Evaluation of first-principles Hubbard and Hund corrected DFT for defect formation energies in non-magnetic transition metal oxides

Abstract

Recent advances have shown that first-principles DFT+U techniques, such as DFT+U+J with parameters from linear response, are capable of high bandgap accuracy in transition metal oxides at a fraction of the computational cost of hybrid functionals. Extending the use of these functionals to defect calculations could save computational resources, but there is limited knowledge on whether such techniques are capable of reliably modelling defect energies. Furthermore, the use of separate U and J values for the same atomic species in different chemical environments, within the same system, can introduce significant errors into formation energy calculations. In this work, for ZrO₂, HfO₂, and TiO_2, we compare calculated defect properties for PBE, DFT+U+J, and prior results from the literature. For ZrO₂ and HfO_2, we identify three different practical methods that address the environment-dependent U and J value problem acceptably well, unlike the default naïve approach that yields unphysical defect formation energies. Our proposed techniques all yield formation energies, transition levels and defect concentration predictions that, while not identical to each other, are qualitatively in line with literature values. In TiO₂, the formation energies are reasonably accurate, yet the localisation behaviour differs from that of the most reliable literature comparators, indicating a remaining difficulty for DFT+U+J with shallow defect levels.