$\text{DFT}+\text{U}$ calculations of the ground state and metastable states of uranium dioxide

We report a study of the ground state and metastable states of uranium dioxide using ab initio $\text{DFT}+\text{U}$ calculations. We highlight that in order to avoid metastable states and systematically reach the ground state of uranium dioxide with $\text{DFT}+\text{U}$, the monitoring of occupation matrices is crucial, as well as allowing the $5f$ electrons to break the cubic symmetry. For this purpose, we use a method based on the monitoring of the occupation matrix of the correlated orbitals on which the Hubbard term is applied. We observe the presence of numerous metastable states in calculations both with and without taking into account the symmetries of the wave functions. We investigate the influence of metastable states on the total energy, as well as on the electronic and structural properties of uranium dioxide. We show that the presence of metastable states induces large differences in the total energy and explain the origin of the discrepancies observed in the results obtained by various authors on crystalline and defect-containing ${\text{UO}}_2$. Finally, in order to check the consistency of the procedure, we determine the structural and electronic properties of the ground state of uranium dioxide and compare them with results obtained in previous studies using the $\text{DFT}+\text{U}$ approximation and hybrid functionals, as well as experimental data.

Figure 1

(Color online) ${\text{UO}}_2$ fluorite structure (12-atom cell, ${\text{U}}_4{\text{O}}_8$) with 1k antiferromagnetic (AFM) order. Blue atoms are uranium atoms while red atoms are oxygen atoms.

Figure 2

Total density of states of the ground state (top) and the first metastable state (bottom) of uranium dioxide.

Figure 3

(Color online) Variation of the 12-atom cell volume with respect to the $U$ and $J$ parameters using the Liechtenstein’s Hubbard term. The black line presents data from a calculation where the occupation matrices have not been monitored (using the VASP package).