Halogen Engineering and Orbital Origins of Large Second-Harmonic Generation in Organic-Inorganic Hybrid Metal Halides

Organic-inorganic hybrid metal halides (OIHMHs) have emerged as promising nonlinear optical (NLO) materials due to their structural tunability and potential for large second-harmonic-generation (SHG) responses. Here, using first-principles density functional theory calculations, we systematically investigate the structural, electronic, and optical properties of 12 noncentrosymmetric compounds in 3-PyDMX₃ and 4-MePDMX₃ (M = Zn, Cd; X = Cl, Br, I). Our results reveal a clear and consistent enhancement of SHG with an increasing halogen atomic size, with iodide compounds exhibiting the strongest responses. In particular, 3-PyDZnI₃ and 4-MePDZnI₃ show large effective SHG responses of 1.34 and 1.39 pm/V, respectively, corresponding to approximately four times that of the benchmark KDP, while maintaining suitable band gaps of 2.83 and 4.21 eV. A strong linear correlation between the effective SHG response and descriptor V/(NE_g) is established across all compounds, indicating the combined roles of electronic polarizability and band gap modulation. Electronic structure analysis reveals that the larger birefringence in 3-PyDZnI₃ originates from the pronounced energy separation between the I 5p_z and I 5p_x/y orbitals, whereas these states are more dispersed in 4-MePDZnI₃, leading to a weaker optical anisotropy. Atom response theory further demonstrates that the SHG response is dominated by the inorganic framework, with halogen and metal atoms contributing ∼70% of the total response, while the organic cations primarily stabilize the noncentrosymmetric structure. These results identify promising hybrid metal halide NLO materials and provide clear guidelines for optimizing SHG performance through targeted compositional and electronic-structure design.