Hybrid Density-Functional Theory and the Insulating Gap of ${\mathrm{U}\mathrm{O}}_2$

We report the first calculations carried out with a periodic boundary condition code capable of examining hybrid density-functional theory (DFT) for $f$-element solids. We apply it to the electronic structure of the traditional Mott insulator ${\mathrm{U}\mathrm{O}}_2$, and find that it correctly yields an antiferromagnetic insulator as opposed to the ferromagnetic metal predicted by the local spin density and generalized gradient approximations. The gap, density of states, and optimum lattice constant are all in good agreement with experiment. We stress that this results from the functional and the variational principle alone. We compare our results with the more traditional approximations.

Figure 1

The total DOS for ${\mathrm{U}\mathrm{O}}_2$ in the LSDA, the PBE GGA, and the PBE1PBE hybrid approximation for the ferromagnetic solution at the experimental lattice constant.

Figure 2

The top panel displays the PBE1PBE partial DOS for ${\mathrm{U}\mathrm{O}}_2$. The peak near $E_f$ is primarily U $5f$ with a very small O $2p$ contribution. The bottom panel reproduces the photoemission energy distribution curves taken by Cox et al. demonstrating the predominantly U $5f$ character of the feature near $E_f$. The incident photon energies correspond to the resonance (98 and 108 eV) and antiresonance (92 eV) in the U $5f$ cross section.