The carbon dioxide reduction reaction is a promising candidate to tackle ecological challenges of our age. This is due to its capability of reducing carbon dioxide emission generated from the combustion of fossil fuels by converting carbon dioxide into valuable hydrocarbons. Oxide-derived metal nanostructures have been found to exhibit unique catalytic characteristics for facilitating the carbon dioxide reduction reaction. In this thesis work, the stability, influence, and effects of subsurface oxygen atoms are investigated by theoretical computations with various levels of theory and models. It is found that subsurface oxygen atoms are stable and that their presence increases the CO adsorption strength and coverage on oxide-derived Cu surface. This is explained by a reduced σ-repulsion and leads to the breaking of scaling relations. Although it does not directly reduce the CO dimerization barrier, the adsorption of H atoms is inhibited thus steering the selectivity. The presence of subsurface oxygen atoms is also concluded from a joint work with experimental and theoretical efforts of X-ray photoelectron spectroscopy. The precursor region of CO desorption from Ru(0001) is studied with the transition potential method. In contrast, for the simulation of the X-ray spectroscopy results on p4g C/Ni(100), which is a surface reconstruction when carbon atoms adsorb on Ni(100), vibrational effects are also needed for understanding the experimental data.