Machine Learning Interatomic Potentials as Emerging Tools for Materials Science

Graph attention neural networks for mapping materials and molecules beyond short-range interatomic correlations

Bringing advances in machine learning to chemical science is leading to a revolutionary change in the way of accelerating materials discovery and atomic-scale simulations. Currently, most successful machine learning schemes can be largely traced to the use of localized atomic environments in the structural representation of materials and molecules. However, this may undermine the reliability of machine learning models for mapping complex systems and describing long-range physical effects because of the lack of non-local correlations between atoms. To overcome such limitations, here we report a graph attention neural network as a unified framework to map materials and molecules into a generalizable and interpretable representation that combines local and non-local information of atomic environments from multiple scales. As an exemplary study, our model is applied to predict the electronic structure properties of metal-organic frameworks (MOFs) which have notable diversity in compositions and structures. The results show that our model achieves the state-of-the-art performance. The clustering analysis further demonstrates that our model enables high-level identification of MOFs with spatial and chemical resolution, which would facilitate the rational design of promising reticular materials. Furthermore, the application of our model in predicting the heat capacity of complex nanoporous materials, a critical property in a carbon capture process, showcases its versatility and accuracy in handling diverse physical properties beyond electronic structures.

Predicting materials properties with generative models: applying generative adversarial networks for heat flux generation

In the realm of materials science, the integration of machine learning techniques has ushered in a transformative era. This study delves into the innovative application of generative adversarial networks (GANs) for generating heat flux data, a pivotal step in predicting lattice thermal conductivity within metallic materials. Leveraging GANs, this research explores the generation of meaningful heat flux data, which has a high degree of similarity with that calculated by molecular dynamics simulations. This study demonstrates the potential of artificial intelligence (AI) in understanding the complex physical meaning of data in materials science. By harnessing the power of such AI to generate data that is previously attainable only through experiments or simulations, new opportunities arise for exploring and predicting properties of materials.

Mechanism of Charge Transport in Lithium Thiophosphate

Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Hydrogen atom scattering at the Al2O3(0001) surface: a combined experimental and theoretical study

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields - from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the α-Al2O3(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as α-Al2O3 are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.

Development of NaCl-MgCl2-CaCl2 Ternary Salt for High-Temperature Thermal Energy Storage Using Machine Learning

NaCl-MgCl2-CaCl2 eutectic ternary chloride salts are potential heat transfer and storage materials for high-temperature thermal energy storage. In this study, first-principles molecular dynamics simulation results were used as a data set to develop an interatomic potential for ternary chloride salts using a neural network machine learning method. Deep potential molecular dynamics (DPMD) simulations were performed to predict the microstructure and thermophysical properties of the NaCl-MgCl2-CaCl2 ternary salt. This work reveals that DPMD simulations can accurately calculate the microstructure and thermophysical properties of ternary chloride salts. The association strength of chloride ions and cations follows the order of Mg2+ > Ca2+ > Na+, and the coordination number decreases gradually with increasing temperature, indicating a progressively looser and more disordered molten structure. Furthermore, thermophysical properties, such as density, specific heat capacity, thermal conductivity, and viscosity, are in good agreement with the experimental measurements. Machine learning molecular dynamics will provide a feasible multivariate molten salt exploration method for the design of next-generation solar power plants and thermal energy storage systems.

Ab initio study of longitudinal and transverse dynamics, including fast sound, in molten UO2 and liquid Li-Pb alloys

The disparity between the masses of the two components in a binary liquid system can lead to the appearance of a peculiar phenomenon named "fast sound," which was identified for the first time in Li4Pb several decades ago and later observed in other Li based alloys. However, the exact characteristics and nature of this phenomenon and the reasons behind its appearance have not totally been identified yet. In this work, we analyze the longitudinal and transverse current correlation functions of UO2, Li4Pb, and Li0.17Pb0.83, as obtained from ab initio molecular dynamics simulations. We find that fast sound appears to occur in the two former systems but not in the latter. Additionally, we discuss some of the properties of the liquid mixtures that may be related to the appearance (or absence) of the phenomenon, such as the composition, the polyhedral structure of the melt, and the type of bonding in the system.

