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The geometries and electronic structures resulting from surface reduction, CO adsorption, and NO2 adsorption at the (110) surface of CeO2 have been calculated using density functional theory corrected for on-site Coulomb interactions, GGA+U. We report a novel electronic structure for the reduced surface, denoted the split vacancy, which is more stable than the previously reported simple vacancy with subsurface CeIII. Analysis of CO adsorption modes highlights the importance of the geometry of the CO molecule when in contact with the surface, with a tilted adsorption mode being most energetically favorable with the formation of a carbonate anion coupled with surface reduction. A new bidentate adsorption mode is observed for NO2 adsorption, accompanied by partial surface oxidation. These novel structures observed on reduction, CO adsorption, and NO2 adsorption are all energetically more stable than the previously reported structures. In all of the systems, it was found that the location of the CeIII ions did not have a strong effect on the energetics, although they were coupled to strong local distortions of the structure.