Despite the wide applications, the ab initio modeling of the ceria based catalyst is challenging. The partial occupation in the 4f orbitals creates a fundamental challenge for commonly used density functional theory (DFT) methods, including semilocal functionals with Hubbard U correction to force localization and hybrid functionals. In this work, we benchmark the random phase approximation (RPA) for ceria surface properties, including surface energy and hydrogenation energy, compared to the results utilizing the DFT + U approach or hybrid functionals. We show that, for the latter approaches, different surface properties require opposite directions of parameter tuning. This forms a dilemma for the parameter based DFT methods, as the improvement of a certain property by tuning parameters will inevitably lead to the worsening of other properties. Our results suggest that the parameter-free many-body perturbation theory methods exemplified by RPA are a promising strategy to escape the dilemma and provide highly accurate descriptions, which will allow us to better understand the catalytic reactions in ceria related systems.