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

Zhi Li, Huiju Lee, Chris Wolverton, Yi Xia

TL;DR

This work develops a high-throughput, first-principles framework that incorporates full anharmonicity—SCPH renormalization, three- and four-phonon scattering, and off-diagonal heat flux—to predict lattice thermal conductivity $k_\mathrm{L}$ across a diverse set of cubic and tetragonal inorganic materials. By systematically building a hierarchy of $k_\mathrm{L}$ values (HA+3ph, SCPH+3ph, SCPH+3,4ph, and OD), the study reveals that for about 60% of materials the harmonic-plus-three-phonon prediction is already close to the fully anharmonic result, while four-phonon processes typically suppress $k_\mathrm{L}$ and SCPH renormalization often increases it; off-diagonal transport becomes relevant mainly in low-$k_\mathrm{L}$ systems. The resulting dataset, validated against PhononDB and literature benchmarks, provides both physical insights into anharmonic phonon behavior and a resource for data-driven materials discovery, including potential development of an “anharmonic importance classifier” to guide when simpler methods suffice. The workflow and data enable rapid screening of extreme thermal materials and offer a foundation for machine-learning approaches to predict hierarchy metrics and guide targeted high-fidelity calculations.

Abstract

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.

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

TL;DR

This work develops a high-throughput, first-principles framework that incorporates full anharmonicity—SCPH renormalization, three- and four-phonon scattering, and off-diagonal heat flux—to predict lattice thermal conductivity across a diverse set of cubic and tetragonal inorganic materials. By systematically building a hierarchy of values (HA+3ph, SCPH+3ph, SCPH+3,4ph, and OD), the study reveals that for about 60% of materials the harmonic-plus-three-phonon prediction is already close to the fully anharmonic result, while four-phonon processes typically suppress and SCPH renormalization often increases it; off-diagonal transport becomes relevant mainly in low- systems. The resulting dataset, validated against PhononDB and literature benchmarks, provides both physical insights into anharmonic phonon behavior and a resource for data-driven materials discovery, including potential development of an “anharmonic importance classifier” to guide when simpler methods suffice. The workflow and data enable rapid screening of extreme thermal materials and offer a foundation for machine-learning approaches to predict hierarchy metrics and guide targeted high-fidelity calculations.

Abstract

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.

Paper Structure

This paper contains 24 sections, 29 equations, 15 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Formalism of lattice dynamics
  4. High-throughput computational workflow
  5. Overview of the dataset
  6. Results and discussion
  7. Benchmark with literature and database
  8. Insights into the hierarchy of $\kappa^\mathrm{HA\,+\,3ph\xspace}_\mathrm{L}$, $\kappa^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{L}$, and $\kappa^\mathrm{SCPH\,+\,3,\,4ph\xspace}_\mathrm{L}$
  9. Off-diagonal thermal conductivity
  10. Conclusion
  11. Data Availability
  12. Code Availability
  13. Supporting Information
  14. Convergence test of lattice thermal conductivity ($\kappa_\mathrm{L}$) calculations
  15. Computational time statistics
  16. ...and 9 more sections

Figures (15)

