1：Experimental Design and Method Selection:

The study involved re-determining the crystal structure of [Ag3S](NO3) using X-ray single crystal diffraction to improve accuracy, and comparing it with [Ag4Te](SO4). Theoretical calculations using density-functional theory (DFT) with the FP-LAPW method were employed for electronic structure analysis.

2：4). Theoretical calculations using density-functional theory (DFT) with the FP-LAPW method were employed for electronic structure analysis. Sample Selection and Data Sources:

2. Sample Selection and Data Sources: Single crystals of [Ag3S](NO3) were synthesized from aqueous solutions of Na2S2O3 and AgNO

3：The crystal structure data were obtained from X-ray diffraction measurements. List of Experimental Equipment and Materials:

Equipment included a STOE StadiVari Pilatus 100 K diffractometer with a Mo-target X-ray tube, a TENSOR-27 IR spectrometer, and computational tools like ELK code and DGrid package. Materials included Na2S2O3, AgNO3, KBr, and ethanol.

4：Experimental Procedures and Operational Workflow:

Synthesis involved mixing solutions to form crystals, followed by washing with ethanol. X-ray data collection was performed at 293 K, with integration and refinement using STOE X-AREA and SHELXTL software. IR spectroscopy was conducted using KBr pellets. DFT calculations were performed with specific parameters for atomic radii and k-point sampling.

5：Data Analysis Methods:

Structural refinement used least-squares procedures, IR spectra were analyzed for vibrational modes, and electronic structure analysis involved DOS, ELF, ELI-D, and charge density calculations using QTAIM approach.