This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.

We describe a new method to calculate the vibrational ground state properties of weakly bound molecular systems and apply it to (HF)2 and HF–HCl. A Bayesian Inference neural network is used to fit an analytic function to a set of ab initio data points, which may then be employed by the quantum diffusion Monte Carlo method to produce ground state vibrational wave functions and properties. The method is general and relatively simple to implement and will be attractive for calculations on systems for which no analytic potential energy surface exists.

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functions in EAM. The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similar to artificial neural network potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting. The quality of this new potential form is measured through a robust cross-validation analysis.

Here we introduce the LASP code, which is designed for large‐scale atomistic simulation of complex materials with neural network (NN) potential. The software architecture and functionalities of LASP will be overviewed. LASP features with the global neural network (G‐NN) potential that is generated by learning the first principles dataset of global PES from stochastic surface walking (SSW) global optimization. The combination of the SSW method with global NN potential facilitates greatly the PES exploration for a wide range of complex materials. Not limited to SSW‐NN global optimization, the software implements standard interfaces to dock with other energy/force evaluation packages and can also perform common tasks for computing PES properties, such as single‐ended and double‐ended transition state search, the molecular dynamics simulation with and without restraints. A few examples are given to illustrate the efficiency and capabilities of LASP code. Our ongoing efforts for code developing and G‐NN potential library building are also presented.

LASP (large-scale atomistic simulation with neural network potential) software developed by our group since 2018 is a powerful platform (www.lasphub.com) for performing atomic simulation of complex materials. The software integrates the neural network (NN) potential technique with the global potential energy surface exploration method, and thus can be utilized widely for structure prediction and reaction mechanism exploration. Here we introduce our recent update on the LASP program version 3.0, focusing on the new functionalities including the advanced neural network training based on the multi-network framework, the newly-introduced S7 and S8 power type structure descriptor (PTSD). These new functionalities are designed to further improve the accuracy of potentials and accelerate the neural network training for multiple-element systems. Taking Cu-C-H-O neural network potential and a heterogeneous catalytic model as the example, we show that these new functionalities can accelerate the training of multi-element neural network potential by using the existing single-network potential as the input. The obtained double-network potential CuCHO is robust in simulation and the introduction of S7 and S8 PTSDs can reduce the root-mean-square errors of energy by a factor of two.

Machine learning potentials have emerged as a powerful tool to extend the time and length scales of first-principles quality simulations. Still, most machine learning potentials cannot distinguish different electronic spin arrangements and thus are not applicable to materials in different magnetic states. Here we propose spin-dependent atom-centered symmetry functions as a type of descriptor taking the atomic spin degrees of freedom into account. When used as an input for a high-dimensional neural network potential (HDNNP), accurate potential energy surfaces of multicomponent systems can be constructed, describing multiple collinear magnetic states. We demonstrate the performance of these magnetic HDNNPs for the case of manganese oxide, MnO. The method predicts the magnetically distorted rhombohedral structure in excellent agreement with density functional theory and experiment. Its efficiency allows to determine the Néel temperature considering structural fluctuations, entropic effects, and defects. The method is general and is expected to be useful also for other types of systems such as oligonuclear transition metal complexes.

Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small molecular systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems containing thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodology of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent atomic energy contributions; second, the description of the atomic environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the reference electronic structure data sets by active learning. In third-generation HDNNPs, in addition, long-range interactions are included employing environment-dependent partial charges expressed by atomic neural networks. In fourth-generation HDNNPs, which are just emerging, in addition, nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations.

Solidification nucleation is an everlasting research topic in the fields of materials science and condensed matter physics. Molecular dynamics (MD) and enhanced sampling methods provide a powerful means to observe the microscopic mechanisms of solidification processes in situ at the atomic level and to analyze the thermodynamic and kinetic properties of phase transitions. Recent advancements in MD simulations, particularly those incorporating machine learning (ML) techniques, have remarkably advanced our understanding of nucleation across different systems. This paper first reviews the basic theory of solidification nucleation and introduces common methods used in solidification nucleation simulation studies. It then delves into the application of ML techniques in three key areas: force fields, enhanced sampling, and order parameters. The paper further highlights several representative systems to demonstrate the practical applications of these methods. Finally, a summary and outlook on the future of ML-assisted MD simulations for studying material solidification were provided.

