1：Experimental Design and Method Selection:

The study involved exploratory synthesis based on the bonding characteristics of Hg and a screening strategy for high-performance crystals. Methods included solid-state synthesis, single-crystal growth via slow cooling, structural determination by single-crystal XRD, optical property measurements (diffuse reflectance, SHG), thermal analysis (DSC), and DFT calculations.

2：Sample Selection and Data Sources:

Polycrystalline and single-crystal samples of BaHgGeSe4 and SrHgGeSe4 were synthesized from stoichiometric mixtures of BaSe/SrSe, HgSe, and GeSe2 (prepared from elements). Data sources included experimental XRD, EDX, optical spectra, SHG signals, and thermal curves.

3：List of Experimental Equipment and Materials:

Equipment: Bruker D8 diffractometer (XRD), Rigaku AFC10 diffractometer (single-crystal XRD), Hitachi S-4800 SEM (EDX), Cary 6000 UV-vis-NIR spectrophotometer (diffuse reflectance), Q-switched Ho:Tm:Cr:YAG laser (SHG), Labsys TG-DTA16 thermal analyzer (DSC). Materials: Ba (99.9%), Sr (99.9%), Ge (99.99%), Se (99.999%), HgSe (99.99%) from Sinopharm; fused-silica tubes; BaSO4 (reflectance standard); AgGaS2 (SHG reference).

4：9%), Sr (9%), Ge (99%), Se (999%), HgSe (99%) from Sinopharm; fused-silica tubes; BaSO4 (reflectance standard); AgGaS2 (SHG reference). Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Synthesis: Ground mixtures in Ar glove box, sealed in evacuated fused-silica tubes, heated to 973 K (polycrystalline) or 1173 K (single crystals) with controlled heating/cooling rates. Characterization: XRD for phase identification, single-crystal XRD for structure solution, EDX for composition, diffuse reflectance for band gap, SHG measurements using Kurtz-Perry method with particle size ranges, DSC for thermal behavior, DFT calculations for electronic and optical properties.

5：Data Analysis Methods:

Structural refinement with SHELXTL, band gap determination from reflectance spectra, SHG coefficient comparison to AgGaS2, thermal analysis for melting points, DFT calculations with CASTEP for band structure, DOS, NLO coefficients, and atom-cutting analysis.