High-throughput computational framework for lattice dynamics and thermal transport including high-order anharmonicity: an application to cubic and tetragonal inorganic compounds

Accurately predicting lattice thermal conductivity (kL) from first principles remains a challenge in identifying materials with extreme thermal behavior. While modern lattice dynamics methods enable routine predictions of kL within the harmonic approximation and three-phonon scattering framework (HA+3ph), reliable results, especially for low-kL compounds, require higher-order anharmonic effects, including self-consistent phonon renormalization, four-phonon scattering, and off-diagonal heat flux (SCPH+3,4ph+OD). We present a high-throughput workflow integrating these effects into a unified framework. Using this, we compute kL for 773 cubic and tetragonal inorganic compounds across diverse chemistries and structures. From 562 dynamically stable compounds, we assess the hierarchical effects of higher-order anharmonicity. For about 60% of materials, HA+3ph predictions closely match those from SCPH+3,4ph+OD. However, SCPH corrections often increase kL, sometimes by over 8 times, while four-phonon scattering universally reduces it, occasionally to 15% of the HA+3ph value. Off-diagonal contributions are minor in high-kL systems but can be comparable to the diagonal ones in highly anharmonic, low-kL compounds. We highlight four cases-Rb2TlAlH6, Cu3VS4, CuBr, and KTlCl4-exhibiting distinct anharmonic behaviors. This work delivers not only a robust workflow for high-fidelity kL dataset but also a quantitative framework to determine when higher-order effects are essential. The hierarchy of kL results, from the HA+3ph to SCPH+3,4ph+OD level, offers a scalable, interpretable route to discovering next-generation extreme thermal materials.