The effect of the isomorphic substitution of silicon by aluminum on the structure of a zeolite cluster and its interaction with methane are studied within the framework of the density functional and the atoms-in-molecules theories. It is found that the inclusion of aluminum into the zeolite lattice leads to the development of Bronsted acid sites and to an increase in the base character of those oxygen atoms not involved in the acid sites. The calculated interaction energies indicate that methane interacts more strongly with the zeolite after the isomorphic substitution takes place, suggesting the importance of the Bronsted acid sites. The topological study clearly shows that the interaction of methane with the zeolite before the isomorphic substitution is dominated by a very weak Si-(OH)-H-...-C van der Waals interaction. After the replacement of silicon by aluminum occurs, the interaction takes place through very weak Si-(OH)-H-...-C and weak O-(HC)-C-... van der Waals interactions, the latter being the main responsible for the stabilization of the complex.