The electronic structure and ground state properties of ${\mathrm{AlB}}_2$ type transition metal diborides ${\mathrm{TMB}}_2$ (TM=Sc, Ti, V, Cr, Mn, Fe, Y, Zr, Nb, Mo, Hf, Ta) have been calculated using the self consistent tight-binding linear muffin-tin orbital method. The equilibrium volume, bulk moduli ${(B}_0),$ pressure derivative of bulk moduli ${(B}_0^{\prime }),$ cohesive energy ${(E}_{\mathrm{coh}}),$ heat of formation $\left(\Delta H\right),$ and electronic specific heat coefficient $\left(\gamma \right)$ are calculated for these systems and compared with the available experimental and other theoretical results. The bonding nature of these diborides is analyzed via the density of states (DOS) histogram as well as the charge density plots, and the chemical stability is analyzed using the band filling principle. The variation in the calculated cohesive properties of these materials is correlated with the band filling effect. The existence of a pseudogap in the total density of states is found to be a common feature for all these compounds. The reason for the creation of the pseudogap is found to be due to the strong covalent interaction between boron p states. We have made spin polarized calculations for ${\mathrm{CrB}}_2,$ ${\mathrm{MnB}}_2,$ and ${\mathrm{FeB}}_2$ and found that finite magnetic moments exist for ${\mathrm{MnB}}_2$ and ${\mathrm{CrB}}_2$ whereas ${\mathrm{FeB}}_2$ is nonmagnetic.

Structural phase stability, electronic structure, optical properties, and high-pressure behavior of polytypes of ${\mathrm{In}}_2{\mathrm{O}}_3$ in three space group symmetries $I{2}_{1}3$, $Ia\overline{3}$, and $R\overline{3}$ are studied by first-principles density-functional calculations. From structural optimization based on total energy calculations, lattice and positional parameters have been established, which are found to be in good agreement with the corresponding experimental data except for $I{2}_{1}3$, where the symmetry analysis for optimized structure indicates that it arrived at the $Ia\overline{3}$ phase. ${\mathrm{In}}_2{\mathrm{O}}_3$ of space group symmetry $Ia\overline{3}$ is found to undergo a pressure-induced phase transition to the $R\overline{3}$ phase at pressures around $3.8\mathrm{GPa}$. From the analysis of band structure coming out from the calculations within the local density and generalized gradient approximations, it is found that ${\mathrm{In}}_2{\mathrm{O}}_3$ of space group symmetry $I{2}_{1}3$ and $R\overline{3}$ are indirect band gap semiconductors, while the other phase of space group $Ia\overline{3}$ is having direct band gap. The calculated carrier effective masses for all these three phases are compared with available experimental and theoretical values. From charge-density and electron localization function analysis, it is found that these phases have dominant ionic bonding with noticeable covalent interaction between indium and oxygen. The magnitudes of the absorption and reflection coefficients for ${\mathrm{In}}_2{\mathrm{O}}_3$ with space groups $Ia\overline{3}$ and $R\overline{3}$ are small in the energy range $0–5\mathrm{eV}$, indicating that these phases can be regarded and classified as transparent.

The stability of ${\mathrm{M}\mathrm{g}\mathrm{H}}_2$ has been studied up to 20 GPa using density-functional total-energy calculations. At ambient pressure $\alpha \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ takes a ${\mathrm{T}\mathrm{i}\mathrm{O}}_2$-rutile-type structure. $\alpha \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ is predicted to transform into $\gamma \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ at 0.39 GPa. The calculated structural data for $\alpha$- and $\gamma \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ are in very good agreement with experimental values. At equilibrium the energy difference between these modifications is very small, and as a result both phases coexist in a certain volume and pressure field. Above 3.84 GPa $\gamma \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ transforms into $\beta \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$, consistent with experimental findings. Two further transformations have been identified at still higher pressure: (i) $\beta$- to $\delta \mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ at 6.73 GPa and (ii) $\delta$- to $ϵ\mathrm{\text{−}}{\mathrm{M}\mathrm{g}\mathrm{H}}_2$ at 10.26 GPa.

The structural stability of ${\mathrm{MgH}}_2$ has been studied up to $16\mathrm{GPa}$ using a high-pressure synchrotron x-ray diffraction technique. Several pressure-induced phase transitions have been identified in this pressure range. Owing to the close structural similarity between the $\alpha$ and $\gamma$ modifications the high-pressure $\gamma$ form can be stabilized as a metastable phase after pressure release. The experimentally observed structural transition sequence and the volume changes at the transition points as well as bulk modulii are found to be in good agreement with theoretically calculated data. The bonding nature of ${\mathrm{MgH}}_2$ is analyzed with the help of charge-density, charge-transfer, electron-localization-function, and Mulliken-population analyses which clearly show that all polymorphs of ${\mathrm{MgH}}_2$ are to be classified as ionic materials with Mg and H in nearly 2+ and $1-$ states, respectively.

In order to understand the unexpected superconducting behavior of ${\mathrm{MgB}}_2$ we have made electronic structure calculations for ${\mathrm{MgB}}_2$ and closely related systems. Our calculated Debye temperature from the elastic properties indicate that the average phonon frequency is very large in ${\mathrm{MgB}}_2$ compared with other superconducting intermetallics and its exceptionally higher $T_c$ can be explained through a BCS mechanism only if phonon softening occurs or the phonon modes are highly anisotropic. We identified a doubly degenerate quasi-two-dimensional key-energy band in the vicinity of $E_F$ along the $\Gamma –A$ direction of BZ (having equal amount of B $p_x$ and $p_y$ character) which plays an important role in deciding the superconducting behavior. Based on this result, we have searched for a similar electronic feature in isoelectronic compounds such as ${\mathrm{BeB}}_2,$ ${\mathrm{CaB}}_2,$ ${\mathrm{SrB}}_2,$ LiBC, and ${\mathrm{MgB}}_2{\mathrm{C}}_2$ and found that hole doped LiBC and ${\mathrm{MgB}}_2{\mathrm{C}}_2$ are potential superconducting materials. We have found that $E_F$ in the closely related compound ${\mathrm{MgB}}_4$ is lying in a pseudogap with a negligibly small density of states at $E_F,$ which is not favorable for superconductivity. There are contradictory experimental results regarding the anisotropy in the elastic properties of ${\mathrm{MgB}}_2$ ranging from isotropic to moderately anisotropic to highly anisotropic. In order to settle this issue we have calculated the single-crystal elastic constants for ${\mathrm{MgB}}_2$ by the accurate full-potential method and derived the directional-dependent linear compressibility, Young’s modulus, shear modulus, and relevant elastic properties from these results. We have observed large anisotropy in the elastic properties consistent with recent high-pressure findings. Our calculated polarized optical dielectric tensor shows highly anisotropic behavior even though it possesses isotropic transport property. ${\mathrm{MgB}}_2$ possesses a mixed bonding character and this has been verified from density of states, charge density, and crystal orbital Hamiltonian population analyses.