Electronic structure and interatomic bonding of crystalline β-${\mathrm{BaB}}_2$${\mathrm{O}}_4$ with comparison to ${\mathrm{LiB}}_3$${\mathrm{O}}_5$

The electronic structure and the linear-optical properties of the nonlinear-optical crystal β-${\mathrm{BaB}}_2$${\mathrm{O}}_4$ (BBO) have been calculated using a first-principles band-structure method with the local-density approximation. The results are compared with those of another nonlinear-optical crystal ${\mathrm{LiB}}_3$${\mathrm{O}}_5$ (LBO). An indirect band gap of 5.52 eV and a direct gap of 5.61 eV at Γ for BBO are obtained, which are to be compared with the measured optical gap of 6.43 eV. It is shown that the electronic structure of the BBO is dominated by the characteristic ionic (${\mathrm{B}}_3$${\mathrm{O}}_6$${)}^{\mathrm{-}3}$ group in which the two different O sites show markedly different bonding structures. Comparison of charge-density distributions in BBO and LBO shows that the ionic groups are linked together in forming a networklike structure. The Ba atom in the BBO crystal is found to be bonded to the O ions in the adjacent layers in a partly covalent, partly ionic manner due to the presence of large semi-core-like 5p orbitals. The calculated optical properties for both BBO and LBO crystals are in good agreement with the measured vacuum ultraviolet spectrum especially in the region of absorption threshold. The agreements between theory and experiment near the absorption edges are much closer than that reflected by the gap values alone.