Geometric and Electronic Properties of Li$_2$GeO$_3$
The 3D ternary Li$_2$GeO$_3$ compound, which could serve as the electrolyte material in Li+-based batteries, exhibits an unusual lattice symmetry (orthorhombic crystal), band structure, charge density distribution and density of states. The essential properties are fully explored through the first-principles method. In the delicate calculations and analyses, the main features of atom-dominated electronic energy spectrum, space-charge distribution, and atom-/orbital-projected density of states are suffi$cient to identify the critical multi-orbital hybridizations of the chemical bonds: 2s-(2p$_x, 2p$_y$, 2p$_z$) and (4s, 4p$_x$, 4p$_y$, 4p$_z$)-(2s, 2p$_x$, 2p$_y$, 2p$_z$), respectively, for Li-O and Ge-O. This system possesses a large indirect gap of Eg = 3.77 eV. There exist a lot of significant covalent bonds, with an obvious non-uniformity and anisotropy. In addition, spin-dependent magnetic configurations are completely absent. The theoretical framework could be developed to investigate the important features of anode and cathode materials related to lithium oxide compounds.