Density-functional theory applied to Rh(111) and CO/Rh(111) systems: Geometries, energies, and chemical shifts

We present extensive density-functional theory (DFT) based calculations of the clean Rh(111) surface and of CO/Rh(111) overlayer systems. We study both ground-state structural properties and core-level shifts from differences in total energies at different coverages and adsorption sites. Most results are obtained using using norm-conserving or ultrasoft pseudopotentials. The overall reliability of the pseudopotential method is analyzed theoretically, and computationally by way of all-electron calculations. In general, core corrections are required in order to correctly simulate all-electron total energies, although the corrections are rather small for the systems considered here. Overall there is a very good agreement both between the pseudopotential and all-electron results as well as with high-resolution experimental spectra. The obtained agreement between theoretical and experimental core-level energies, however, requires that the correct geometrical parameters are used. For instance, inclusion of bucklings of the first Rh layer in the $(2\mathrm{}\times 2)-1\mathrm{C}\mathrm{O}$ and $(\sqrt{3}\times \sqrt{3})R30\mathrm{}°-1\mathrm{C}\mathrm{O}$ overlayers is essential. For the overlayers studied here, different competing adsorption sites give almost the same frozen-lattice adsorption energies. However, the C $1s$ binding energy shows large differences between CO adsorbed in different sites. Thus calculations of the C $1s$ shifts allow us to predict the adsorption sites despite the small differences in ground-state energies. We also analyze sources of the shifts in terms of differences in Hartree potential and relaxation at different sites. As the DFT core eigenvalue lies above rather than below the core excitation energy some care is required in order to properly identify a relaxation energy in a DFT framework. In order to clarify the question we relate the DFT approach for core energies to approaches based on self-energies or the Hartree-Fock approximation.