Atomistic modeling of the mechanical properties: the rise of machine learning interatomic potentials

Machine Learning Interatomic Potential for Modeling the Mechanical and Thermal Properties of Naphthyl-Based Nanotubes

Two-dimensional (2D) nanomaterials are at the forefront of potential technological advancements. Carbon-based materials have been extensively studied since synthesizing graphene, which revealed properties of great interest for novel applications across diverse scientific and technological domains. New carbon allotropes continue to be explored theoretically, with several successful synthesis processes for carbon-based materials recently achieved. In this context, this study investigates the mechanical and thermal properties of DHQ-based monolayers and nanotubes, a carbon allotrope characterized by 4-, 6-, and 10-membered carbon rings, with a potential synthesis route using naphthalene as a molecular precursor. A machine-learned interatomic potential (MLIP) was developed to explore this nanomaterial's mechanical and thermal behavior at larger scales than those accessible through the first-principles calculations. The MLIP was trained on data derived from the DFT/PBE (density functional theory/Perdew-Burke-Ernzerhof) level using ab initio molecular dynamics (AIMD). Classical molecular dynamics (CMD) simulations, employing the trained MLIP, revealed that Young's modulus of DHQ-based nanotubes ranges from 127 to 243 N/m, depending on chirality and diameter, with fracture occurring at strains between 13.6 and 17.4% of the initial length. Regarding thermal response, a critical temperature of 2200 K was identified, marking the onset of a transition to an amorphous phase at higher temperatures.

Data Generation for Machine Learning Interatomic Potentials and Beyond

The field of data-driven chemistry is undergoing an evolution, driven by innovations in machine learning models for predicting molecular properties and behavior. Recent strides in ML-based interatomic potentials have paved the way for accurate modeling of diverse chemical and structural properties at the atomic level. The key determinant defining MLIP reliability remains the quality of the training data. A paramount challenge lies in constructing training sets that capture specific domains in the vast chemical and structural space. This Review navigates the intricate landscape of essential components and integrity of training data that ensure the extensibility and transferability of the resulting models. We delve into the details of active learning, discussing its various facets and implementations. We outline different types of uncertainty quantification applied to atomistic data acquisition and the correlations between estimated uncertainty and true error. The role of atomistic data samplers in generating diverse and informative structures is highlighted. Furthermore, we discuss data acquisition via modified and surrogate potential energy surfaces as an innovative approach to diversify training data. The Review also provides a list of publicly available data sets that cover essential domains of chemical space.

Thermal transport in C6N7monolayer: a machine learning based molecular dynamics study

The successful synthesis of a novel C6N7carbon nitride monolayer offers expansive prospects for applications in the fields of semiconductors, sensors, and gas separation technologies, in which the thermal transport properties of C6N7are crucial for optimizing the functionality and reliability of these applications. In this work, based on our developed machine learning potential (MLP), molecular dynamics (MD) simulations including homogeneous non-equilibrium, non-equilibrium, and their respective spectral decomposition methods are performed to investigate the effects of phonon transport, temperature, and length on the thermal conductivity of C6N7monolayer. Our results reveal that low-frequency and in-plane phonon modes dominate the thermal conductivity. Notably, thermal conductivity decreases with an increase in temperature due to temperature-induced increase in phonon-phonon scattering of in-plane phonon modes, while it increases with an extension in sample length. Our findings based on MD simulations with MLP contribute new insights into the lattice thermal conductivity of holey carbon nitride compounds, which is helpful for the development of next-generation electronic and photonic devices.

