Hybrid functionals with nonempirical Hartree-Fock parameters for electronic structure calculation of layered oxides

Accurate electronic structure descriptions of layered oxides are highly relevant yet complex to obtain by ab initio methods. The functionalities of layered transition metal oxides are usually heavily influenced by their electronic structure and the hybridization/delocalization of d electrons of the transition metals. Therefore understanding the electronic structure can enable a more rational design of this highly important material class, which is widely utilized in practical applications such as cathodes in secondary batteries of portable electronic devices and electric vehicles. However, it is well known that standard quantum-mechanic approximations to the many-body problem overlocalize (Hartree-Fock) or overdelocalize (density functional theory) electrons in these systems. A mixture of different methods (hybrid functionals) can partially resolve the problem but introduces at least one additional parameter (the mixing parameter) that has to be determined by e.g., higher levels of theory (GW). In this study, we focus on the electronic structure of lithiated layered transition-metal oxides based on Co, Ni, Mn, and their binary systems that form the foundation of state-of-the-art lithium-ion batteries. The influence of Hartree-Fock mixing in the PBE0 hybrid functional on the electronic structure is compared as well as using different Hartree-Fock mixings as starting points for GW calculations. Two nonempirical GW-based fitting approaches to determine the optimal Hartree-Fock mixing are considered. We show that one of the fitting approaches suggests small mixing parameters and is in satisfactory agreement with experimental results, while the other approach has a stronger theoretical foundation and indicates higher mixing parameters, which are close to the value obtained by perturbation theory by Perdew, Ernzerhof, and Burke. Finally, it is shown that larger mixing parameters are required when screening is introduced to the Hartree-Fock term.