  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.
