Ab initio calculations were used to investigate properties of complexes formed from the association of CH4 with Al2O3, Al4O6, and Al8O12 alumina clusters. Methane attaches to a surface Al atom of the cluster to form a complex with an Al-C separation that varies between 2.2 and 2.5 Angstrom. The rotational motion for methane in these complexes is highly fluxional. Extrapolated G2MP2 well depths fbr the CH4- - -Al2O3, CH4- - -Al4O6. and CH4- - -Al8O12 complexes are 21, 14, and 17 kcal/mol, respectively. These different well depths ale determined by the accessibility of the Al atom to which CH4 binds and the size of the alumina cluster. The electrostatics of the three alumina clusters are very similar, with a charge on the surface Al atom of + 2.2 to 2.3. The potential energy surface for a CH4- - -Al2nO3n cluster is represented semiquantitatively by an analytic Function consisting of two-body potentials. The results of this study suggest that the adsorption energy for alkane molecules binding to alumina materials depends very strongly on the structure of the binding site.