If each proton interacted only with the applied field two singlets only would be obtained. But proton H_A actually experiences two slightly different fields: the applied field plus the field of H_X or the applied field minus the field of H_X. H_X acts either to increase or to decrease the field experienced by H_A. The position of a resonance depends on the field experienced by the proton so these two situations give rise to two slightly different peak-a doublet as it is called. And whatever happens to H_A happens to H_X as well, so the spectrum has two doublets, one for each proton. Each couples with the other. The field of a proton is a very small indeed in comparison with the field of the magnet and the separation between the lines of a doublet is very small.

The second explanation takes into account the energy levels of the nucleus. Electronic energy levels on neighbouring atoms interact with each other and splitting to produce new molecular energy levels, some higher in energy and some lower in energy than the original atomic energy levels. When hydrogen nuclei are near each other in a molecule, the nuclear energy levels also interact and split and produce new energy levels. If a single hydrogen nucleus interacts with a magnetic field there are two energy levels as the nucleus can be aligned with or against the applied magnetic field, there is one energy jump possible, and there is a resonance at one frequency.


•  This representation shows H_A protons independent of the influence of H_X. Each had two energy levels, each gave a singlet, and there were two lines in the spectrum. But, if each proton has hydrogen nucleus nearby and then there are now four energy levels. Each nucleus H_A and H_X can be aligned with or against the applied field. There is one most stable energy level where they are both aligned with the field and one least stable level where they are both aligned against. In between there are two different energy levels in which one nucleus is aligned with the field and one against. Exciting H_A from alignment with to alignment against the applied field can be done in two slightly different ways, shown as A₁ and A₂ on the diagram given below. The result is two resonances very close together in the spectrum. If there are two slightly different energy jumps to excite H_A, there must also be two slightly different energy jumps to excite H_X. The difference between A₁ and A₂ is exactly the same as the difference between X₁ and X₂. Each proton now gives two lines (a doublet) in the NMR spectrum and the splitting of the two doublets is exactly the same. This situation is described as coupling. We say ‘A and X are coupled' or ‘X is coupled to A'(and vice versa, of course). Now look back at the spectrum of cytosine at the beginning of this section. Each is split by the same amount and the separation of the lines is the coupling constant and is denoted by J. Coupling constants J are measured in Hz because the same number regardless of the frequency of the spectrometer.