Assessment of PBE+U and HSE06 methods and determination of optimal parameter U for the structural and energetic properties of rare earth oxides

Rare earth oxides are attracting increasing interest as a relatively unexplored group of materials with potential applications in heterogeneous catalysis and electrocatalysis; therefore, a credible and universal computational approach is needed for modeling their reactivity. In this work, we systematically assessed the performance of the PBE+U method against the results of the hybrid HSE06 method with respect to the description of structural parameters and energetic properties of the selected hexagonal lanthanide sesquioxides and the cubic fluorite-type cerium dioxide. In addition, we evaluated the performance of PBE+U in describing the electronic structure and adsorption properties of the CeO2(111) and Nd2O3(0001) surfaces. The HSE06 method reproduces rather well the lattice parameters and selected energetic properties with respect to the experimental values. The PBE+U method is able to reproduce the results of HSE06 or the experimental values only if the U parameter is selected from an appropriate range of values. The U value around 3 eV gives the best description of the lattice parameters of most bulk oxides. 2 eV–3 eV is also found to be the optimal range of U for the reaction energies of bulk La2O3, Ce2O3, Nd2O3, Er2O3, and Ho2O3. U = 1 eV gives the best results for Pr2O3, Pm2O3, Eu2O3, Tm2O3, and Lu2O3, whereas Gd2O3 could not be accurately described by the PBE+U method. The U values (∼3 eV) found optimal for most bulk oxides also work well in the calculations of adsorption of small molecules on Nd2O3(0001) and CeO2(111), although larger U values are required to obtain sufficient localization of 4f electrons.