凝固形核是材料科学、凝聚态物理等领域长盛不衰的研究热点。分子动力学以及增强采样方法为从原子尺度原位观察凝固过程微观机理、解析相变热力学与动力学性质提供了有力手段。近年来，该领域的研究者们开发了一些融合机器学习技术的先进分子动力学模拟新方法，在多种体系的形核研究中取得了一定成果。本文首先回顾了凝固形核的基本理论，并从势函数、增强采样、形核序参量3个方面介绍凝固形核模拟研究中的常用方法以及机器学习技术在其中的应用。然后，选取了几个具有代表性的体系并介绍相关方法的实际应用。最后，对机器学习分子动力学辅助材料凝固形核模拟研究领域进行了总结与展望。

Ferroelectric materials, which are characterized by tunable spontaneous polarization, show remarkable application potential for nonvolatile information storage; however they present various challenges. The performance of these materials is strongly influenced by their dynamic polarization behavior under multiple external fields. Due to the limited precision of experimental observations, precise atomic-level material simulations are crucial. Although molecular dynamics (MD) offers an ideal method for investigating material dynamics over a wide spatiotemporal range, its application to new materials is often limited by challenges such as low accuracy, complex development, and limited portability of conventional classical force fields. Advances in machine learning have provided new possibilities for developing force fields. Among different machine learning potentials, deep potential (DP) based on deep neural networks stands out. DP offers accuracy comparable to that of density functional theory while providing computational efficiency similar to that of conventional classical force fields. This review primarily focused on the development and application of DP in ferroelectric materials, specifically examining the phase transition mechanisms and polarization reversal processes at the atomic scale. Considerable efforts have been made to develop and evaluate DP for crucial ferroelectric materials such as hafnium dioxide (HfO2) and classic perovskite ferroelectric materials. Furthermore, this review explores the high oxygen-ion migration kinetics in HfO2 using DP and investigates the flexoelectricity induced by polar domain boundaries and the bulk photovoltaic effects in strontium titanate. By highlighting the use of DP molecular dynamics approaches in ferroelectric materials, this review emphasizes the role of machine learning approaches in optimizing and accelerating material simulations to facilitate further breakthroughs and discoveries.

Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mechanical interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for molecules and materials, where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study on the quantum-mechanical properties of C20-fullerene that would have been infeasible with regular ab initio molecular dynamics.

In recent years, machine learning (ML) methods have become increasingly popular in computational chemistry. After being trained on appropriate ab initio reference data, these methods allow for accurately predicting the properties of chemical systems, circumventing the need for explicitly solving the electronic Schrödinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chemical applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chemical systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chemical reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qualitatively correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala): The optimized geometry of helical Ala predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased molecular dynamics (MD) simulations of Ala on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol according to the reference ab initio calculations.

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.© 2022. The Author(s).

A simultaneously accurate and computationally efficient parametrization of the potential energy surface of molecules and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interatomic potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Molecular simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.© 2023. The Author(s).

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on similar to 60 000 crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps, and elastic moduli of crystals, achieving better than density functional theory accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy, and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure, and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli).

Interatomic potentials (IAPs), which describe the potential energy surface of atoms, are a fundamental input for atomistic simulations. However, existing IAPs are either fitted to narrow chemistries or too inaccurate for general applications. Here we report a universal IAP for materials based on graph neural networks with three-body interactions (M3GNet). The M3GNet IAP was trained on the massive database of structural relaxations performed by the Materials Project over the past ten years and has broad applications in structural relaxation, dynamic simulations and property prediction of materials across diverse chemical spaces. About 1.8 million materials from a screening of 31 million hypothetical crystal structures were identified to be potentially stable against existing Materials Project crystals based on M3GNet energies. Of the top 2,000 materials with the lowest energies above the convex hull, 1,578 were verified to be stable using density functional theory calculations. These results demonstrate a machine learning-accelerated pathway to the discovery of synthesizable materials with exceptional properties.© 2022. The Author(s), under exclusive licence to Springer Nature America, Inc.

