Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations

Moiré-Driven Interfacial Thermal Transport in Twisted Transition Metal Dichalcogenides

Cross-plane thermal conductivity in homogeneous transition metal dichalcogenides (TMDs) exhibits a pronounced dependence on interfacial twist angle, originating from atomic reconstruction within moiré superlattices. This reconstruction redistributes interlayer stacking modes, reducing high-efficiency thermal transport regions and softening the transverse acoustic phonon modes as the twist angle increases. We propose a general theoretical framework to capture this behavior, validated against nonequilibrium molecular dynamics simulations across both homo- and heterogeneous twisted TMD structures, as well as homogeneous twisted graphene and hexagonal boron nitride stacks. Our model reveals that the interfacial thermal conductance (ITC) scales with the twist angle (θ) as ln ( ITC ) ∝ e - θ . These findings advance the understanding of twist-engineered interfacial thermal transport, offering design principles for optimizing thermal management in devices based on van der Waals layered materials.

Anisotropic Heat Conduction of Silicon Nanocube through Strain Gradient Engineering

Precise control of directional heat flow is essential for advancing applications such as microchip cooling and building thermal regulation. However, existing methods often face challenges related to manufacturing complexity, structural instability, and limited reversibility. Here, we present strain-gradient-induced crystal symmetry breaking as an effective strategy to achieve anisotropic heat conduction. We model a uniaxially bent silicon nanocube and predict an anisotropy ratio of 1.20 at a strain gradient of 0.44%/nm (12% bending strain). This anisotropy arises from two distinct types of strain within the bent lattice: static strain along the axial direction, which significantly impedes heat conduction, and dynamic strain in the transverse directions, which poses a minimal effect on heat flow. The static strain broadens the phonon spectrum and induces phonon overdamping, thereby enhancing scattering and leading to marked reductions in the thermal conductivity. These findings highlight strain-gradient-induced phonon spectrum engineering as a reversible and robust method for directional thermal regulation.

Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials

Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity often makes it challenging to address potential finite-size effects. Here, we present a specialized graphics processing units (GPUs) implementation of PIMD methods, including ring-polymer molecular dynamics (RPMD) and thermostatted ring-polymer molecular dynamics (TRPMD), into the open-source Graphics Processing Units Molecular Dynamics (GPUMD) package, combined with highly accurate and efficient machine-learned neuroevolution potential (NEP) models. This approach achieves almost the accuracy of first-principles calculations with the computational efficiency of empirical potentials, enabling large-scale atomistic simulations that incorporate nuclear quantum effects, effectively overcoming finite-size limitations at a relatively affordable computational cost. We validate and demonstrate the efficacy of the combined NEP-PIMD approach by examining various thermal properties of diverse materials, including lithium hydride (LiH), three porous metal-organic frameworks (MOFs), liquid water, and elemental aluminum. For LiH, our NEP-PIMD simulations successfully capture the isotope effect, reproducing the experimentally observed dependence of the lattice parameter on the reduced mass. For MOFs, our results reveal that achieving good agreement with experimental data requires consideration of both nuclear quantum effects and dispersive interactions. For water, our PIMD simulations capture the significant impact of nuclear quantum effects on its microscopic structure. For aluminum, the TRPMD method effectively captures thermal expansion and phonon properties, aligning well with quantum mechanical predictions. This efficient GPU-accelerated NEP-PIMD implementation in the GPUMD package provides an alternative, accessible, accurate, and scalable tool for exploring complex material properties influenced by nuclear quantum effects, with potential applications across a broad range of materials.

Mathematically inspired structure design in nanoscale thermal transport

Mathematically inspired structure design has emerged as a powerful approach for tailoring material properties, especially in nanoscale thermal transport, with promising applications both within this field and beyond. By employing mathematical principles, based on number theory, such as periodicity and quasi-periodic organizations, researchers have developed advanced structures with unique thermal behaviours. Although periodic phononic crystals have been extensively explored, various structural design methods based on alternative mathematical sequences have gained attention in recent years. This review provides an in-depth overview of these mathematical frameworks, focusing on nanoscale thermal transport. We examine key mathematical sequences, their foundational principles, and analyze the influence of thermal behavior, highlighting recent advancements in this field. Looking ahead, further exploration of mathematical sequences offers significant potential for the development of next-generation materials with tailored, multi-functional properties suited to diverse technological applications.

