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The three-dimensional ternary Li 2 GeO 3 compound presents various unusual essential properties. The main features are thoroughly explored from the first-principles calculations. The concise pictures, the critical orbital hybridizations in Li-O and Ge-O bonds, are clearly examined through the optimal geometric structure, the atom-dominated electronic energy spectrum, the spatial charge densities, the atom and orbital-decomposed van Hove singularities, and the strong optical responses. The unusual optical transitions cover the red-shift optical gap, various frequency-dependent absorption structures and the most prominent plasmon mode in terms of the dielectric functions, energy loss functions, reflectance spectra, and absorption coefficients. Optical excitations, depending on the directions of electric polarization, are strongly affected by excitonic effects. The close combinations of electronic and optical properties can identify a significant orbital hybridization for each available excitation channel. The developed theoretical framework will be very useful in fully understanding the diverse phenomena of other emergent materials.

The diverse structural and electronic properties of the Si-adsorbed and -substituted monolayer graphene systems are studied by a complete theoretical framework under the first-principles calculations, including the adatom-diversified geometric structures, the Si- and C-dominated energy bands, the spatial charge densities, variations in the spatial charge densities and the atom- and orbital-projected density of states (DOSs). These critical physical quantities are unified together to display a distinct physical and chemical picture in the studying systems. Under the Si-adsorption and Si-substitution effects, the planar geometric structures are still remained mainly owing to the very strong C-C and Si-C bonds on the honeycomb lattices, respectively. The Si-adsorption cases can create free carriers, while the finite- or zero-gap semiconducting behaviors are revealed in various Si-substitution configurations. The developed theoretical framework can be fully generalized to other emergent layered materials. The Si-doped graphene systems might be a highly promising anode material in the lithium-ion battery owing to its rich potential properties.

Diverse magnetic and electronic properties of halogen-adsorbed silicene are investigated by the first-principle theoretical framework, including the adatom-diversified geometric structures, atom-dominated energy bands, spatial spin density distributions, spatial charge density distributions and its variations, and orbital-projected density of states. Also, such physical quantities are sufficient to identify similar and different features in the double-side and single-side adsorptions. The former belongs to the concentration-depended finite gap semiconductors or p-type metals, while the latter display the valence energy bands with/without spin-splitting intersecting with the Fermi level. Both adsorption types show the halogen-related weakly dispersed bands at deep energies, the adatom-modified middle-energy σ bands, and the recovery of low-energy π bands during the decrease of the halogen concentrations. Such feature-rich band structures can be verified by the angle-resolved photoemission spectroscopy experiment.

The dramatic changes in electronic and magnetic properties are investigated using the first-principles calculations for halogen(X: Cl, Br, I, At)-adsorbed graphene nanoribbons. The rich and unique features are clearly revealed in the atoms-dominated electronic band structures, spin arrangement/magnetic moment, spatial charge distribution, and orbital- and spin-projected density of states. Halogen adsorptions can create the non-magnetic, ferromagnetic or anti-ferromagnetic metals, being mainly determined by concentrations and edge structures. The number of holes per unit cell increases with the adatom concentrations. Furthermore, magnetism becomes nonmagnetic when the adatom concentration is beyond 60% adsorption. There are many low-lying spin-dependent van Hove singularities. The diversified properties are attributed to the significant X-C bonds, the strong X-X bonds, and the adatom- and edge-carbon-induced spin states.

The significant halogenation effects on the essential properties of graphene are investigated by the first-principles method. The geometric structures, electronic properties, and magnetic configurations are greatly diversified under the various halogen adsorptions. Fluorination, with the strong multi-orbital chemical bondings, can create the buckled graphene structure, while the other halogenations do not change the planar s bonding in the presence of single-orbital hybridization. Electronic structures consist of the carbon-, adatom- and (carbon, adatom)-dominated energy bands. All halogenated graphenes belong to holedoped metals except that fluorinated systems are middle-gap semiconductors at sufficiently high concentration. Moreover, the metallic ferromagnetism is revealed in certain adatom distributions. The unusual hybridization-induced features are clearly evidenced in many van Hove singularities of density of states. The structure- and adatom-enriched essential properties are compared with the measured results, and potential applications are also discussed.