This study introduces a novel artificial intelligence (AI) force field, namely a graph-based pre-trained transformer force field (GPTFF), which can simulate arbitrary inorganic systems with good precision and generalizability. Harnessing a large trove of the data and the attention mechanism of transformer algorithms, the model can accurately predict energy, atomic force, and stress with mean absolute error (MAE) values of 32 meV/atom, 71 meV/Å, and 0.365 GPa, respectively. The dataset used to train the model includes 37.8 million single-point energies, 11.7 billion force pairs, and 340.2 million stresses. We also demonstrated that the GPTFF can be universally used to simulate various physical systems, such as crystal structure optimization, phase transition simulations, and mass transport. The model is publicly released with this paper, enabling anyone to use it immediately without needing to train it.Copyright © 2024 Science China Press. Published by Elsevier B.V. All rights reserved.

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are computationally expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate. Empirically, we observe that the optimality criterion sharply decreases the number of training examples the learner needs in order to achieve good performance.

The on-the-fly generation of machine-learning force fields by active-learning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to self-learn an interatomic potential and construct machine-learned models on the fly during simulations. State-of-the-art query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are first-principles calculations carried out. Otherwise, the yet available machine-learned model is used to update the atomic positions. In this manner, most of the first-principles calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost first-principles accuracy. In this Perspective, after describing essential components of the active-learning algorithms, we demonstrate the power of the schemes by presenting recent applications.

The choice of simulation methods in computational materials science is driven by a fundamental trade-off: bridging large time- and length-scales with highly accurate simulations at an affordable computational cost. Venturing the investigation of complex phenomena on large scales requires fast yet accurate computational methods. We review the emerging field of machine-learned potentials, which promises to reach the accuracy of quantum mechanical computations at a substantially reduced computational cost. This Review will summarize the basic principles of the underlying machine learning methods, the data acquisition process and active learning procedures. We highlight multiple recent applications of machine-learned potentials in various fields, ranging from organic chemistry and biomolecules to inorganic crystal structure predictions and surface science. We furthermore discuss the developments required to promote a broader use of ML potentials, and the possibility of using them to help solve open questions in materials science and facilitate fully computational materials design.

We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the FES, allowing the efficient exploration and accurate determination of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et al 2003 Science \n 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100–1700 K is unique.

The knowledge of diffusion mechanisms in materials is crucial for predicting their high-temperature performance and stability, yet accurately capturing the underlying physics like thermal effects remains challenging. In particular, the origin of the experimentally observed non-Arrhenius diffusion behavior has remained elusive, largely due to the lack of effective computational tools. Here we propose an efficient ab initio framework to compute the Gibbs energy of the transition state in vacancy-mediated diffusion including the relevant thermal excitations at the density-functional-theory level. With the aid of a bespoke machine-learning interatomic potential, the temperature-dependent vacancy formation and migration Gibbs energies of the prototype system body-centered cubic (BCC) tungsten are shown to be strongly affected by anharmonicity. This finding explains the physical origin of the experimentally observed non-Arrhenius behavior of tungsten self-diffusion. A remarkable agreement between the calculated and experimental temperature-dependent self-diffusivity and, in particular, its curvature is revealed. The proposed computational framework is robust and broadly applicable, as evidenced by first tests for a hexagonal close-packed (HCP) multicomponent high-entropy alloy. The successful applications underscore the attainability of an accurate ab initio diffusion database.

The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines. The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design. However, as of now a method to compute efficiently, yet with high accuracy the thermodynamic properties of such alloys has been missing. One of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent alloys. In this work, a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.

We present the magnetic Moment Tensor Potentials (mMTPs), a class of machine-learning interatomic potentials, accurately reproducing both vibrational and magnetic degrees of freedom as provided, e.g., from first-principles calculations. The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space. The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron, with applications to phonon calculations for different magnetic states, and molecular-dynamics simulations with fluctuating magnetic moments.

