1：Experimental Design and Method Selection:

The study involved designing heteropolynuclear complexes [(YbL)2Tbx] through supramolecular assembly, using steady-state and time-resolved luminescence experiments to investigate photophysical properties. Theoretical models included DFT calculations for structural analysis and kinetic models for energy transfer mechanisms.

2：Sample Selection and Data Sources:

Samples were prepared from aqueous solutions of Yb and Tb complexes with ligand L, using D2O and H2O as solvents. Data were sourced from spectroscopic measurements, NMR, and X-ray crystallography.

3：List of Experimental Equipment and Materials:

Quartz cuvettes (Helma Analytics), Perkin-Elmer lambda 950 spectrometer, Edinburgh Instrument FLP920 spectrometer, Hamamatsu photomultipliers (R928 and R5509-72), 980 nm LED, laser diode (975 nm), power meters (Coherent FieldMate, Newport 1917R, Ophir 30A-BB-18), avalanche photodiode (Excelitas SPCM-AQRH-16), time-correlated single photon counting board (Becker-Hickl SPC-830), and various filters (e.g., 850 nm high-pass, 399 nm cutoff). Materials included Yb and Tb complexes, ligand L, and solvents D2O and H2O.

4：2O. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Complexes were synthesized and characterized using NMR and X-ray crystallography. Titrations with Tb salts were performed, adjusting pD. Emission spectra were recorded upon 980 nm excitation, with power-dependent and time-resolved measurements. Data were analyzed using fitting models for kinetic parameters.

5：Data Analysis Methods:

Data were analyzed using linear fits for paramagnetic shifts, DFT calculations for geometry, and kinetic models for UC rates. Software included Matlab for fitting and SPCM for photon counting.