The interplay between chemical bonding, lattice anharmonicity, and thermal transport plays a central role in determining the thermoelectric performance of crystalline solids. Here, we systematically investigate the structural stability, lattice dynamics, thermal transport, and thermoelectric properties of the $M\mathrm{Ag}C{h}_2$ ($M=\mathrm{Sc}$, Y; $Ch=\mathrm{S}$, Se, Te) family. The calculated formation energies, phonon dispersions, and finite-temperature radial distribution functions confirm the thermodynamic, dynamical, and thermal stability of all six compounds. Furthermore, the predicted lattice parameters show excellent agreement with available experimental measurements, supporting the reliability of the theoretical framework. Chemical-bonding analysis reveals a distinct bonding hierarchy characterized by strong $M$–$\mathit{Ch}$ interactions and substantially weaker Ag–$\mathit{Ch}$ bonds. This weakly bonded Ag sublattice gives rise to highly anisotropic atomic vibrations, large mean-square displacements, and dense low-frequency optical phonon modes. As a result, pronounced acoustic–optical phonon overlap and strong anharmonicity emerge throughout the series. The lattice thermal conductivity decreases systematically from sulfides to tellurides and remains below 1 W/mK at elevated temperatures. Notably, wave-like phonon transport contributes significantly to the lattice thermal conductivity, accounting for approximately 45–56% of the heat conduction at 900 K, highlighting the breakdown of a purely particle-like phonon picture. Electronic structure calculations reveal progressive band gap narrowing and reduced carrier effective masses from S to Te, leading to enhanced carrier transport in the tellurides. Owing to the combination of intrinsically low lattice thermal conductivity and favorable electronic transport properties, ${\mathrm{ScAgTe}}_2$ and ${\mathrm{YAgTe}}_2$ exhibit the best thermoelectric performance, with predicted peak $\mathit{zT}$ values approaching 3.5 and 3.0 along the preferred transport direction, respectively. These findings identify $M\mathrm{Ag}C{h}_2$ as a promising thermoelectric material family and demonstrate the critical role of weak Ag-centered bonding, higher-order anharmonicity, and coherent phonon transport in achieving ultralow thermal conductivity.

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• Electronic structure
• First-principles calculations
• Seebeck effect
• Spin-orbit coupling
• Thermal conductivity
• Thermoelectrics
• Chalcogenides
• Density functional theory
• Machine learning