We propose a machine-learning interatomic potential for multi-component magnetic materials. In this potential we consider magnetic moments as degrees of freedom (features) along with atomic positions, atomic types, and lattice vectors. We create a training set with constrained DFT (cDFT) that allows us to calculate energies of configurations with non-equilibrium (excited) magnetic moments and, thus, it is possible to construct the training set in a wide configuration space with great variety of non-equilibrium atomic positions, magnetic moments, and lattice vectors. Such a training set makes possible to fit reliable potentials that will allow us to predict properties of configurations in the excited states (including the ones with non-equilibrium magnetic moments). We verify the trained potentials on the system of bcc Fe-Al with different concentrations of Al and Fe and different ways Al and Fe atoms occupy the supercell sites. Here, we show that the formation energies, the equilibrium lattice parameters, and the total magnetic moments of the unit cell for different Fe-Al structures calculated with machine-learning potentials are in good correspondence with the ones obtained with DFT. We also demonstrate that the theoretical calculations conducted in this study qualitatively reproduce the experimentally-observed anomalous volume-composition dependence in the Fe-Al system.© 2023. The Author(s).

We present the electronic moment tensor potentials (eMTPs), a class of machine-learning interatomic models and a generalization of the classical MTPs, reproducing both the electronic and vibrational degrees of freedom, up to the accuracy of ab initio calculations. Following the original polynomial interpolation idea of the MTPs, the eMTPs are defined as polynomials of vibrational and electronic degrees of freedom, corrected to have a finite interatomic cutoff. Practically, an eMTP is constructed from the classical MTPs fitted to a training set, whose energies and forces are calculated with electronic temperatures corresponding to the Chebyshev nodes on a given temperature interval. The eMTP energy is hence a Chebyshev interpolation of the classical MTPs. Using the eMTP, one can obtain the temperature-dependent vibrational free energy including anharmonicity coming from phonon interactions, the electronic free energy coming from electron interactions, and the coupling of atomic vibrations and electronic excitations. Each of the contributions can be accessed individually using the proposed formalism. The performance of eMTPs is demonstrated for two refractory systems which have a significant electronic, vibrational and coupling contribution up to the melting point—unary Nb, and a disordered TaVCrW high-entropy alloy. Highly accurate thermodynamic and kinetic quantities can now be obtained just by using eMTPs, without any further ab initio calculations. The proposed construction to include the electronic degree of freedom can also be applied to other machine-learning models.

\n Chemically complex multicomponent alloys possess exceptional properties derived from an inexhaustible compositional space. The complexity however makes interatomic potential development challenging. We explore two complementary machine-learned potentials—the moment tensor potential (MTP) and the Gaussian moment neural network (GM-NN)—in simultaneously describing configurational\n and\n vibrational degrees of freedom in the Ta-V-Cr-W alloy family. Both models are equally accurate with excellent performance evaluated against density-functional-theory. They achieve root-mean-square-errors (RMSEs) in energies of less than a few meV/atom across 0 K ordered and high-temperature disordered configurations included in the training. Even for compositions not in training, relative energy RMSEs at high temperatures are within a few meV/atom. High-temperature molecular dynamics forces have similarly small RMSEs of about 0.15 eV/Å for the disordered quaternary included in, and ternaries not part of training. MTPs achieve faster convergence with training size; GM-NNs are faster in execution. Active learning is partially beneficial and should be complemented with conventional human-based training set generation.\n

Refractory high-entropy alloys (RHEAs) are designed for high elevated-temperature strength, with both edge and screw dislocations playing an important role for plastic deformation. However, they can also display a significant energetic driving force for chemical short-range ordering (SRO). Here, we investigate mechanisms underlying the mobilities of screw and edge dislocations in the body-centered cubic MoNbTaW RHEA over a wide temperature range using extensive molecular dynamics simulations based on a highly-accurate machine-learning interatomic potential. Further, we specifically evaluate how these mechanisms are affected by the presence of SRO. The mobility of edge dislocations is found to be enhanced by the presence of SRO, whereas the rate of double-kink nucleation in the motion of screw dislocations is reduced, although this influence of SRO appears to be attenuated at increasing temperature. Independent of the presence of SRO, a cross-slip locking mechanism is observed for the motion of screws, which provides for extra strengthening for refractory high-entropy alloy system.© 2021. The Author(s).

