Featured properties of Li⁺-based battery anode: Li₄Ti₅O₁₂

3D ternary Li₄Ti₅O₁₂, a Li⁺-based battery anode, presents an unusual lattice symmetry (triclinic crystal), band structure, charge density, and density of states under first-principles calculations. It is a large direct-gap semiconductor with E ^d _g ∼ 2.98 eV. The atom-dominated valence and conduction bands, the spatial charge distribution and the atom- and orbital-decomposed van Hove singularities are available for delicate identifications of multi-orbital hybridizations in Li-O and Ti-O bonds. The extremely non-uniform chemical environment, which induces very complicated hopping integrals, directly arises from the large bonding fluctuations and the highly anisotropic configurations. Also, the developed theoretical framework is very useful for fully understanding cathodes and electrolytes of oxide compounds.