Density functional study of CO on Rh(111)

We present detailed density functional calculations for CO on Rh(111). At low coverage, the applied semilocal functionals clearly favor CO adsorption in the hollow site. This is in disagreement with experimental studies which all point towards atop adsorption at low coverage. The experimental assignment is confirmed by theoretical calculations of the vibrational frequencies and core level shifts at various coverages, ranging from $1∕9\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}3∕4$ $[(2\ifmmode\times\else\texttimes\fi{}2)\text{\ensuremath{-}}3\mathrm{C}\mathrm{O}]$ monolayer CO. For atop adsorption the calculated vibrational frequencies and the Rh surface core level shifts are indeed found to agree very well with experiment. To understand these controversial results, a molecular $\mathrm{GGA}+\mathrm{U}$ method is applied, which allows one to shift the CO $2\ensuremath{\pi}*$ orbital towards the vacuum level. This reduces the binding energy in the hollow site and brings the theoretical site preference in agreement with experiment. It is investigated how this molecular $\mathrm{GGA}+\mathrm{U}$ method influences the vibrational properties and the surface core level shifts. Furthermore, details on the molecular $\mathrm{GGA}+\mathrm{U}$ method are presented.