We investigate the geometric, electric, and optical properties of two-dimensional honeycomb lattices using first-principles simulations. The main focus of this work is on the similarities and differences in their characteristics, as well as the delicate connection of orbital hybridizations and spin-polarizations with electronic and optical properties. Graphene, silicene, germanene, and their semi-hydrogenated systems, in turn, display sp², sp²–sp³, and sp³s hybridizations. These bonding configurations are critical factors affecting the geometric structure, the electronic band structure, van Hove singularities in density of states, the magnetic configurations, the dielectric functions, and energy loss functions. Furthermore, the meta-stable and stable exciton states are expected to survive in pristine and semi-hydrogenated group IV monolayers, respectively. The theoretical predictions established in this work are important not only for basic science but also for high-tech applications.

We perform the electronic and optical properties of the Li₆PS₅Cl compound using first-principles calculation.

How to form carbon nanoscrolls with non-uniform curvatures is worthy of a detailed investigation. The first-principles method is suitable for studying the combined effects due to the finite-size confinement, the edge-dependent interactions, the interlayer atomic interactions, the mechanical strains, and the magnetic configurations. The complex mechanisms can induce unusual essential properties, e.g., the optimal structures, magnetism, band gaps and energy dispersions. To reach a stable spiral profile, the requirements on the critical nanoribbon width and overlapping length will be thoroughly explored by evaluating the width-dependent scrolling energies. A comparison of formation energy between armchair and zigzag nanoscrolls is useful in understanding the experimental characterizations. The spin-up and spin-down distributions near the zigzag edges are examined for their magnetic environments. This accounts for the conservation or destruction of spin degeneracy. The various curved surfaces on a relaxed nanoscroll will create complicated multi-orbital hybridizations so that the low-lying energy dispersions and energy gaps are expected to be very sensitive to ribbon width, especially for those of armchair systems. Finally, the planar, curved, folded, and scrolled graphene nanoribbons are compared with one another to illustrate the geometry-induced diversity.

We use first-principles calculations within the density functional theory (DFT) to explore the electronic properties of stage-1 Li- and Li⁺-graphite-intercalation compounds (GIC) for different concentrations of LiC_x/Li⁺C_x, with x = 6, 12, 18, 24, 32 and 36. The essential properties, e.g., geometric structures, band structures and spatial charge distributions are determined by the hybridization of the orbitals, the main focus of our work. The band structures/density of states/spatial charge distributions display that Li-GIC shows a blue shift of Fermi energy just like metals, but Li⁺-GIC still remains as in the original graphite or exhibits so-called semi-metallic properties, possessing the same densities of free electrons and holes. According to these properties, we find that there exist weak but significant van der Waals interactions between interlayers of graphite, and 2s-2p_z hybridization between Li and C. There scarcely exist strong interactions between Li⁺-C. The dominant interaction between the Li and C is 2s-2p_z orbital-orbital coupling; the orbital-orbital coupling is not significant in the Li⁺ and C cases, but dipole-diploe coupling is.

Up to now, many guest atoms/molecules/ions have been successfully synthesized into graphite to form various compounds. For example, alkali-atom graphite intercalation compounds are verified to reveal stage-n structures, including LiC_6n and LiM_8n [M = K, Rb, and Cs; n = 1, 2, 3; 4]. On the other side, AlCl₄ ⁻-ion/AlCl₄-molecule compounds are found to show stage-4 and stage-3 structures at room and lower temperatures, respectively. Stage-1 and stage-2 configurations, with the higher intercalant concentrations, cannot be synthesized in experimental laboratories. This might arise from the fact that it is quite difficult to build periodical arrangements along the longitudinal z and transverse directions simultaneously for large ions or molecules. Our work is mainly focused on stage-1 and stage-2 systems in terms of geometric and electronic properties. The critical features, being associated with the atom-dominated energy spectra and wave functions within the specific energy ranges, the active multi-orbital hybridization in distinct chemical bonds, and atom- & orbital-decomposed van Hove singularities, will be thoroughly clarified by the delicate simulations and analyses.

Exercises, which cover the classical and quantum pictures of the basic and applied sciences, are closely related to very interesting topics and certain mainstream materials. The high-symmetry physical environments are fully supported by the planar/normal carbon-honeycomb lattices that are very suitable for the basic science researches under the phenomenological models. The adatom alkalizations are expected to exhibit the metal-semiconductor/metal-semimetal transitions because of the strong electron transfer from the guest to host atoms under their angle-orbital interlayer hybridizations. The global impact of greenhouse gases from the internal combustion energies and coalfired power has attracted much research on green energy, e.g., the ingathering and storing of electrical energy from wind and solar power. A solar cell is an electrical device that transforms light energy into electrical energy via the photovoltaic effect.