The ordered vacancy compounds $A{M}_2{X}_4$ have gained significant attention in thermoelectric research due to their promising electrical and thermoelectric properties. In this work, we present a first-principles-based high-throughput approach to screen 450 ordered vacancy compounds $A{M}_2{X}_4$ for potential thermoelectric applications. Initial screening criteria such as band gap, stability, and Pugh's ratio, followed by the phonon spectrum analysis through interception frequency, were used to identify promising candidates, highlighting a strong correlation between lattice thermal conductivity and Pugh's ratio. Despite sharing similar crystal structure of $\mathrm{Mg}{M}_2{\mathrm{Te}}_4$ $(\mathrm{M}=\mathrm{Sc}, \mathrm{Y}, \mathrm{Ga}, \text{and} \mathrm{In})$, ${\mathrm{MgY}}_2{\mathrm{Te}}_4$ exhibits an exceptionally low lattice thermal conductivity of 0.12 W/mK, in stark contrast to ${\mathrm{MgGa}}_2{\mathrm{Te}}_4$ (6.88 W/mK). This discrepancy is attributed to the significantly weaker bonding strength of Sc/Y-Te compared to Ga/In-Te, which enhances lattice anharmonicity and phonon scattering. Additionally, candidate materials with ultralow lattice thermal conductivity are characterized by low-frequency phonons contributing <2 THz, among which ${\mathrm{MgY}}_2{\mathrm{Te}}_4$ demonstrates excellent thermoelectric performance with a maximum ZT of ∼4.7. This work not only unravels the importance of strong anharmonicity and phonon scattering induced by weak-bonded heavy elements on the thermoelectric performance in the $A{M}_2{X}_4$ family, but also showcases that the screening through Pugh's ratio and interception frequency is an effective strategy for discovering high-performance flexible thermoelectric materials.

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• Anharmonic lattice dynamics
• Electron-phonon coupling
• Electronic structure
• Phonons
• Scattering theory
• Seebeck effect
• Thermal conductivity
• Thermoelectric effects
• Thermoelectrics
• 3-dimensional systems
• Ab initio molecular dynamics
• Boltzmann theory
• Density functional calculations
• High-throughput calculations