A Molecular View of Methane Activation on Ni(111) through Enhanced Sampling and Machine Learning

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a data set constructed via ab initio molecular dynamics simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that upon incorporation of collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting density functional theory-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression toward the transition state involves a CH4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C-H bond. This leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

TH-graphyne: a new porous bidimensional carbon allotrope

Graphyne and two-dimensional porous carbon-based materials have garnered significant attention due to their interesting structural characteristics and essential properties for new technological applications. Within this scope, this work investigates the structural, thermal, electronic, optical, and mechanical properties of a novel two-dimensional allotrope that combines triangular (T) and hexagonal (H) rings, connected by acetylenic linkages (graphyne-like), thus named TH-graphyne (TH-GY). This study comprehensively characterizes the proposed system's behavior using density functional theory, ab initio molecular dynamics, and classical reactive molecular dynamics simulations. Our results confirm the structural stability of TH-GY. AIMD simulations demonstrate the material's thermal stability at elevated temperatures, while phonon dispersions indicate its dynamical stability. Electronic band structure calculations show that the system is metallic. The analysis of optical properties reveals intense activity in the visible and UV regions, with pronounced anisotropy. A machine learning interatomic potentials model was developed for TH-GY and used to determine the mechanical behavior of the system, which exhibits Young's modulus ranging from 263 to 356 GPa, highlighting its flexibility. Classical reactive MD simulations elucidate the fracture behavior of TH-GY, revealing distinct fracture patterns and mechanical anisotropy.

Designing Accurate Moment Tensor Potentials for Phonon-Related Properties of Crystalline Polymers

The phonon-related properties of crystalline polymers are highly relevant for various applications. Their simulation is, however, particularly challenging, as the systems that need to be modeled are often too extended to be treated by ab initio methods, while classical force fields are too inaccurate. Machine-learned potentials parametrized against material-specific ab initio data hold the promise of being extremely accurate and also highly efficient. Still, for their successful application, protocols for their parametrization need to be established to ensure an optimal performance, and the resulting potentials need to be thoroughly benchmarked. These tasks are tackled in the current manuscript, where we devise a protocol for parametrizing moment tensor potentials (MTPs) to describe the structural properties, phonon band structures, elastic constants, and forces in molecular dynamics simulations for three prototypical crystalline polymers: polyethylene (PE), polythiophene (PT), and poly-3-hexylthiophene (P3HT). For PE, the thermal conductivity and thermal expansion are also simulated and compared to experiments. A central element of the approach is to choose training data in view of the considered use case of the MTPs. This not only yields a massive speedup for complex calculations while essentially maintaining DFT accuracy, but also enables the reliable simulation of properties that, so far, have been entirely out of reach.

Biomimetic fusion: Platyper's dual vision for predicting protein-surface interactions

Predicting protein binding with the material surface still remains a challenge. Here, a novel approach, platypus dual perception neural network (Platyper), was developed to describe the interactions in protein-surface systems involving bioceramics with BMPs. The resulting model integrates a graph convolutional neural network (GCN) based on interatomic potentials with a convolutional neural network (CNN) model based on images of molecular structures. This dual-vision approach, inspired by the platypus's adaptive sensory system, addresses the challenge of accurately predicting the complex binding and unbinding dynamics in steered molecular dynamics (SMD) simulations. The model's effectiveness is demonstrated through its application in predicting surface interactions in protein-ligand systems. Notably, Platyper improves computational efficiency compared to classical SMD-based methods and overcomes the limitations of GNN-based methods for large-scale atomic simulations. The incorporation of heat maps enhances model's interpretability, providing valuable insights into its predictive capabilities. Overall, Platyper represents a promising advancement in the accurate and efficient prediction of protein-surface interactions in the context of bioceramics and growth factors.

Exploring fracture of H-BN and graphene by neural network force fields

Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture often lead to catastrophic failure of materials and structures. Understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Atomistic simulations offer 'first-principles' tools to resolve the progressive microstructural changes at crack fronts and are widely used to explore the underlying processes of mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g. kinking, branching). Empirical force fields developed based on atomic-level structural descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, especially for the nonlinear, anisotropic stress-strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of bond-breaking and (re)formation events during fracture, which, unfortunately, have not been taken into account in either the state-of-the-art empirical or machine-learning force fields. Based on data generated by density functional theory calculations, we report a neural network-based force field for fracture (NN-F3) constructed by using the end-to-end symmetry preserving framework of deep potential-smooth edition (DeepPot-SE). The workflow combines pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F3is demonstrated by studying the rupture of hexagonal boron nitride (h-BN) and twisted bilayer graphene as model problems. The simulation results elucidate the roughening physics of fracture defined by the lattice asymmetry in h-BN, explaining recent experimental findings, and predict the interaction between cross-layer cracks in twisted graphene bilayers, which leads to a toughening effect.

