  We present a systematic theoretical investigation of the surface properties,
stability and reactivity, of rock-salt type alkaline-earth metal oxides
including MgO, CaO, SrO, and BaO. The accuracy of commonly used
exchange-correlation density functionals (LDA, PBE, RPBE, PBEsol, BEEF-vdW and
hybrid HSE) and random-phase approximation (RPA) is evaluated and compared to
existing experimental values. Calculated surface energies of the four most
stable surface facets under vacuum conditions: the (100) surface, the metal and
oxygen terminated octopolar (111), and the (110) surfaces exhibit a monotonic
increase in stability from MgO to BaO. On the MgO(100) surface, adsorption of
CO, NO, CH4 is characterized by physisorption while H2O chemisorbs, which is in
agreement with experimental findings. We further use the on-top metal
adsorption of CO and NO molecules to map out the surface energetics of each
alkaline-earth metal oxide surface. The considered functionals all
qualitatively predict similar adsorption energy trends. The ordering between
the adsorption energies on different surface facets can be attributed to
differences in the local geometrical surface structure and the electronic
structure of the metal constituent of the alkaline-earth metal oxide. The
striking observation that CO adsorption strength is weaker than NO adsorption
on the (100) terraces as the period of the alkaline-earth metal in the oxide
increases, is analyzed in detail in terms of charge redistribution within the
{\sigma} and {\pi} channels of adsorbates. Finally, we also present oxygen
adsorption and oxygen vacancy formation energies in these oxide systems.
