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 JAX, 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 JAX, 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.
