Using machine-learned force fields for achieving a quantitatively accurate understanding of thermal transport in complex materials.
Egbert Zojer
Institute of Solid State Physics, TU Graz
https://tugraz.webex.com/meet/egbert.zojer
11:15 - 12:15 Wednesday 01 October 2025 Heat conduction is a crucial process for all applications in which excess heat needs to be either dissipated or supplied. As the focus in the current presentation is on electrically insulating materials, the transport of thermal energy occurs via lattice vibrations, which can either be described in real space via atomic motions or in reciprocal space via phonons. To develop reliable structure-to-property relations, an atomistic understanding of the underlying processes is crucial. This understanding can be best achieved via atomistic computer simulations, provided that they are capable of providing a quantitatively accurate description of the relevant processes.
This raises two fundamental questions: which computational approach should be chosen to describe thermal transport, and how could one reliably describe the involved inter-atomic interactions. For the latter, density functional theory (DFT) would be the natural choice, but DFT is not efficient enough to calculate forces between (tens of) thousands of atoms several million times. At the other end of the computational spectrum would be classical, transferable force fields, but they are way to inaccurate to providing a reliable description. This dilemma can be resolved by using force fields system-specifically trained on DFT data, where we focus on moment-tensor potentials trained via a specially adapted active learning approach.1,2 They yield essentially DFT accuracy at sharply reduced computational costs. This allows a quantitatively reliable description of heat transport processes for MOFs1 as well as for molecular crystals,3 the two classes of materials in the focus of the current presentation. Quantitative agreement with accurate experiments (often on single crystals) is achieved both, when extracting thermal conductivities from the particle trajectories of non-equilibrium molecular dynamics simulations1,4 and when basing the analysis on harmonic and anharmonic phonon properties.3,4 When properly accounting for the shortcomings of both approaches, also a simultaneous analysis of heat transport in real and reciprocal space becomes possible,5 with the quantitative accuracy of the results improved when relying on use-case specific force-field parametrizations.6
The distinct advantage of considering both real- and reciprocal-space approaches is that they provide complementary insight into the physical aspects of heat transport: from an analysis of the real-space effective temperature distribution in MOFs subject to a thermal gradient, one can, for example, identify the interfaces between linkers and nodes as the bottlenecks to thermal transport.4,7 A similar role is played by the inter-molecular interfaces in molecular crystals. In contrast, analyzing the phonon dynamics shows that in low thermal-conductivity materials it is not sufficient to describe heat transport merely as a diffusive transport of particle-like phonons. Rather, one also needs to consider coherences contributions arising from phonon tunneling between the lifetime-broadened phonon bands.3 This has the consequence that not only low-frequency acoustic phonons contribute to heat transport, but that also more complex, higher-lying optical phonons become relevant. Based on phonon properties, one can also understand, why in molecular crystals like naphthalene the thermal conductivity increases by about an order magnitude at elevated pressures of ~2-3 GPa.8 In this context it is worth noting that even at such extreme conditions, MTPs still allow a quantitatively accurate description of the situation provided that they have been properly parametrized.8
[1] Sandro Wieser and Egbert Zojer, npj Comput. Mater. 2024, 10, 18; [2] Nina Strasser, Sandro Wieser, and Egbert Zojer, Int. J. Mol. Sci. 2024, 25, 3023; [3] Lukas Legenstein, Lukas Reicht, Sandro Wieser, Michele Simoncelli, Egbert Zojer, npj Comput. Mater. 2025, 11, 29.; [4] Sandro Wieser, Tomas Kamencek, Johannes P. Dürholt, Rochus Schmid, Natalia Bedoya-Martínez, Egbert Zojer, Adv. Theory Simul. 2021, 4, 2000211; [5] Lukas Reicht, Lukas Legenstein, Sandro Wieser, Egbert Zojer, arXiv 2503.14289; [6] Lukas Reicht, Lukas Legenstein, Sandro Wieser and Egbert Zojer, Molecules, 2024, 29, 3724; [7] Sandro Wieser, Tomas Kamencek, Rochus Schmid, Natalia Bedoya-Martínez, and Egbert Zojer, Nanomaterials 2022, 12, 2142; [8] Lukas Legenstein and Egbert Zojer, in preparation.
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Institute of Solid State Physics