Quantum-accurate machine learning potentials for metal-organic frameworks using temperature driven active learning

Understanding structural flexibility of metal-organic frameworks (MOFs) via molecular dynamics simulations is crucial to design better MOFs. Density functional theory (DFT) and quantum-chemistry methods provide highly accurate molecular dynamics, but the computational overheads limit their use in long time-dependent simulations. In contrast, classical force fields struggle with the description of coordination bonds. Here we develop a DFT-accurate machine-learning spectral neighbor analysis potentials for two representative MOFs. Their structural and vibrational properties are then studied and tightly compared with available experimental data. Most importantly, we demonstrate an active-learning algorithm, based on mapping the relevant internal coordinates, which drastically reduces the number of training data to be computed at the DFT level. Thus, the workflow presented here appears as an efficient strategy for the study of flexible MOFs with DFT accuracy, but at a fraction of the DFT computational cost.

Correcting force error-induced underestimation of lattice thermal conductivity in machine learning molecular dynamics

Machine learned potentials (MLPs) have been widely employed in molecular dynamics simulations to study thermal transport. However, the literature results indicate that MLPs generally underestimate the lattice thermal conductivity (LTC) of typical solids. Here, we quantitatively analyze this underestimation in the context of the neuroevolution potential (NEP), which is a representative MLP that balances efficiency and accuracy. Taking crystalline silicon, gallium arsenide, graphene, and lead telluride as examples, we reveal that the fitting errors in the machine-learned forces against the reference ones are responsible for the underestimated LTC as they constitute external perturbations to the interatomic forces. Since the force errors of a NEP model and the random forces in the Langevin thermostat both follow a Gaussian distribution, we propose an approach to correcting the LTC by intentionally introducing different levels of force noises via the Langevin thermostat and then extrapolating to the limit of zero force error. Excellent agreement with experiments is obtained by using this correction for all the prototypical materials over a wide range of temperatures. Based on spectral analyses, we find that the LTC underestimation mainly arises from increased phonon scatterings in the low-frequency region caused by the random force errors.

Correlating Young's Modulus with High Thermal Conductivity in Organic Conjugated Small Molecules

Attaining elevated thermal conductivity in organic materials stands as a coveted objective, particularly within electronic packaging, thermal interface materials, and organic matrix heat exchangers. These applications have reignited interest in researching thermally conductive organic materials. The understanding of thermal transport mechanisms in these organic materials is currently constrained. This study concentrates on N, N'-dioctyl-3,4,9,10-perylenedicarboximide (PTCDI-C8), an organic conjugated crystal. A correlation between elevated thermal conductivity and augmented Young's modulus is substantiated through meticulous experimentation. Achievement via employing the physical vapor transport method, capitalizing on the robust C═C covalent linkages running through the organic matrix chain, bolstered by π-π stacking and noncovalent affiliations that intertwine the chains. The coexistence of these dynamic interactions, alongside the perpendicular alignment of PTCDI-C8 molecules, is confirmed through structural analysis. PTCDI-C8 thin film exhibits an out-of-plane thermal conductivity of 3.1 ± 0.1 W m-1 K-1, as determined by time-domain thermoreflectance. This outpaces conventional organic materials by an order of magnitude. Nanoindentation tests and molecular dynamics simulations elucidate how molecular orientation and intermolecular forces within PTCDI-C8 molecules drive the film's high Young's modulus, contributing to its elevated thermal conductivity. This study's progress offers theoretical guidance for designing high thermal conductivity organic materials, expanding their applications and performance potential.

Machine learning potential for modelling H2 adsorption/diffusion in MOFs with open metal sites

