Accurate electronic properties and intercalation voltages of Li-ion cathode materials from extended Hubbard functionals

The design of novel cathode materials for Li-ion batteries requires accurate first-principles predictions of their properties. Density-functional theory (DFT) with standard (semi-)local functionals fails due to the strong self-interaction errors of partially filled d shells of transition-metal elements. Here, we perform a detailed comparative study of the phospho-olivine cathode materials using four electronic-structure methods: DFT, DFT+U, DFT+U+V, and HSE06. We show that DFT+U+V, with onsite U and intersite V Hubbard parameters determined from first-principles and self-consistently with respect to the structural parameters by means of density-functional perturbation theory (linear response), provides the most accurate description of the electronic structure of these challenging compounds. In particular, we demonstrate that DFT+U+V displays clearly "digital'' changes in oxidation states of the transition-metal ions in all compounds, including the mixed-valence phases occurring at intermediate Li concentrations, leading to voltages in remarkable agreement with experiments. We thus show that the inclusion of intersite Hubbard interactions is essential for the accurate prediction of thermodynamic quantities.