The nonlinear optical (NLO) properties in La₉Na₃B₈O₂₇, La₂Na₃B₃O₉ and La₂CaB₁₀O₁₉are investigated using a plane-wave pseudopotential method. Based on the first-principles electronic band structures, the birefringence and second harmonic generation (SHG) coefficients for the three crystals are determined. The calculated values match well with the experimental results. In order to elucidate the microscopic origins of the NLO performances in these crystals, a real-space atom-cutting method is adopted to calculate the contribution from the respective ions and groups. It is revealed that the La cations have covalent interactions with the neighbor O ions so as to form the La–O groups. The La–O bond covalency, combined with the distortion of La–O groups, makes the large contribution to the overall SHG coefficients in addition to the B–O groups, as also intuitively demonstrated by a SHG-density analysis. 

Journal of Physics: Condensed Matter, 2015