Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds

We compare the accuracy of conventional semilocal density functional theory (DFT), the $\text{DFT}+U$ method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox reaction energies, and formation energies of transition metal compounds. Conventional DFT functionals significantly underestimate redox potentials for these compounds. Zhou et al. [Phys. Rev. B 70, 235121 (2004)] addressed this issue with $\text{DFT}+U$ and a linear-response scheme for calculating $U$ values. We show that the Li intercalation potentials of prominent Li-ion intercalation battery materials, such as the layered ${\text{Li}}_{x}M{\text{O}}_{2}$ ($M=\text{Co}$ and Ni), ${\text{Li}}_{x}{\text{TiS}}_{2}$; olivine ${\text{Li}}_{x}M{\text{PO}}_{4}$ ($M=\text{Mn}$, Fe, Co, and Ni); and spinel-like ${\text{Li}}_{x}{\text{Mn}}_{2}{\text{O}}_{4}$, ${\text{Li}}_{x}{\text{Ti}}_{2}{\text{O}}_{4}$, are also well reproduced by HSE06, due to the self-interaction error correction from the partial inclusion of Hartree-Fock exchange. For formation energies, HSE06 performs well for transition metal compounds, which typically are not well reproduced by conventional DFT functionals but does not significantly improve the results of nontransition metal oxides. Hence, we find that hybrid functionals provide a good alternative to $\text{DFT}+U$ for transition metal applications when the large extra computational effort is compensated by the benefits of (i) avoiding species-specific adjustable parameters and (ii) a more universal treatment of the self-interaction error that is not exclusive to specific atomic orbital projections on selected ions.