Self-consistent parametrization of DFT + U framework using linear response approach: Application to evaluation of redox potentials of battery cathodes

The accuracy of DFT +U calculations, applied to the study of electronic structure and energetics of strongly correlated materials, heavily depends on U parameters, chosen for adequate treatment of d and f states. Computational evaluation of U parameters, which does not require fitting to experimental measurements or results of computationally expensive schemes, is highly desirable for the study of novel materials and even more so for materials not yet synthesized to date. Within this work, we show that the linear response method could provide U parameters which can yield redox potentials of battery cathode materials in much better agreement with experiment than conventional density functional theory (DFT). In our approach, we evaluate U values self-consistently, ensuring agreement between U calculated using linear response with the value used for DFT +U calculations. We find that such self-consistency is necessary for determination of adequate values of U . We also studied the impact of using various PAW (projector augmented wave) potentials for transition-metal ions, that differ by the number of electrons treated as valence. We find that redox potentials are reasonably well reproduced for all cases, although a slightly higher degree of accuracy corresponds to PAW potentials with semicore electrons treated as valence. Importantly, we find that converged values of U are substantially different for various PAW potentials of transition-metal ions of the same material. Overall, we find that self-consistent DFT +U /linear response calculations provide quite accurate values of redox potentials for materials with purely ionic bonding (e.g., LiFePO₄, LiCoPO₄, LiCoO₂, LiMnPO₄, NaFePO₄), whereas for materials with covalent p d hybridization (e.g., LiNiO₂) or conducting materials (e.g., LiTiS₂) the agreement with experimental redox voltage is lower. This emphasizes the need for application of more advanced techniques (e.g., DFT +U +V method) for accurate study of partially covalent and metallic materials, which contain transition-metal ions.