We present ab initio periodic Hartree-Fock calculations (CRYSTAL program) of the adsorption of small molecules on TiO2 and MgO. These may be molecular or dissociative, depending on the acidic and basic properties of the molecules in gas phase and of the nature of the surface oxide. Far the molecular adsorption, the molecules are adsorbed as bases on Ti(SN) sites, the adsorption energies correlate with the proton affinities. The dissociations on the surface correlate with the gas phase cleavages of the molecule; they also depend on the surface oxide; the oxygen atom of MgO, in spite of its large charge, is poorly reactive and dissociation on MgO is not favorable. The surface hydrosyl of MgO are more basic than the O of the lattice and water is not dissociated under adsorption. As experimentally observed, NH3 adsorbs preferentially on TiO2 and CO2 on MgO. However, this difference of reactivity should not be expressed in terms of acid vs basic behavior, but in terms of hard and soft acidity. MgO surface is a "soft" acidic surface that reacts preferentially with the soft base, CO2. Another important factor is the adsorbate-adsorbate interaction: favorable cases are the sequence of H-bonds for the hydroxyl groups resulting from the water dissociation and the mode of adsorption for the ammonium ions. Lateral interactions also force the adsorbed CO2 molecules to bend over the surface, so that their mutual orientation resembles the geometry of the CO2 dimer. (C) 1999 Elsevier Science B.V. All rights reserved.