Surface properties of ${\mathrm{CeO}}_2$ from first principles

The surface energies and electronic structure of (111), (110), and (100) surfaces of ${\mathrm{CeO}}_2$ have been studied using the first-principles projector augmented-wave method within the local density approximation (LDA) and generalized gradient approximation (GGA) and are compared with molecular dynamics (MD) simulations at 10 K. Slabs of the same thicknesses were used for the two methods (lamellar three-dimensional boxes in the case of density functional theory and two-dimensional isolated slabs in the MD simulations). The polar (100) surface of ${\mathrm{CeO}}_2$ was modeled as an oxygen-terminated surface with half of the oxygen atoms moved from one surface to the other to fulfill the stoichiometric formula. Among a number of different possible terminations, the checkerboard termination was found to be the most stable. Out of all three low-index surfaces, the (111) surface was found to be the most stable, in agreement with experiment and previous calculations. Our calculated surface energy is $1.0{\mathrm{J}/\mathrm{m}}^2$ (LDA) and $0.7{\mathrm{J}/\mathrm{m}}^2$ (GGA). Both values are lower than most calculated surface energies for this surface in the literature, including our present MD results $\left(1.4\mathrm{}{\mathrm{J}/\mathrm{m}}^2\right).\mathrm{}$ For (110) our surface energies (LDA, GGA, and MD) are 40%–60% higher than for (111). The structural relaxation is considerably larger for (110) than for (111) and shows excellent agreement between LDA, GGA, and MD. Also the electronic density of states shows larger differences between surface and bulk for the (110) surface than for (111), with, for example, a decrease of the band gap between the valence band (essentially O $2p)$ and the empty Ce $4f$ band in the (110) surface region compared to the bulk.