Quantum mechanical methods using a point-charge embedded cluster technique have been applied to the Ti/MgCl2-supported Ziegler-Natta catalyst to investigate how different oxidation states of Ti (III and IV) and different surface structures of the beta-MgCl2 crystal ((100) and (110) planes) influence the geometries and energetics of (i) Ti complexes adsorbed on the surfaces of the beta-MgCl2 crystal and (ii) the precoordinated-ethylene Ti complexes adsorbed on the same surfaces. Our calculations indicate that the Ti(III) complexes will be adsorbed on the surface of the (100) plane more strongly than those of Ti(IV). We also find that Ti(III) complexes bind more strongly to the (110) than to the (100) plane. Finally, our comparison of the energies of precoordinated-ethylene Ti complexes adsorbed on the different surfaces suggests that the atomic arrangement of the surfaces of the beta-MgCl2 crystal is crucial in stabilising such surface complexes.