Remarkably high tensile strength and lattice thermal conductivity in wide band gap oxidized holey graphene C2O nanosheet

Recently, the synthesis of oxidized holey graphene with the chemical formula C2O has been reported (J. Am. Chem. Soc. 2024, 146, 4532). We herein employed a combination of density functional theory (DFT) and machine learning interatomic potential (MLIP) calculations to investigate the electronic, optical, mechanical and thermal properties of the C2O monolayer, and compared our findings with those of its C2N counterpart. Our analysis shows that while the C2N monolayer exhibits delocalized π-conjugation and shows a 2.47 eV direct-gap semiconducting behavior, the C2O counterpart exhibits an indirect gap of 3.47 eV. We found that while the C2N monolayer exhibits strong absorption in the visible spectrum, the initial absorption peaks in the C2O lattice occur at around 5 eV, falling within the UV spectrum. Notably, we found that the C2O nanosheet presents significantly higher tensile strength compared to its C2N counterpart. MLIP-based calculations show that at room temperature, the C2O nanosheet can exhibit remarkably high tensile strength and lattice thermal conductivity of 42 GPa and 129 W/mK, respectively. The combined insights from DFT and MLIP-based results provide a comprehensive understanding of the electronic and optical properties of C2O nanosheets, suggesting them as mechanically robust and highly thermally conductive wide bandgap semiconductors.

Goldene: An Anisotropic Metallic Monolayer with Remarkable Stability and Rigidity and Low Lattice Thermal Conductivity

In a recent breakthrough in the field of two-dimensional (2D) nanomaterials, the first synthesis of a single-atom-thick gold lattice of goldene has been reported through an innovative wet chemical removal of Ti3C2 from the layered Ti3AuC2. Inspired by this advancement, in this communication and for the first time, a comprehensive first-principles investigation using a combination of density functional theory (DFT) and machine learning interatomic potential (MLIP) calculations has been conducted to delve into the stability, electronic, mechanical and thermal properties of the single-layer and free-standing goldene. The presented results confirm thermal stability at 700 K as well as remarkable dynamical stability of the stress-free and strained goldene monolayer. At the ground state, the elastic modulus and tensile strength of the goldene monolayer are predicted to be over 226 and 12 GPa, respectively. Through validated MLIP-based molecular dynamics calculations, it is found that at room temperature, the goldene nanosheet can exhibit anisotropic tensile strength over 9 GPa and a low lattice thermal conductivity around 10 ± 2 W/(m.K), respectively. We finally show that the native metallic nature of the goldene monolayer stays intact under large tensile strains. The combined insights from DFT and MLIP-based results provide a comprehensive understanding of the stability, mechanical, thermal and electronic properties of goldene nanosheets.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

Global machine learning potentials for molecular crystals

Molecular crystals are difficult to model with accurate first-principles methods due to large unit cells. On the other hand, accurate modeling is required as polymorphs often differ by only 1 kJ/mol. Machine learning interatomic potentials promise to provide accuracy of the baseline first-principles methods with a cost lower by orders of magnitude. Using the existing databases of the density functional theory calculations for molecular crystals and molecules, we train global machine learning interatomic potentials, usable for any molecular crystal. We test the performance of the potentials on experimental benchmarks and show that they perform better than classical force fields and, in some cases, are comparable to the density functional theory calculations.

Transferable Machine Learning Interatomic Potential for Bond Dissociation Energy Prediction of Drug-like Molecules

