The lithium manganese oxide spinel ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$, with $0\le x\le 2$, is an important example for cathode materials in lithium ion batteries. However, an accurate description of ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$ 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 ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$ correctly. Here, we report an extensive benchmark for different ${\mathrm{Li}}_x{\mathrm{Mn}}_y{\mathrm{O}}_z$ 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 onsite 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 ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$ shows that two Mn oxidation states, $+\mathrm{III}$ and $+\mathrm{IV}$, coexist. The ${\mathrm{Mn}}^{\text{III}}$ ions are in the high-spin state and the corresponding ${\mathrm{MnO}}_6$ octahedra are Jahn-Teller distorted. The ratio between ${\mathrm{Mn}}^{\text{III}}$ and ${\mathrm{Mn}}^{\text{IV}}$ 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 ${\mathrm{Li}}_x{\mathrm{Mn}}_y{\mathrm{O}}_z$ systems.

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• Band gap
• Density of states
• Electrochemical properties
• First-principles calculations
• Jahn-Teller effect
• Magnetic order
• Structural properties
• Thermodynamics
• Density functional theory
• Hybrid functionals