  • Figure 1: a) Workflow for high-throughput lattice thermal conductivity calculations. Outputs discussed in this work are highlighted in yellow. b) Elemental distribution of 773 materials included in the dataset. c) Dataset overview across the lattice-dynamics theory hierarchy. At each theory level, solid boxes/arrows trace materials without imaginary modes (IM) at 0 K (under harmonic approximation, HA) or/and 300 K (after self-consistent phonon renormalization, SCPH), whereas dashed boxes/arrows show materials with IM at 0 K (HA) or/and 300 K (SCPH). The banner on each row reports the number of materials with data available at that level in our released dataset.
  • Figure 2: a) Mode-averaged phonon-frequency deviations between this work and PhononDB. b) Examples of compounds with significant (ReO$_3$, top) and moderate (Be$_2$SrN$_2$, bottom) frequency differences compared to PhononDB. c) Mode-resolved comparison of phonon frequencies across two datasets. d) Benchmark of calculated $\kappa_\mathrm{L}$ against reported experimental and DFT values from the literature. e) Variation in calculated $\kappa_\mathrm{L}$ using different levels of lattice dynamics theory. Materials are ordered by increasing $\kappa^\mathrm{HA\,+\,3ph\xspace}_\mathrm{L}$. For visual clarity, bars for NaBH$_4$ with $R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$ = 8.7, $R^\mathrm{SCPH\,+\,3,\,4ph\xspace}_\mathrm{HA\,+\,3ph}$ = 7.0, and $R^\mathrm{SCPH\,+\,3,\,4ph\,+\,OD\xspace}_\mathrm{HA\,+\,3ph\xspace}$ = 8.6 are truncated at 3.0.
  • Figure 3: a) Mean absolute percentage difference (MAPD) between SCPH and HA phonon frequencies plotted against the average HA frequency for each compound. b) Compound-wise comparison of positive and negative mean percentage differences (MPD$^+$ and MPD$^-$) in mode frequencies between SCPH and HA. c) Distribution of $R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$. d) Distribution of $R^\mathrm{SCPH\,+3,\,4ph}_\mathrm{SCPH\,+\,3ph\xspace}$. e) Top-10 compounds ranked by: (top) highest $R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$, (middle) lowest $R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$, and (bottom) lowest $R^\mathrm{SCPH\,+3,\,4ph}_\mathrm{SCPH\,+\,3ph\xspace}$. f) Comparison of $\kappa^\mathrm{HA\,+\,3ph\xspace}_\mathrm{L}$ and associated ratios for the top-10 (upper panel) and bottom-10 (lower panel) compounds ranked by $\kappa^\mathrm{SCPH\,+\,3,\,4ph\xspace}_\mathrm{L}$. Red dashed lines denote when ratio equals 1.
  • Figure 4: Crystal structures, phonon dispersion, and frequency-dependent phonon density of states, linewidth and cumulative $\kappa_\mathrm{L}$ (SCPH + 3(,4)ph: green solid lines; HA + 3ph: yellow dashed lines), and P3/P4 phase space or SCPH interaction parameter $I_{\lambda\lambda_1}$ for a) Rb$_2$TlAlH$_6$ ($R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$ = 9.46), b) Cu$_3$VSe$_4$ ($R^\mathrm{SCPH\,+\,3ph\xspace}_\mathrm{HA\,+\,3ph\xspace}$ = 0.84), and c) CuBr ($R^\mathrm{SCPH\,+3,\,4ph}_\mathrm{SCPH\,+\,3ph\xspace}$ = 0.16).
  • Figure 5: a) Distribution of $R^\mathrm{OD}_\mathrm{SCPH\,+\,3,\,4ph\xspace}$. b) Dependence of $R^\mathrm{OD}_\mathrm{SCPH\,+\,3,\,4ph\xspace}$ on the logarithm of $\kappa^\mathrm{SCPH\,+\,3,\,4ph\xspace}_\mathrm{L}$. c) Crystal structure of KTlCl$_4$. d) Top 10 compounds with the highest $R^\mathrm{OD}_\mathrm{SCPH\,+\,3,\,4ph\xspace}$. e) Phonon transport properties of KTlCl$_4$. Left: phonon dispersion at 0 K (HA) and 300 K (SCPH); Middle: density of states; Right: cumulative $\kappa_\mathrm{L}$ and phonon linewidths versus phonon frequency. f) and g) Spectral decomposition of the off-diagonal and diagonal contribution to $\kappa_\mathrm{L}$ as a functions of phonon mode pair frequencies $\omega_s$ and $\omega_{s'}$. Frequency above 8 THz are truncated due to negligible contributions.
  • ...and 10 more figures