A Hybrid Density Functional Theory Benchmark Study on Lithium Manganese Oxides

The lithium manganese oxide spinel Li$_x$Mn$_2$O$_4$, with $0\leq x\leq 2$, is an important example for cathode materials in lithium ion batteries. However, an accurate description of Li$_x$Mn$_2$O$_4$ by first-principles methods like density functional theory is far from trivial due to its complex electronic structure, with a variety of energetically close electronic and magnetic states. It was found that the local density approximation as well as the generalized gradient approximation (GGA) are unable to describe Li$_x$Mn$_2$O$_4$ correctly. Here, we report an extensive benchmark for different Li$_x$Mn$_y$O$_z$ systems using the hybrid functionals PBE0 and HSE06, as well as the recently introduced local hybrid functional PBE0r. We find that all of these functionals yield energetic, structural, electronic, and magnetic properties in good agreement with experimental data. The notable benefit of the PBE0r functional, which relies on on-site Hartree-Fock exchange only, is a much reduced computational effort that is comparable to GGA functionals. Furthermore, the Hartree-Fock mixing factors in PBE0r are smaller than in PBE0, which improves the results for (lithium) manganese oxides. The investigation of Li$_x$Mn$_2$O$_4$ shows that two Mn oxidation states, +III and +IV, coexist. The Mn$^\text{III}$ ions are in the high-spin state and the corresponding MnO$_6$ octahedra are Jahn-Teller distorted. The ratio between Mn$^\text{III}$ and Mn$^\text{IV}$ and thus the electronic structure changes with the Li content while no major structural changes occur in the range from $x=0$ to $1$. This work demonstrates that the PBE0r functional provides an equally accurate and efficient description of the investigated Li$_x$Mn$_y$O$_z$ systems.