¹H NMR Signal Multiplicity: Splitting Patterns

Proton signals split due to spin-spin coupling between nonequivalent protons separated by three or fewer bonds. When a coupled proton experiences different nuclear spin states of neighboring protons, it requires different excitation frequencies. This creates multiple peaks in the NMR spectrum, with peak separation determined by the coupling constant J, measured in Hertz.

Peak intensity in a split signal depends on the population distribution of nuclear spin states. Because coupled protons have approximately equal populations in spin-up and spin-down states, the number of protons excited at each frequency is roughly equal. This produces peaks of equal intensity within a multiplet, centered at the proton's chemical shift.

The coupling constant J, expressed in Hertz, directly equals the frequency difference between split peaks. For example, if proton A couples with proton X, the separation between A's two peaks equals JAX, the same value separating X's peaks. This mutual relationship reflects the symmetric nature of spin-spin coupling between the two nuclei.

Spin-spin coupling requires that protons be NMR-active, nonequivalent, and separated by three or fewer bonds. In exceptional cases, coupling can occur between nuclei separated by more than three bonds. The coupling constant for proton-proton coupling typically ranges from 0–20 Hz, depending on the structural relationship and bond angles between the coupled nuclei.

When proton X exists in a spin-up state, it modifies the energy required to excite proton A, creating one excitation frequency. When X is in a spin-down state, A requires a different excitation frequency. Since X populates both states equally, proton A absorbs at two distinct frequencies, producing a doublet with two equally intense peaks in the NMR spectrum.

Spin-spin coupling is mutual because the frequency difference between coupled proton A's two peaks equals the frequency difference between coupled proton X's two peaks. Both protons experience the same coupling constant J, reflecting the symmetric nature of their nuclear spin interaction. This reciprocal relationship means coupling effects appear identically in both protons' NMR signals.

Nuclear spin energy levels of coupled protons are slightly modified by their mutual interaction. This modification creates two possible excitation frequencies for each proton, depending on the spin state of its coupling partner. The resulting energy level splitting directly causes signal multiplicity, with the number and intensity of peaks reflecting the spin populations and coupling relationships between nuclei.