When a nucleus has a spin quantum number, I, greater than 1/2 it has a quadrupole moment. In that case, coupling of nuclear spin angular momentum with rotational angular momentum causes splitting of the rotational energy levels. If the quantum number J of a rotational level is greater than I,  levels are produced; but if J is less than I,  levels result. The effect is one type of hyperfine splitting. For example, with N () in HCN, all levels with J > 0 are split into 3. The energies of the sub-levels are proportional to the nuclear quadrupole moment and a function of F and J. where , . Thus, observation of nuclear quadrupole splitting permits the magnitude of the nuclear quadrupole moment to be determined.
This is an alternative method to the use of nuclear quadrupole resonance spectroscopy. The selection rule for rotational transitions becomes