A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential.

The electronic structure and ground state properties of AlB 2 type transition metal diborides TMB 2 ͑TMϭSc, Ti, V, Cr, Mn, Fe, Y, Zr, Nb, Mo, Hf, Ta͒ 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 Ј), cohesive energy (E coh), heat of formation (⌬H), and electronic specific heat coefficient (␥) 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 ͑DOS͒ 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 CrB 2 , MnB 2 , and FeB 2 and found that finite magnetic moments exist for MnB 2 and CrB 2 whereas FeB 2 is nonmagnetic.

Structural phase stability, electronic structure, optical properties, and high-pressure behavior of polytypes of In 2 O 3 in three space group symmetry I2 1 3, Ia3 and R3 are studied by first-principles density functional calculations. From structural optimization studies lattice and positional parameters have been calculated, which are found to be in good agreement with the corresponding experimental data. In 2 O 3 of space group symmetry I2 1 3 and Ia3 are shown to undergo a pressureinduced phase transition to IO3 at pressures around 3.83 GPa. From analysis of band structure it is found that In 2 O 3 of space group symmetry I2 1 3 is indirect band gap semiconductors, while the other phase of space group Ia3 is direct band gap. The calculated carrier effective masses for all these three phases are compared with available experimental and theoretical values. From chargedensity and electron localization function analysis it is found that these phases have dominant ionic bonding. The magnitude of the absorption and reflection coefficients of In 2 O 3 with space group Ia3 and R3 are small in the energy range 0-5 eV, so that these materials can re regarded and classified as transparent.

The computational framework of this study is based on the local-spin-density approximation with firstprinciples full-potential linear muffin-tin orbital calculations including orbital polarization ͑OP͒ correction. We have studied the magnetic anisotropy for a series of bilayer CuAu͑I͒-type materials such as FeX, MnX (X ϭNi,Pd,Pt), CoPt, NiPt, MnHg, and MnRh in a ferromagnetic state using experimental structural parameters to understand the microscopic origin of magnetic-anisotropy energy ͑MAE͒ in magnetic multilayers. Except for MnRh and MnHg, all these phases show perpendicular magnetization. We have analyzed our results in terms of angular momentum-, spin-and site-projected density of states, magnetic-angular-momentumprojected density of states, orbital-moment density of states, and total density of states. The orbital-moment number of states and the orbital-moment anisotropy for FeX (XϭNi,Pd,Pt) are calculated as a function of band filling to study its effect on MAE. The total and site-projected spin and orbital moments for all these systems are calculated with and without OP when the magnetization is along or perpendicular to the plane. The results are compared with available experimental as well as theoretical results. Our calculations show that OP always enhances the orbital moment in these phases and brings them closer to experimental values. The changes in MAE are analyzed in terms of exchange splitting, spin-orbit splitting, and tetragonal distortion/crystal-field splitting. The calculated MAE is found to be in good agreement with experimental values when the OP correction is included. Some of the materials considered here show large magnetic anisotropy of the order of meV. In particular we found that MnPt will have a very large MAE if it could be stabilized in a ferromagnetic configuration. Our analysis indicates that apart from large spin-orbit interaction and exchange interaction from at least one of the constituents, a large crystal-field splitting originating from the tetragonal distortion is also a necessary condition for having large magnetic anisotropy in these materials. Our calculation predicts large orbital moment in the hard axis in the case of FePt, MnRh, and MnHg against expectation.

The chemical bonding, electronic structure, and optical properties of metal-organic framework-5 (MOF-5) were systematically investigated using ab initio density functional calculations. The unit cell volume and atomic positions were optimized with the Perdew-Burke-Ernzerhof (PBE) functional leading to a good agreement between the experimental and the theoretical equilibrium structural parameters. The calculated bulk modulus indicates that MOF-5 is a soft material. The estimated band gap from a density of state (DOS) calculation for MOF-5 is about 3.4 eV, indicating a nonmetallic character. As MOFs are considered as potential materials for photocatalysts, active components in hybrid solar cells, and electroluminescence cells, the optical properties of this material were investigated. The detailed analysis of chemical bonding in MOF-5 reveals the nature of the Zn-O, O-C, H-C, and C-C bonds, that is, Zn-O having mainly ionic interaction whereas O-C, H-C, and C-C exhibit mainly covalent interactions. The findings in this paper may contribute to a comprehensive understanding about this kind of material and shed insight into the synthesis and application of novel and stable MOFs.

The magneto-optic ͑MO͒ Kerr and Faraday spectra for manganese pnictides are calculated using the all electron, relativistic, full-potential linear muffin-tin orbital method. The amplitude of our calculated spectra are found to be in good agreement with corresponding experimental spectra. Although the MO property is a rather complicated function of the diagonal and off-diagonal elements of the optical conductivity tensor, present theory nevertheless provides very practical insight about its origin in these compounds. The largest Kerr effect observed in MnBi can be understood as a combined effect of maximal exchange splitting of Mn 3d states and the nearly maximal spin-orbit ͑s-o͒ coupling of Bi. The frequency-dependent optical properties, namely reflectivity, absorption coefficient, electron-energy-loss spectra, refractive index, extinction coefficient are given. From our calculations ͑including spin-orbit coupling and orbital polarization͒ the site-projected spin and orbital moments are also obtained and compared to the available experimental values and a good agreement is found. The magnetic anisotropy energy is calculated with a minimal number of approximations for the three systems. A disagreement between theory and experiment is found. Using the generalized gradient corrected fullpotential linear augmented plane-wave method we have calculated the unscreened plasma frequencies and the hyperfine parameters such as electric-field gradient as well as the hyperfine field. ͓S0163-1829͑99͒01419-8͔

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