The origins of the optical effects and the chemical stability of BiB3O6 are studied by gradient-corrected hybrid B3PW density functional theory within the Gaussian-orbital-based CO-LCAO scheme. Including spin-orbit coupling, B3PW yields an estimate of the indirect band gap of 4.29~4.99 eV which is closer to the experimental value of 4.3 eV than the HF, LDA or GGA results. The crystal orbital overlap population is carried out to give a detailed first-principles analysis of chemical bonding. It is found that the Bi 6s couples with the O 2p in the primary interaction, which eventually forms both bonding and antibonding orbitals below the Fermi level. The Bi 6p is further involved in the secondary interaction with the filled Bi 6s-O 2p antibonding orbitals. The stereochemical activity of the Bi lone-pairs mainly originates from the primary interaction for the occupied Bi 6s-O 2p antibonding orbitals. It is found that the Bi 6p orbitals are not critically responsible for the non-spherical shape of the Bi lone-pairs. The densities of optical absorptions for the total BiB3O6 crystal, [BiO4]5- and [BO3]3- and [BO4]5- subunits are individually calculated by convoluting the total occupied density of states and the virtual densities of states of the corresponding unit. It is found that the [BiO4]5- units are mainly responsible for the optics of BiB3O6 in the long wavelength region. The reason is that the Bi-O covalent bonds lead to large spatial orbital overlappings and thus favor the electronic transfer from the occupied O 2p to the empty Bi 6p orbitals. The relativistic and correlation effects lead to fundamental differences of the band structure, chemical bonds and optical effects for BiB3O6 compared with non-relativistic and uncorrelated calculations. The harmonic frequencies of BiB3O6 are calculated by applying the numerical-difference technique. The complete 13 A and 14 B vibrational modes are assigned, graphically visualized and classified according to the Bi-O and B-O motions. Comparisons with previous experimental reports are discussed in detail. Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets are derived, in line with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Köln variety, for calculating periodic bulk materials containing trivalent lanthanide ions, particularly in this thesis for the investigation of the relative stability of C2 and I2 phases of LnB3O6. Different segmented contraction schemes are calibrated on A-type Pm2O3 studying the basis set size effects. Further applications to the geometry optimization of other A-type Ln2O3 (Ln=La-Nd) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d]. The cohesive energies of A-Ln2O3 within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes are evaluated by using the corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for the atomic energies of free lanthanide atoms. The I2 phases of LaB3O6 and GdB3O6 crystals are more stable than C2 phases according to both of the calculated energetic data and first-principles bond analysis. This is in agreement with the experimental results. A new method is developed to calculate the optical properties for large systems based on available wavefunction correlation approaches in the framework of the incremental scheme. The convergence behaviors of first- and second-order polarizabilities with respect to the domain distances and incremental expansion orders are examined and discussed for the model system Ga4As4H18
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