Metal-organic frameworks (MOFs) incorporating open metal sites (OMS) have been identified as promising sorbents for many societally relevant-adsorption applications including CO2 capture, natural gas purification and H2 storage. This has been ascribed to strong specific interactions between OMS and the guest molecules that enable the MOF to achieve an effective capture even under low gas pressure conditions. In particular, the presence of OMS in MOFs was demonstrated to substantially boost the H2 binding energy for achieving high adsorbed hydrogen densities and large usable hydrogen capacities. So far, there is a critical bottleneck to computationally attain a full understanding of the thermodynamics and dynamics of H2 in this sub-class of MOFs since the generic classical force fields (FFs) are known to fail to accurately describe the interactions between OMS and any guest molecules, in particular H2. This clearly hampers the computational-assisted identification of MOFs containing OMS for a target adsorption-related application since the standard high-throughput screening approach based on these generic FFs is not applicable. Therefore, there is a need to derive novel FFs to achieve accurate and effective evaluation of MOFs for H2 adsorption. On this path, as a proof-of-concept, the soc-MOF-1d containing OMS, previously envisaged as a potential platform for H2 adsorption, was selected as a benchmark material and a machine learning potential (MLP) was derived for the Al-soc-MOF-1d from a dataset initially generated by ab initio molecular dynamics (AIMD) simulations. This MLP was further implemented in MD simulations to explore the H2 binding modes as well as the temperature dependence distribution of H2 in the MOF pores from 10 K to 80 K. MLP-Grand Canonical Monte Carlo (GCMC) simulations were then performed to predict the H2 sorption isotherm of Al-soc-MOF-1d at 77 K that was further confirmed using sorption data we collected on this sample. As a further step, MLP-based molecular dynamics (MD) simulations were conducted to anticipate the kinetics of H2 in this MOF. This work delivers the first MLP able to describe accurately the interactions between the challenging H2 guest molecule and MOFs containing OMS. This innovative strategy applied to one of the most complex molecules owing to its highly polarizable nature, paves the way towards a more systematic accurate and efficient in silico assessment of MOFs containing OMS for H2 adsorption and beyond to the low-pressure capture of diverse molecules.

Predicting Spin-Dependent Phonon Band Structures of HKUST-1 Using Density Functional Theory and Machine-Learned Interatomic Potentials

The present study focuses on the spin-dependent vibrational properties of HKUST-1, a metal-organic framework with potential applications in gas storage and separation. Employing density functional theory (DFT), we explore the consequences of spin couplings in the copper paddle wheels (as the secondary building units of HKUST-1) on the material's vibrational properties. By systematically screening the impact of the spin state on the phonon bands and densities of states in the various frequency regions, we identify asymmetric -COO- stretching vibrations as being most affected by different types of magnetic couplings. Notably, we also show that the DFT-derived insights can be quantitatively reproduced employing suitably parametrized, state-of-the-art machine-learned classical potentials with root-mean-square deviations from the DFT results between 3 cm-1 and 7 cm-1. This demonstrates the potential of machine-learned classical force fields for predicting the spin-dependent properties of complex materials, even when explicitly considering spins only for the generation of the reference data used in the force-field parametrization process.

Unravelling abnormal in-plane stretchability of two-dimensional metal-organic frameworks by machine learning potential molecular dynamics

Two-dimensional (2D) metal-organic frameworks (MOFs) hold immense potential for various applications due to their distinctive intrinsic properties compared to their 3D analogues. Herein, we designed a highly stable NiF2(pyrazine)2 2D MOF in silico with a two-dimensional periodic wine-rack architecture. Extensive first-principles calculations and molecular dynamics (MD) simulations based on a newly developed machine learning potential (MLP) revealed that this 2D MOF exhibits huge in-plane Poisson's ratio anisotropy. This results in anomalous negative in-plane stretchability, as evidenced by an uncommon decrease in its in-plane area upon the application of uniaxial tensile strain, which makes this 2D MOF particularly attractive for flexible wearable electronics and ultra-thin sensor applications. We further demonstrated the unique capability of MLP to accurately predict the finite-temperature properties of MOFs on a large scale, exemplified by MLP-MD simulations with a dimension of 28.2 × 28.2 nm2, relevant to the length scale experimentally attainable for the fabrication of MOF films.

Combining the D3 dispersion correction with the neuroevolution machine-learned potential

Machine-learned potentials (MLPs) have become a popular approach of modeling interatomic interactions in atomistic simulations, but to keep the computational cost under control, a relatively short cutoff must be imposed, which put serious restrictions on the capability of the MLPs for modeling relatively long-ranged dispersion interactions. In this paper, we propose to combine the neuroevolution potential (NEP) with the popular D3 correction to achieve a unified NEP-D3 model that can simultaneously model relatively short-ranged bonded interactions and relatively long-ranged dispersion interactions. We show that improved descriptions of the binding and sliding energies in bilayer graphene can be obtained by the NEP-D3 approach compared to the pure NEP approach. We implement the D3 part into thegpumdpackage such that it can be used out of the box for many exchange-correlation functionals. As a realistic application, we show that dispersion interactions result in approximately a 10% reduction in thermal conductivity for three typical metal-organic frameworks.