Point-defect formation energies in uranium dioxide ${\text{UO}}_2$ are still a matter of debate due to the significant discrepancies between the various studies published in the literature. These discrepancies stem from the density functional theory $\left(\text{DFT}\right)+U$ approximation that creates multiple energy minima and complexifies the search for the ground state. We report here $\text{DFT}+U$ values of the formation energies for the single oxygen interstitial and vacancy in ${\text{UO}}_2$, both in the fluorite and the Jahn-Teller distorted structures, using a scheme developed on bulk ${\text{UO}}_2$ [B. Dorado, B. Amadon, M. Freyss, and M. Bertolus, Phys. Rev. B 79, 235125 (2009)] and based on occupation matrix control. We first investigate the Jahn-Teller distortion in ${\text{UO}}_2$ in the noncollinear antiferromagnetic order and we show that the distortion stabilizes the system by $50\text{meV}/{\text{UO}}_2$ compared to the fluorite structure. Moreover, it is found that the oxygen atoms are displaced in the $⟨111⟩$ directions, in agreement with experiments. For the bulk fluorite structure, we show that the use of the Dudarev approach of the $\text{DFT}+U$ without occupation matrix control systematically yields the first metastable state, located $45\text{meV}/{\text{UO}}_2$ above the ground state. As a result, all previously published point-defect formation energies are largely underestimated. We then use the occupation matrix control scheme to calculate the formation energies of the single oxygen interstitial and vacancy in ${\text{UO}}_2$. We confirm that this scheme always allows one to reach the lowest energy states and therefore yields reliable formation energies. Finally, we compare our values with those obtained in previous studies and show that the discrepancies observed stem from the calculations of defective supercells which have reached different metastable states.

• Received 8 October 2009

DOI:https://doi.org/10.1103/PhysRevB.82.035114