First-principles generalized gradient approximation (GGA) + Ud + Up studies of electronic structures and optical properties in cubic HfO2

The electronic structures and optical properties of cubic HfO2 are calculated by means of generalized gradient approximation (GGA) + U approach. Without on-site Coulomb interactions, the band gap of cubic HfO2 is 2.92 eV, much lower than the experimental value (5.7 eV). Introducing the Coulomb interactions of 5d orbitals on Hf atom (Ud) and of 2p orbitals on O atom (Up), we can reproduce the experimental value of the band gap. The resulting dielectric function of cubic HfO2 by the GGA + Ud + Up approach predicts the presence of a shoulder structure below the main peak of the absorption spectrum. These indicate that the GGA + Ud + UP approach is a convenient and powerful method to calculate and predict the electronic structures and the optical properties of wide-gap optical materials.