Influence of {\it xc} functional on thermal-elastic properties of Ceria: A DFT-based Debye-Gr{\"u}neisen model approach

Ceria (CeO$_{2-x}$) is widely studied as a choice electrolyte material for intermediate-temperature ($\sim800$\,K) solid oxide fuel cells. At this temperature, maintaining its chemical stability and thermal-mechanical integrity of this oxide are of utmost importance. To understand their thermal-elastic properties, we firstly test the influence of various approximations to the density-functional theory (DFT) $xc$ functionals on specific thermal-elastic properties of both CeO$_2$ and Ce$_2$O$_3$. Namely, we consider the local-density approximation (LDA), the generalized gradient approximation (GGA-PBE) with and without additional Hubbard $U$ as applied to the $4f$ electron of Ce, as well as the recently popularized hybrid functional due to Heyd-Scuseria-Ernzehof (HSE06). Next, we then couple this to a volume-dependent Debye-Gr{\"u}neisen model to determine the thermodynamic quantities of ceria at arbitrary temperatures. We find an explicit description of the strong correlation (e.g. via the DFT$+U$ and hybrid functional approach) is necessary to have a good agreement with experimental values, in contrast to the mean-field treatment in standard xc approximations (such as LDA or GGA-PBE).