Vibrational frequencies utilized for the assessment of exchange–correlation functionals in the description of metal–adsorbate systems: C2H2 and C2H4 on transition-metal surfaces†

Describing the interaction between reactive species and surfaces is crucial for designing catalyst materials. Density-functional approximation is able to quantitatively model such interaction, but its accuracy strongly depends on the choice of exchange–correlation (XC) functional approximation. In this work, we assess the performance of XC functionals for describing the interaction of C₂H₂ and C₂H₄ with the (111) surfaces of Cu, Pt, Pd, and Rh by particularly focusing on RPBE and mBEEF functionals. We study the geometry and the vibrational frequencies associated with the adsorbed molecules as well as the adsorption energies and the reaction enthalpy of semi-hydrogenation of C₂H₂ in the gas phase. Crucially, experimental values for vibrational frequencies of molecules adsorbed on metal surfaces are available for more systems compared to physical quantities typically used to benchmark XC functionals, such as adsorption energies. Thus, vibrational frequencies can be utilized as a reference to assess the reliability of the exchange–correlation functionals. We find that the mean percentage errors (MPEs) of RPBE and mBEEF with respect to reported experimental values of vibrational frequencies are 0.64% and −3.88%, respectively (36 data points). For adsorption enthalpy, RPBE and mBEEF provide MPEs of 27.61% and −59.81%, respectively, with respect to reported experimental values (7 data points). Therefore, the performance of RPBE is superior to that of mBEEF for the considered systems.