This dataset supports the density functional theory (DFT) study of H2 activation and H2-induced oxidation on reduced CeO2, with an emphasis on how oxygen-vacancy configurations regulate heterolytic versus homolytic dissociation pathways. It contains atomic structures and energetics for stoichiometric and reduced CeO2 surfaces featuring distinct surface and cross-layer oxygen-vacancy arrangements, together with computed adsorption geometries, reaction pathways, and transition states for H2 dissociation leading to hydroxyl/hydride products or paired hydrides accompanied by Ce3+ oxidation.