Thermodynamic study of benzene and hydrogen coadsorption on Pd(111)

Periodic density functional theory (DFT) has been used to study the coadsorption of hydrogen and benzene on Pd(111). The most stable coverages are predicted by constructing the thermodynamic phase diagram as a function of gas-phase temperature and pressure. The common approximation that neglects vibrational contributions to the surface Gibbs free energy, using the PW91 functional, is compared to the one that includes vibrational contributions. Higher coverages are predicted to be thermodynamically the most stable including vibrational frequencies, mainly due to the different entropy contributions. The first approach is also compared to the one using a (optPBE-vdW) vdW-DF functional without vibrational contributions, which predicts higher benzene coverages for benzene adsorption, and lower hydrogen coverages for hydrogen adsorption and coadsorption with a fixed benzene coverage. Inclusion of vibrational contributions using the vdW-DF method has not been implemented due to computational constraints. However, an estimate of the expected result is proposed by adding PW91 vibrational contributions to the optPBE-vdW electronic energies, and under typical hydrogenation conditions high coverages of about theta(H) = 0.89 are expected. Inclusion of vibrational contributions to the surface Gibbs free energy and a proper description of van der Waals interaction are recommended to predict the thermodynamically most stable surface coverage.