First-Principles Electronic Structure Study of the Monoclinic Crystal Bismuth Triborate BiB₃O₆

Monoclinic BiB₃O₆ is an excellent nonlinear optical material with many advantages compared to other borate crystals. The origins of the optical effects and the chemical stability of BiB₃O₆ are studied with gradient-corrected hybrid B3PW density functional theory within the Gaussian-orbital-based CO-LCAO scheme. Including spin−orbit coupling, the B3PW hybrid functional provides an estimate of the indirect band gap of 4.29−4.99 eV closer to the experimental value of 4.3 eV than HF, LDA, or GGA. The crystal orbital overlap population to give a detailed first-principles analysis of chemical bonding and the density of optical absorptions by convoluting the occupied density of states and the virtual density of states have been calculated. Obvious Bi−O covalent bonds have been found with different energy ranges for 6s−2p and 6p−2p interactions. The reason that [BiO₄]^5- units are mainly responsible for the optics of BiB₃O₆ in the long-wavelength region is due to the electronic transfer from occupied O 2p to empty Bi 6p orbitals favored by the Bi−O covalent bonds. The relativistic and correlation effects lead to fundamental differences of the band structure, chemical bonds, and optical effects for BiB₃O₆ compared with nonrelativistic and uncorrelated calculations.