Electronic structure and optical properties of the nonlinear optical crystal Pb{sub 4}O(BO{sub 3}){sub 2} by first-principles calculations

Pb{sub 4}O(BO{sub 3}){sub 2} has a layered-type arrangement with optimally aligned BO{sub 3} triangles. The optical band gap is 3.317 eV obtained via the extrapolation method from the UV-vis-IR optical diffuse reflectance spectrum, consequently the absorption edge is about 374 nm. Density functional calculations using a generalized gradient approximation were utilized to investigate the electronic structures and optical properties of Pb{sub 4}O(BO{sub 3}){sub 2}. The calculated band structures show a direct gap of 2.608 eV, which is in agreement with the experimental optical band gap. A delocalized {pi} bonding of BO{sub 3} triangles and the stereo-effect of the lone pair 6s{sup 2} of lead cations are studied in electron densities. The birefringence is about 0.039-0.061 with the wavelength larger than about 375 nm. The calculated second-order susceptibility d{sub 24}=3.5 d{sub 36} (KDP) which is well consistent with the powder SHG intensity. - Graphical abstract: The density of state (DOS) show that the bottom of the valence bands is mainly derived from of the lone pair 6s{sup 2} of Pb{sup 2+}, and the top of the valence band is attributed to the hybridization orbitals from B-O groups. Calculated electronic structures indicate that the BO{sub 3} group with typical delocalization {pi} orbitalsmore » and strongly distorted lead oxygen polyhedra with highly asymmetric lobes on lead cations make a large SHG effect in Pb{sub 4}O(BO{sub 3}){sub 2}. Highlights: Black-Right-Pointing-Pointer Lone pair effect on Pb{sup 2+} and delocalization {pi} orbital in BO{sub 3} group is studied. Black-Right-Pointing-Pointer The combination of PbO{sub n} (n=3,4,5) and BO{sub 3} group makes Pb{sub 4}O(BO{sub 3}){sub 2} a large SHG effect. Black-Right-Pointing-Pointer Pb{sub 4}O(BO{sub 3}){sub 2} is a direct gap material with the gap 2.608 eV by the ab initio method. Black-Right-Pointing-Pointer The calculated birefringence is about 0.039-0.061 with the wavelength of about 375 nm. Black-Right-Pointing-Pointer The second-order susceptibility d{sub 24}=3.5d{sub 36} (KDP) in accordance with the experimental result.« less