The translational motion of benzene molecules on the surfaces of a number of different types of materials, such as silica and a Pt/silica catalyst, has been studied using deuteron NMR techniques. When the temperature dependence of the correlation time for this motion was correlated using an Arrhenius type expression, it was found that a compensation effect was observed, This means that there was a linear relationship between the activation energy and the natural logarithm of the pre-exponential factor. The origin of this effect has been explained by a theory for the molecular motion based on the fractal nature of the surfaces over which the benzene molecules are moving.