Comparison of the full-potential and frozen-core approximation approaches to density-functional calculations of surfaces

We scrutinize the accuracy of the pseudopotential approximation in density-functional theory calculations of surfaces by systematically comparing to results obtained within a full-potential setup. As model system we choose the CO oxidation at a $\mathrm{Ru}{\mathrm{O}}_{2}(110)$ surface and focus in particular on the adsorbate binding energies and reaction barriers as target quantities for the comparison. Rather surprisingly, the major reason for discrepancy does not result from the neglected semicore state relaxation in the frozen-core approximation, but from an inadequate description of the local part of the Ru pseudopotential, responsible for the scattering of $f$-like waves. Tiny, seemingly irrelevant, imprecisions appearing in these properties can have a noticeable influence on the surface energetics. At least for the present example, we obtain excellent agreement between both approaches, if the pseudopotential describes these scattering properties accurately.