The 3D ternary Li_4Ti_5O_12, the Li+-based battery anode, presents the unusual lattice symmetry (a triclinic crystal), band structure, charge density, and density of states, under the first-principles calculations. It belongs to a large direct-gap semiconductor of E_g^d~ 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 in the delicate identifications of multi-orbital hybridizations in Li-O and Ti-O bonds. The extremely non-uniform chemical environment, which induce the very complicated hopping integrals, directly arise from the large bonding fluctuations and the highly anisotropic configurations. Also, the developed theoretical framework is very useful for fully understanding the cathodes and electrolytes of oxide compounds.
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