Effects of Hubbard term correction on the structural parameters and electronic properties of wurtzite Zn

The effects of including the Hubbard on-site Coulombic correction to the structural parameters and valence energy states of wurtzite ZnO was explored. Due to the changes in the structural parameters caused by correction of hybridization between Zn d states and O p states, suitable parameters of Hubbard terms have to be determined for an accurate prediction of ZnO properties. Using the LDA+${U}$ method by applying Hubbard corrections $U_p$ to Zn 3d states and $U_p$ to O 2p states, the lattice constants were underestimated for all tested Hubbard parameters. The combination of both $U_d$ and $U_p$ correction terms managed to widen the band gap of wurtzite ZnO to the experimental value. Pairs of $U_p$ and $U_p$ parameters with the correct positioning of d-band and accurate bandwidths were selected, in addition to predicting an accurate band gap value. Inspection of vibrational properties, however, revealed mismatches between the estimated gamma phonon frequencies and experimental values. The selection of Hubbard terms based on electronic band properties alone cannot ensure an accurate vibrational description in LDA+${U}$ calculation.