If so, a quadrupole-quadrupole interaction (see next section) can be considered as a two step dipole-dipole interaction, e.g. For example, <math> Y_{2_{i}}^{+2_{i}}Y_{2_{j}}^{-2_{j}}=4Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}}Y_{1_{j}}^{-1_{j}}Y_{1_{j}}^{-1_{j}} </math>, so the one step quadrupole transiton <math> Y_{2_{i}}^{+2_{i}} </math> on site <math> i </math> now becomes a two steps of dipole transition <mat> Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}} </math>. However, it is not a perturbation expansion but just a mathematical technique. The high rank multi-exchange terms are not necessarily smaller than low rank terms. In many cases, high rank terms are more important than low rank terms.<ref name="Review"/>
