The magnetoelectric behavior of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ has been explored on the basis of accurate density functional calculations. We are able to predict structural, electronic, magnetic, and ferroelectric properties of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ correctly without including any strong correlation effect in the calculation. Unlike earlier calculations, the equilibrium structural parameters are found to be in very good agreement with the experimental findings. In particular, the present calculation correctly reproduced experimentally observed elongation of cubic perovskitelike lattice along the [111] direction. At high pressure we predicted a pressure-induced structural transition from rhombohedral $\left(R3c\right)$ to an orthorhombic $\left(Pnma\right)$ structure. The total-energy calculations at expanded lattice show two lower energy ferroelectric phases (with monoclinic $Cm$ and tetragonal $P4mm$ structures), closer in energy to the ground-state phase. Spin-polarized band-structure calculations show that $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ will be an insulator in $A$- and $G$-type antiferromagnetic phases and a metal in $C$-type antiferromagnetic, ferromagnetic configurations, and in the nonmagnetic state. Chemical bonding in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ has been analyzed using partial density of states, charge density, charge transfer, electron localization function, Born-effective-charge tensor, and crystal orbital Hamiltonian population analyses. Our electron localization function analysis shows that stereochemically active lone-pair electrons are present at the Bi sites which are responsible for displacements of the Bi atoms from the centrosymmetric to the noncentrosymmetric structure and hence the ferroelectricity. A large ferroelectric polarization of $88.7\mu \mathrm{C}∕{\mathrm{cm}}^2$ is predicted in accordance with recent experimental findings, but differing by an order of magnitude from earlier experimental values. The strong spontaneous polarization is related to the large values of the Born-effective charges at the Bi sites along with their large displacement along the [111] direction of the cubic perovskite-type reference structure. Our polarization analysis shows that partial contributions to polarization from the Fe and O atoms almost cancel each other and the net polarization present in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ mainly $(>98\%)$ originates from Bi atoms. We found that the large scatter in experimentally reported polarization values in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ is associated with the large anisotropy in the spontaneous polarization.

Formation energies of various intrinsic defects and defect complexes in ZnO have been calculated using a density-functional-theory-based pseudopotential all-electron method. The various defects considered are oxygen vacancy (${\mathrm{V}}_{\mathrm{O}}$), zinc vacancy (${\mathrm{V}}_{\mathrm{Zn}}$), oxygen at an interstitial site (${\mathrm{O}}_i$), Zn at an interstitial site (${\mathrm{Zn}}_i$), Zn at ${\mathrm{V}}_{\mathrm{O}}$ (${\mathrm{Zn}}_{\mathrm{O}}$), O at ${\mathrm{V}}_{\mathrm{Zn}}$(${\mathrm{O}}_{\mathrm{Zn}}$), and an antisite pair (combination of the preceding two defects). In addition, defect complexes like (${\mathrm{V}}_{\mathrm{O}}+{\mathrm{Zn}}_i$) and Zn-vacancy clusters are studied. The Schokkty pair (${\mathrm{V}}_{\mathrm{O}}+{\mathrm{V}}_{\mathrm{Zn}}$) and Frenkel pairs [(${\mathrm{V}}_{\mathrm{O}}+{\mathrm{O}}_i$) and (${\mathrm{V}}_{\mathrm{Zn}}+{\mathrm{Zn}}_i$)] are considered theoretically for the first time. Upon comparing the formation energies of these defects, we find that ${\mathrm{V}}_{\mathrm{O}}$ would be the dominant intrinsic defect under both Zn-rich and O-rich conditions and it is a deep double donor. Both ${\mathrm{Zn}}_{\mathrm{O}}$ and ${\mathrm{Zn}}_i$ are found to be shallow donors. The low formation energy of donor-type intrinsic defects could lead to difficulty in achieving $p$-type conductivity in ZnO. Defect complexes have charge transitions deep inside the band gap. The red, yellow, and green photoluminescence peaks of undoped samples can be assigned to some of the defect complexes considered. It is believed that the red luminescence originates from an electronic transition in ${\mathrm{V}}_{\mathrm{O}}$, but we find that it can originate from the antisite ${\mathrm{Zn}}_{\mathrm{O}}$ defect. Charge density and electron-localization function analyses have been used to understand the effect of these defects on the ZnO lattice. The electronic structure of ZnO with intrinsic defects has been studied using density-of-states and electronic band structure plots. The acceptor levels introduced by ${\mathrm{V}}_{\mathrm{Zn}}$ are relatively localized, making it difficult to achieve $p$-type conductivity with sufficient hole mobility.

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.

The electronic structure and structural stability of the technologically interesting material ${\mathrm{NaAlH}}_4$ are studied using an ab initio projected augmented plane-wave method for different possible structure modifications. We predict that $\mathrm{\alpha -}{\mathrm{NaAlH}}_4$ converts to $\mathrm{\beta -}{\mathrm{NaAlH}}_4$ at 6.43 GPa with a 4 % volume contraction. Both modifications have nonmetallic character with finite energy gaps, the calculated band gap for $\mathrm{\beta -}{\mathrm{NaAlH}}_4$ being almost half of that for the α phase. $\mathrm{\beta -}{\mathrm{NaAlH}}_4$ stores hydrogen more volume efficient than the α phase and would if stabilized at ambient conditions be an interesting candidate for further studies with regard to hydrogen absorption/desorption efficiency.

A detailed high-pressure study on ${\mathrm{LiAlH}}_4$ has been carried out using the ab initio projected augmented plane-wave method. Application of pressure transforms $\alpha -$ to $\beta -{\mathrm{LiAlH}}_4$ $(\alpha -{\mathrm{NaAlH}}_4$-type structure) at 2.6 GPa with a huge volume collapse of 17%. This abnormal behavior is associated with electronic transition from $\mathrm{Al}-s$ to -$p$ states. At 33.8 GPa, a $\beta$ to $\gamma$ transition is predicted from $\alpha -{\mathrm{NaAlH}}_4$-type to ${\mathrm{KGaH}}_4$-type structure. Up to 40 GPa ${\mathrm{LiAlH}}_4$ remains nonmetallic. The high weight percent of hydrogen, around 22% smaller equilibrium volume, and drastically different bonding behavior than $\alpha$-phase indicate that $\beta -{\mathrm{LiAlH}}_4$ is expected to be a potential hydrogen storage material.

Using gradient-corrected, full-potential, density-functional calculations, including structural relaxations, it is found that the metal hydrides $RT{\mathrm{I}\mathrm{n}\mathrm{H}}_{1.333}$ ($R=\mathrm{L}\mathrm{a}$, Ce, Pr, or Nd; $T=\mathrm{N}\mathrm{i}$, Pd, or Pt) possess unusually short H-H separations. The most extreme value (1.454 Å) ever obtained for metal hydrides occurs for ${\mathrm{L}\mathrm{a}\mathrm{P}\mathrm{t}\mathrm{I}\mathrm{n}\mathrm{H}}_{1.333}$. This finding violates the empirical rule for metal hydrides, which states that the minimum H-H separation is 2 Å. The paired, localized, and bosonic nature of the electron distribution at the H site are polarized towards La and In which reduces the repulsive interaction between negatively charged H atoms. Also, $R\mathrm{\text{−}}R$ interactions contribute to shielding of the repulsive interactions between the H atoms.