet. The $CH_3$ protons have two neighboring $CH_2$ protons, so they appear as a triplet.

Equivalent protons do not split each other. Two protons are considered equivalent if they're in the same chemical environment and have the same coupling relationships with every other proton in the molecule.

• Chemical equivalence means the protons have the same chemical shift. The three protons of a methyl group are chemically equivalent because rapid rotation makes their environments identical.
• Magnetic equivalence is a stricter requirement: the protons must also couple equally to every other proton in the molecule. In a para-disubstituted benzene ring, for instance, protons that are chemically equivalent may not be magnetically equivalent because they have different coupling relationships to the other ring protons.

Protons on the same carbon (geminal) or on adjacent carbons (vicinal) are often non-equivalent and cause splitting. A special case worth knowing: diastereotopic protons are two protons on the same carbon that are non-equivalent because of a nearby stereocenter. They can have different chemical shifts and different coupling patterns, which sometimes makes spectra more complex than you'd initially expect.

Coupling constants for structural analysis

Coupling constants ($J$) carry information about both the number of bonds between interacting protons and their geometric relationship.

Typical $J$ value ranges:

The Karplus relationship connects vicinal coupling constants ($^3J$) to the dihedral angle between the two C–H bonds:

• At $0°$ (syn-periplanar) or $180°$ (anti-periplanar), orbital overlap is maximized, giving large $^3J$ values (8–14 Hz)
• At $60°$ (gauche), overlap is poor, giving small $^3J$ values (2–6 Hz)

This relationship is especially useful for distinguishing stereoisomers. For example, trans alkene protons typically show $^3J$ values of 12–18 Hz, while cis alkene protons show 6–12 Hz. In cyclic systems, axial-axial protons (180° dihedral) couple more strongly than axial-equatorial or equatorial-equatorial pairs.