Insight into the Origin of Second Harmonic Generation and Rational Design in the Metal Halide Borates

Metal halide borates are promising candidates for high-performance nonlinear optical (NLO) applications, yet the origins of their second harmonic generation (SHG) properties remain unclear. Using atom response theory combined with density functional theory calculations, this study investigates why halogen substitution leads to distinctly different SHG responses in halide monoborates (Pb₂BO₃X) versus halide pentaborates (Pb₂B₅O₉X). We find that the SHG origins vary between these two families due to differences in the strength of the Pb-X interactions. Interestingly, the stereochemically active lone pairs are not shown to be the primary contributors to SHG; instead, these hybridized asymmetric orbitals can introduce negative contributions. Utilizing the d_eff^p vs α_sum/(NE_g) linear relationship, we predict 12 new NLO borates with strong SHG responses, including the promising NLO material Sn₂B₅O₉I (19.2 × KDP), which is expected to exhibit the highest SHG response among halide borates reported to date. This work provides valuable insights into the relationship between elemental substitution and SHG modulation, guiding the design of advanced NLO materials.