Calibrating transition-metal energy levels and oxygen bands in first-principles calculations: Accurate prediction of redox potentials and charge transfer in lithium transition-metal oxides

Transition-metal (TM) oxides play an increasingly important role in technology today, including applications such as catalysis, solar energy harvesting, and energy storage. In many of these applications, the details of their electronic structure near the Fermi level are critically important for their properties. We propose a first-principles--based computational methodology for the accurate prediction of oxygen charge transfer in TM oxides and lithium TM (Li-TM) oxides. To obtain accurate electronic structures, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional is adopted, and the amount of exact Hartree-Fock exchange (mixing parameter) is adjusted to reproduce reference band gaps. We show that the HSE06 functional with optimal mixing parameter yields not only improved electronic densities of states, but also better energetics (Li-intercalation voltages) for $\mathrm{LiCo}{\mathrm{O}}_{2}$ and $\mathrm{LiNi}{\mathrm{O}}_{2}$ as compared to the generalized gradient approximation (GGA), Hubbard $U$ corrected GGA ($\mathrm{GGA}+U$), and standard HSE06. We find that the optimal mixing parameters for TM oxides are system specific and correlate with the covalency (ionicity) of the TM species. The strong covalent (ionic) nature of TM-O bonding leads to lower (higher) optimal mixing parameters. We find that optimized HSE06 functionals predict stronger hybridization of the $\mathrm{Co}\phantom{\rule{0.28em}{0ex}}3d$ and $\mathrm{O}\phantom{\rule{0.28em}{0ex}}2p$ orbitals as compared to GGA, resulting in a greater contribution from oxygen states to charge compensation upon delithiation in $\mathrm{LiCo}{\mathrm{O}}_{2}$. We also find that the band gaps of Li-TM oxides increase linearly with the mixing parameter, enabling the straightforward determination of optimal mixing parameters based on GGA ($\ensuremath{\alpha}=0.0$) and HSE06 $(\ensuremath{\alpha}=0.25)$ calculations. Our results also show that ${G}_{0}{W}_{0}@\mathrm{GGA}+U$ band gaps of TM oxides ($M\mathrm{O},\phantom{\rule{0.28em}{0ex}}M=\mathrm{Mn},\phantom{\rule{0.28em}{0ex}}\mathrm{Co},\phantom{\rule{0.28em}{0ex}}\mathrm{Ni}$) and $\mathrm{LiCo}{\mathrm{O}}_{2}$ agree well with experimental references, suggesting that ${G}_{0}{W}_{0}$ calculations can be used as a reference for the calibration of the mixing parameter in cases when no experimental band gap has been reported.