Hybrid functionals applied to rare-earth oxides: The example of ceria

We report periodic density functional theory (DFT) calculations for ${\mathrm{CeO}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ using the Perdew-Burke-Ernzerhof (PBE0) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functionals that include nonlocal Fock exchange. We study structural, electronic, and magnetic ground state properties. Hybrid functionals correctly predict ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ to be an insulator as opposed to the ferromagnetic metal predicted by the local spin density (LDA) and generalized gradient (GGA) approximations. The equilibrium volumes of both structures are in very good agreement with experiments, improving upon the description of the LDA and GGA. The calculated ${\mathrm{CeO}}_{2}$ (O $2p$--Ce $5d$) and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ $(\mathrm{Ce}\phantom{\rule{0.3em}{0ex}}4f\text{\ensuremath{-}}5d4f)$ band gaps are larger by up to 45% (PBE0) and 15% (HSE) than found in experiments. Furthermore, we calculate atomization energies, heats of formation, and the reduction energy of $2{\mathrm{CeO}}_{2}\ensuremath{\rightarrow}{\mathrm{Ce}}_{2}{\mathrm{O}}_{3}+(1∕2){\mathrm{O}}_{2}$. The latter is underestimated by $\ensuremath{\sim}0.4--0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with respect to available experimental data at room temperature. We compare our results with the more traditional DFT+$U$ (LDA$+U$ and PBE$+U$) approach and discuss the role played by the Hubbard $U$ parameter.