Melting properties are critical for designing novel materials, especially for discovering high-performance, high-melting refractory materials. Experimental measurements of these properties are extremely challenging due to their high melting temperatures. Complementary theoretical predictions are, therefore, indispensable. One of the most accurate approaches for this purpose is the ab initio free-energy approach based on density functional theory (DFT). However, it generally involves expensive thermodynamic integration using ab initio molecular dynamic simulations. The high computational cost makes high-throughput calculations infeasible. Here, we propose a highly efficient DFT-based method aided by a specially designed machine learning potential. As the machine learning potential can closely reproduce the ab initio phase-space distribution, even for multi-component alloys, the costly thermodynamic integration can be fully substituted with more efficient free energy perturbation calculations. The method achieves overall savings of computational resources by 80% compared to current alternatives. We apply the method to the high-entropy alloy TaVCrW and calculate its melting properties, including the melting temperature, entropy and enthalpy of fusion, and volume change at the melting point. Additionally, the heat capacities of solid and liquid TaVCrW are calculated. The results agree reasonably with the CALPHAD extrapolated values.

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive phase transitions are usually slow due to the large energy barrier. Nevertheless, the reconstructive phase transformation from β- to λ-Ti3O5 exhibits an ultrafast and reversible behavior. Despite extensive studies, the underlying microscopic mechanism remains unclear. Here, we discover a kinetically favorable in-plane nucleated layer-by-layer transformation mechanism through metadynamics and large-scale molecular dynamics simulations. This is enabled by developing an efficient machine learning potential with near first-principles accuracy through an on-the-fly active learning method and an advanced sampling technique. Our results reveal that the β−λ phase transformation initiates with the formation of two-dimensional nuclei in the a\n b-plane and then proceeds layer-by-layer through a multistep barrier-lowering kinetic process via intermediate metastable phases. Our work not only provides important insight into the ultrafast and reversible nature of the β−λ transition, but also presents useful strategies and methods for tackling other complex structural phase transitions.

Realistically modelling how solvents affect catalytic reactions is a longstanding challenge due to its prohibitive computational cost. Typically, an explicit atomistic treatment of the solvent molecules is needed together with molecular dynamics (MD) simulations and enhanced sampling methods. Here, we demonstrate the utility of machine learning interatomic potentials (MLIPs), coupled with active learning, to enable fast and accurate explicit solvent modelling of adsorption and reactions on heterogeneous catalysts. MLIPs trained on-the-fly were able to accelerate MD simulations by up to 4 orders of magnitude while reproducing with high fidelity the geometrical features of water in the bulk and at metal-water interfaces. Using these ML-accelerated simulations, we accurately predicted key catalytic quantities such as the adsorption energies of CO*, OH*, COH*, HCO*, and OCCHO* on Cu surfaces and the free energy barriers of C-H scission of ethylene glycol over Cu and Pd surfaces, as validated with calculations. We envision that such simulations will pave the way towards detailed and realistic studies of solvated catalysts at large time- and length-scales.This journal is © The Royal Society of Chemistry.

We accelerate the global search of adsorbate molecule positions using machine-learning interatomic potentials with active learning.

CO adsorption on the Pt(111) surface is studied using first-principles methods. As found in a recent study [Feibelman et al., J. Phys. Chem. B 105, 4018 (2001)], we find the preferred adsorption site within density functional theory to be the hollow site, whereas experimentally it is found that the top site is preferred. The influence of pseudopotential and exchange-correlation functional error on the CO binding energy and site preference is carefully investigated. We also compare the site preference energy of CO on Pt(111) with the reaction energy of formaldehyde formation from H2 and CO. We show that the discrepancies between the experimental and theoretical results are due to the generalized gradient approximation (GGA) treating different bond orders with varying accuracy. We can therefore expect that GGA results will contain significant error whenever bonds of different bond order are broken and formed.