Hierarchy of exchange-correlation functionals in computing lattice thermal conductivities of rocksalt and zinc-blende semiconductors

Lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) is a crucial characteristic of crystalline solids with significant implications for thermal management, energy conversion, and thermal barrier coating. The advancement of computational tools based on density functional theory (DFT) has enabled the effective utilization of phonon quasiparticle-based approaches to unravel the underlying physics of various crystalline systems. While the higher order of anharmonicity is commonly used for explaining extraordinary heat transfer behaviors in crystals, the impact of exchange-correlation (XC) functionals in DFT on describing anharmonicity has been largely overlooked. The XC functional is essential for determining the accuracy of DFT in describing interactions among electrons/ions in solids and molecules. However, most XC functionals in solid-state physics are primarily focused on computing the properties that only require small atomic displacements from the equilibrium (within the harmonic approximation), such as harmonic phonons and elastic constants, while anharmonicity involves larger atomic displacements. Therefore, it is more challenging for XC functionals to accurately describe atomic interactions at the anharmonicity level. In this study, we systematically investigate the room-temperature ${\kappa }_{\mathrm{L}}$ of 16 binary compounds with rocksalt and zinc-blende structures using various XC functionals such as local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), revised PBE for solid and surface (PBEsol), optimized B86b functional (optB86b), revised Tao-Perdew-Staroverov-Scuseria (revTPSS), strongly constrained and appropriately normed functional (SCAN), regularized SCAN (rSCAN), and regularized-restored SCAN (${\mathrm{r}}^2\mathrm{SCAN}$) in combination with different perturbation orders, including phonon within harmonic approximation (HA) plus three-phonon scattering ($\mathrm{HA}+3\mathrm{ph}$), phonon calculated using self-consistent phonon theory (SCPH) plus three-phonon scattering (SCPH $+$ 3ph), and SCPH phonon plus three- and four-phonon scattering (SCPH $+$ 3,4ph). Our results show that the XC functional exhibits strong entanglement with perturbation order and the mean relative absolute error (MRAE) of the computed ${\kappa }_{\mathrm{L}}$ is strongly influenced by both the XC functional and perturbation order, leading to error cancellation or amplification. The minimal (maximal) MRAE is achieved with revTPSS (rSCAN) at the HA $+$ 3ph level, SCAN (${\mathrm{r}}^2\mathrm{SCAN}$) at the SCPH $+$ 3ph level, and PBEsol (rSCAN) at the SCPH $+$ 3,4ph level. Among these functionals, PBEsol exhibits the highest accuracy at the highest perturbation order. The SCAN-related functionals demonstrate moderate accuracy but are suffer from numerical instability and high computational costs. Furthermore, the different impacts of quartic anharmonicity on ${\kappa }_{\mathrm{L}}$ in rocksalt and zinc-blende structures are identified by all XC functionals, attributed to the distinct lattice anharmonicity in these two structures. These findings serve as a valuable reference for selecting appropriate functionals for describing anharmonic phonons and offer insights into high-order force constant calculations that could facilitate the development of more accurate XC functionals for solid materials.