We present a transferable MACE interatomic potential that is applicable to open- and closed-shell drug-like molecules containing hydrogen, carbon, and oxygen atoms. Including an accurate description of radical species extends the scope of possible applications to bond dissociation energy (BDE) prediction, for example, in the context of cytochrome P450 (CYP) metabolism. The transferability of the MACE potential was validated on the COMP6 data set, containing only closed-shell molecules, where it reaches better accuracy than the readily available general ANI-2x potential. MACE achieves similar accuracy on two CYP metabolism-specific data sets, which include open- and closed-shell structures. This model enables us to calculate the aliphatic C-H BDE, which allows us to compare reaction energies of hydrogen abstraction, which is the rate-limiting step of the aliphatic hydroxylation reaction catalyzed by CYPs. On the "CYP 3A4" data set, MACE achieves a BDE RMSE of 1.37 kcal/mol and better prediction of BDE ranks than alternatives: the semiempirical AM1 and GFN2-xTB methods and the ALFABET model that directly predicts bond dissociation enthalpies. Finally, we highlight the smoothness of the MACE potential over paths of sp3C-H bond elongation and show that a minimal extension is enough for the MACE model to start finding reasonable minimum energy paths of methoxy radical-mediated hydrogen abstraction. Altogether, this work lays the ground for further extensions of scope in terms of chemical elements, (CYP-mediated) reaction classes and modeling the full reaction paths, not only BDEs.

The thermoelastic properties of monolayer covalent organic frameworks studied by machine-learning molecular dynamics

Two-dimensional (2D) covalent organic frameworks (COFs) are emerging as promising 2D polymeric materials with broad applications owing to their unique properties, among which the mechanical properties are quite important for various applications. However, the mechanical properties of 2D COFs have not been systematically studied yet. Herein, a machine-learned neuroevolution potential (NEP) was developed to study the elastic properties of two representative monolayer 2D COFs, namely COF-1 and COF-5. The trained NEP enables one to study the elastic properties of 2D COFs in realistic situations (e.g., finite size and temperature) and possesses greatly improved computational efficiency when compared with density functional theory calculations. With the aid of the obtained NEP, molecular dynamics (MD) simulations together with a strain-fluctuation method were employed to evaluate the elastic constants of the considered 2D COFs at different temperatures. The elastic constants of COF-1 and COF-5 monolayers were found to decrease with an increase in the temperature, though they were almost isotropic irrespective of the temperature. The thermally induced softening of 2D COFs below a critical temperature was observed, which is mainly attributed to their inherent ripple configurations at finite temperatures, while above the critical temperature, the damping effect of anharmonic vibrations became the dominant factor. Based on the proposed mechanisms, analytical models were developed for capturing the temperature dependence of elastic constants, which were found to agree with the MD simulation results well. This work provides an in-depth insight into the thermoelastic properties of monolayer COFs, which can guide the development of 2D COF materials with tailored mechanical behaviors for enhancing their performance in various applications.

Investigation of phase transition, mechanical behavior and lattice thermal conductivity of halogen perovskites using machine learning interatomic potentials

Using a machine learning (ML) approach to fit DFT data, interatomic potentials have been successfully extracted. In this study, the phase transition, mechanical behavior and lattice thermal conductivity are investigated for halogen perovskites using NEP-based MD simulations in a large supercell including 16 000 atoms, which breaks through the size and temperature effects in DFT. A clear phase transition from orthorhombic (γ) → tetragonal (β) → cubic (α) is observed during the heating process. During the cooling process, CsPbCl3 and CsPbBr3 exhibit perfect reversible behavior, while CsPbI3 only undergoes a phase transition from α to β. Then, the key mechanical parameters, including Poisson's ratio, tensile strength, critical strain and bulk modulus, are predicted. The thermal conductivity is also investigated using the NEP-based MD simulations. At room temperature, they exhibit extremely low thermal conductivity. The predicted results are compared with the experimental results, and the rationality of ML potentials has been confirmed.

Chemical evolution in nitrogen shocked beyond the molecular stability limit

Evolution of nitrogen under shock compression up to 100 GPa is revisited via molecular dynamics simulations using a machine-learned interatomic potential. The model is shown to be capable of recovering the structure, dynamics, speciation, and kinetics in hot compressed liquid nitrogen predicted by first-principles molecular dynamics, as well as the measured principal shock Hugoniot and double shock experimental data, albeit without shock cooling. Our results indicate that a purely molecular dissociation description of nitrogen chemistry under shock compression provides an incomplete picture and that short oligomers form in non-negligible quantities. This suggests that classical models representing the shock dissociation of nitrogen as a transition to an atomic fluid need to be revised to include reversible polymerization effects.