The importance of an accurate knowledge of the crystal potential for theoretical modelling of reactions at metal oxide surfaces is investigated for some model systems: atomic oxygen adsorption on MgO(001) and CaO(001), a simple model of CO oxidation using an atomically adsorbed oxygen and finally the migration barrier of an oxygen atom on the MgO(001) and CaO(001) surfaces. Oxygen is found to adsorb at an anion site, with a geometry that is independent of the crystal potential. The binding energy strongly depends on the value of the potential. The location of the transition state in the CO oxidation reaction and the computed barrier are only weakly dependent on the potential, while the exothermicity shows a strong dependence. The binding energies of oxygen to a regular anion site in MgO(001) is found to be much smaller than in CaO(001). The effects of this finding on the N2O decomposition mechanism over the respective surfaces are discussed.