Four-phonon thermal conductivity: Numerical sensitivities, convergence, and machine-learning acceleration

Abstract

While the prediction of lattice thermal conductivity has traditionally relied on three-phonon interaction frameworks, accurately modeling highly anharmonic materials or extreme temperature regimes increasingly demands the inclusion of higher-order effects. This tutorial presents a comprehensive computational framework for predicting four-phonon scattering processes and the associated phonon thermal conductivity. The physical conditions that necessitate fourth-order interactions are first outlined, followed by a detailed analysis of quartic interatomic force constant (IFC) extraction, four-phonon scattering calculations, and machine-learning acceleration modules. Utilizing Lennard-Jones argon and Stillinger–Weber silicon as model systems, a systematic sensitivity analysis is performed to isolate the numerical artifacts and error propagation inherent to finite-difference routines vs Taylor-series regression-fitting methods for quartic IFC extraction. The role of primary density functional theory parameters, specifically plane wave energy cutoffs, electronic k-point grids, minimization algorithms, and parallelization schemes, on the fidelity of computed atomic forces is established using cubic boron arsenide as a representative test system. Crucially, the convergence behavior of four-phonon-driven thermal conductivity across various numerical parameters is shown to be highly material-dependent. Finally, it is demonstrated that the severe computational bottlenecks traditionally associated with establishing parameter convergence can be effectively mitigated by integrating machine-learning-accelerated approaches, offering a robust paradigm for next-generation, high-fidelity transport simulations.