The results of a theoretical study on the point defects of monoclinic ␤-Ga 2 O 3 are reported here. The point defects considered here are vacancies, interstitials together with dopant ions such as Be, Mg, In, Cr, Si, Ge, Sn, and Zr. Since the low symmetry of the monoclinic lattice does not provide an unambiguous location of interstitial sites and migration paths, we propose a unique way for their identification in terms of the electron density topology. Special attention has also been given to the preference among the lattice and interstitial sites for the impurity defects, and its explanation in terms of structural, electrostatic, and electron density arguments. The calculated results find the most prominent features in the lattice to be the existence of ͑i͒ empty channels along the b direction, and ͑ii͒ atomic layers perpendicular to them. Their interplay governs the stability and mobility of the point defects in ␤-Ga 2 O 3. The anionic Frenkel pair consisting of the oxygen vacancy and oxygen interstitial is predicted to dominate the defect structure in the lattice. The dopants considered here are likely to be stabilized at the octahedral gallium sites, except for Be +2 , which prefers a tetrahedral gallium site in the lattice. Some of the possible migration paths have been determined, and the pseudoactivation energies for the intrinsic, oxygen-rich, and oxygen-deficient conditions are computed as a function of temperature. It is suggested that tuning the concentration of oxygen can lead to a change in the anisotropy of the ionic conductivity in ␤-Ga 2 O 3 .

We present the results of a first-principles study on BaF 2 in its stable (cubic) and high-pressure phases. A linear combination of atomic orbitals approach in the framework of density functional theory is employed for total energy calculations in cubic, orthorhombic and hexagonal phases of BaF 2. A fitting of the energy surface to the equation of state yields the lattice constant and the bulk modulus of these phases at zero pressure which are in good agreement with the corresponding experimental values. Analysis of band structure determines the high-pressure phases to be direct-gap materials and no metallization of BaF 2 is predicted to occur for pressures up to 50 GPa. Furthermore, several peaks observed in the spectroscopic experiments have been identified with interband transitions in the cubic BaF 2. The calculated mean value of the refractive index is found to increase in going from the cubic to orthorhombic to hexagonal phases of BaF 2 .

The results of electronic structure calculations for PbF 2 in ambient and highpressure phases are reported here. We employ the linear combination of atomic orbital-density functional theory approximation using the CRYSTAL program package whose capabilities were expanded to include the so-called soft-core pseudopotentials with higher-order components (e.g. d, f, and g) of the angular momentum terms for heavier atoms in the periodic table. The band structure and density of states of the cubic, orthorhombic, and hexagonal phases were calculated. A direct band gap at X is predicted for the cubic phase, whereas an indirect band gap is predicted for the high-pressure phases. The density of states reveals hybridization features involving Pb s and F p orbitals in the upper valence band of PbF 2 .

Native and rare-earth-doped point-defects in ␤-PbF 2 are studied in the framework of the pair-potential approximation coupled with the shell model description of the lattice ions. For the perfect lattice, a new set of potential parameters are obtained which reproduce structure, elastic and dielectric constants of PbF 2 very well. The calculated formation energies for native defects suggest that the anion Frenkel disorder is preferred over the cation Frenkel and Schottky-like disorder in PbF 2. The computed temperature behavior of the ionic conductivity agrees very well with the available experimental data. In the rare-earth doped PbF 2 , a site preference of the charge-compensating fluorine interstitial appears to change from nearest to next-nearest neighbor with the increase in the rare-earth ionic radius.

Large unit cell calculations of the properties of charged point defects in insulators largely neglect dielectric polarization of the crystal, because the periodically repeated cells are so small. Embedded quantum cluster calculations with shell-model crystals, representing a single defect in a large crystal, are able to represent the polarization more realistically. For such embedded quantum clusters, we evaluate the optical excitation energy for the nitrogen vacancy in charge state (+3): v 3+ N in AlN. This is done with and without dielectric polarization of the embedding crystal. A discrepancy of a few per cent is found, when both ground and excited state orbitals are well-localized within the vacancy. We show that the discrepancy rises rapidly as the excited state becomes more diffuse. We conclude that an embedded cluster approach will be required for transitions that involve even somewhat diffuse states. The investigation is based on a new model for AlN that shows promise for quantitative accuracy.