¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A₁ and A₂), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A₁ and A₂, indicated by J_AX, equals the difference between the excitation frequencies for X, X₁ and X₂. Because both A and X have approximately equal populations in the spin-up and spin-down states, the number of A that are excited by frequency A₁ is the same as the number of A that are excited by frequency A₂. Similarly, equal numbers of X are excited by frequencies X₁ and X₂.

Indeed, the NMR signal for proton A is split into two peaks with equal intensity, centered at the chemical shift of A, and likewise for X. The peaks in each doublet are separated by J_AX, the coupling constant, which ranges from 0–20 Hz for proton–proton coupling. For spin–spin coupling to occur, the nuclei have to be NMR-active, nonequivalent, and separated by three or fewer bonds. However, in some exceptional cases, coupling can occur between nuclei that are separated by more than three bonds.