Machine Learning Interatomic Potentials for Reactive Hydrogen Dynamics at Metal Surfaces Based on Iterative Refinement of Reaction Probabilities

The reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction design, but studying dynamics at surfaces is computationally challenging due to the complex electronic structure at interfaces and the high sensitivity of dynamics to reaction barriers. In addition, ab initio molecular dynamics, based on density functional theory, is too computationally demanding to accurately predict reactive sticking or desorption probabilities, as it requires averaging over tens of thousands of initial conditions. High-dimensional machine learning-based interatomic potentials are starting to be more commonly used in gas-surface dynamics, yet robust approaches to generate reliable training data and assess how model uncertainty affects the prediction of dynamic observables are not well established. Here, we employ ensemble learning to adaptively generate training data while assessing model performance with full uncertainty quantification (UQ) for reaction probabilities of hydrogen scattering on different copper facets. We use this approach to investigate the performance of two message-passing neural networks, SchNet and PaiNN. Ensemble-based UQ and iterative refinement allow us to expose the shortcomings of the invariant pairwise-distance-based feature representation in the SchNet model for gas-surface dynamics.

Coarse-Graining and Forecasting Atomic Material Simulations with Descriptors

Atomic simulations of materials require significant resources to generate, store, and analyze. Here, descriptor functions are proposed as a general, metric latent space for atomic structures, ideal for use in large-scale simulations. Descriptors can regress a broad range of properties, including character-dependent dislocation densities, stress states, or radial distribution functions. A vector autoregressive model can generate trajectories over yield points, resample from new initial conditions and forecast trajectory futures. A forecast confidence, essential for practical application, is derived by propagating forecasts through the Mahalanobis outlier distance, providing a powerful tool to assess coarse-grained models. Application to nanoparticles and yielding of nanoscale dislocation networks confirms low uncertainty forecasts are accurate and resampling allows for the propagation of smooth property distributions. Yielding is associated with a collapse in the intrinsic dimension of the descriptor manifold, which is discussed in relation to the yield surface.

Machine learning for structure-property mapping of Ising models: Scalability and limitations

We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of Ising models. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide-and-conquer approach, and the locality of physical properties is key to partitioning the system into subdomains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed. While the two-dimensional Ising model is used to demonstrate the proposed approach, the ML framework can be generalized to other many-body or condensed-matter systems.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

A streamlined molecular-dynamics workflow for computing solubilities of molecular and ionic crystals

Computing the solubility of crystals in a solvent using atomistic simulations is notoriously challenging due to the complexities and convergence issues associated with free-energy methods, as well as the slow equilibration in direct-coexistence simulations. This paper introduces a molecular-dynamics workflow that simplifies and robustly computes the solubility of molecular or ionic crystals. This method is considerably more straightforward than the state-of-the-art, as we have streamlined and optimised each step of the process. Specifically, we calculate the chemical potential of the crystal using the gas-phase molecule as a reference state, and employ the S0 method to determine the concentration dependence of the chemical potential of the solute. We use this workflow to predict the solubilities of sodium chloride in water, urea polymorphs in water, and paracetamol polymorphs in both water and ethanol. Our findings indicate that the predicted solubility is sensitive to the chosen potential energy surface. Furthermore, we note that the harmonic approximation often fails for both molecular crystals and gas molecules at or above room temperature, and that the assumption of an ideal solution becomes less valid for highly soluble substances.

ACEpotentials.jl: A Julia implementation of the atomic cluster expansion

We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion [R. Drautz, Phys. Rev. B 99, 014104 (2019)]. As the latter provides a complete description of atomic environments, including invariance to overall translation and rotation as well as permutation of like atoms, the resulting potentials are systematically improvable and data efficient. Furthermore, the descriptor's expressiveness enables use of a linear model, facilitating rapid evaluation and straightforward application of Bayesian techniques for active learning. We summarize the capabilities of ACEpotentials.jl and demonstrate its strengths (simplicity, interpretability, robustness, performance) on a selection of prototypical atomistic modelling workflows.

Reducing the Cost of Neural Network Potential Generation for Reactive Molecular Systems

Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.

How to train a neural network potential

The introduction of modern Machine Learning Potentials (MLPs) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow us to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations, provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form, the construction of MLPs has to be done with great care. In this Tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.

Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

Hyperactive learning for data-driven interatomic potentials

Data-driven interatomic potentials have emerged as a powerful tool for approximating ab initio potential energy surfaces. The most time-consuming step in creating these interatomic potentials is typically the generation of a suitable training database. To aid this process hyperactive learning (HAL), an accelerated active learning scheme, is presented as a method for rapid automated training database assembly. HAL adds a biasing term to a physically motivated sampler (e.g. molecular dynamics) driving atomic structures towards uncertainty in turn generating unseen or valuable training configurations. The proposed HAL framework is used to develop atomic cluster expansion (ACE) interatomic potentials for the AlSi10 alloy and polyethylene glycol (PEG) polymer starting from roughly a dozen initial configurations. The HAL generated ACE potentials are shown to be able to determine macroscopic properties, such as melting temperature and density, with close to experimental accuracy.

Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Exploring Configurations of Nanocrystal Ligands Using Machine-Learned Force Fields

Semiconducting nanocrystals passivated with organic ligands have emerged as a powerful platform for light harvesting, light-driven chemical reactions, and sensing. Due to their complexity and size, little structural information is available from experiments, making these systems challenging to model computationally. Here, we develop a machine-learned force field trained on DFT data and use it to investigate the surface chemistry of a PbS nanocrystal interfaced with acetate ligands. In doing so, we go beyond considering individual local minimum energy geometries and, importantly, circumvent a precarious issue associated with the assumption of a single assigned atomic partial charge for each element in a nanocrystal, independent of its structural position. We demonstrate that the carboxylate ligands passivate the metal-rich surfaces by adopting a very wide range of "tilted-bridge" and "bridge" geometries and investigate the corresponding ligand IR spectrum. This work illustrates the potential of machine-learned force fields to transform computational modeling of these materials.

Renaissance of elemental phosphorus materials: properties, synthesis, and applications in sustainable energy and environment

The polymorphism of phosphorus-based materials has garnered much research interest, and the variable chemical bonding structures give rise to a variety of micro and nanostructures. Among the different types of materials containing phosphorus, elemental phosphorus materials (EPMs) constitute the foundation for the synthesis of related compounds. EPMs are experiencing a renaissance in the post-graphene era, thanks to recent advancements in the scaling-down of black phosphorus, amorphous red phosphorus, violet phosphorus, and fibrous phosphorus and consequently, diverse classes of low-dimensional sheets, ribbons, and dots of EPMs with intriguing properties have been produced. The nanostructured EPMs featuring tunable bandgaps, moderate carrier mobility, and excellent optical absorption have shown great potential in energy conversion, energy storage, and environmental remediation. It is thus important to have a good understanding of the differences and interrelationships among diverse EPMs, their intrinsic physical and chemical properties, the synthesis of specific structures, and the selection of suitable nanostructures of EPMs for particular applications. In this comprehensive review, we aim to provide an in-depth analysis and discussion of the fundamental physicochemical properties, synthesis, and applications of EPMs in the areas of energy conversion, energy storage, and environmental remediation. Our evaluations are based on recent literature on well-established phosphorus allotropes and theoretical predictions of new EPMs. The objective of this review is to enhance our comprehension of the characteristics of EPMs, keep abreast of recent advances, and provide guidance for future research of EPMs in the fields of chemistry and materials science.

Machine-Learning-Enabled Framework in Engineering Plastics Discovery: A Case Study of Designing Polyimides with Desired Glass-Transition Temperature

Great and continuous efforts have been made to discover high-performance engineering plastics with specific properties to replace traditional engineering materials in many fields. The utilization of machine learning (ML) has brought more opportunities for the discovery of high-performing engineering plastics. However, hindered by either the relatively small database or a lack of accurate structure descriptors with clear physical and chemical meanings relating to polymer properties, the current ML studies show some flaws in the accuracy and efficiency in polymer development. Herein, we collected a dataset of 878 polyimides (PI), one of the best engineering plastics, with experimentally measured glass-transition temperature (Tg) values, and developed a rapid and accurate ML approach to design PI candidates with the desired Tg value. After the conversion from PI structures into "mechanically identifiable" SMILES (Simplified molecular input line entry system) language, the eight most critical descriptors were ultimately obtained by multiple analysis methods. The physiochemical meaning of the key descriptors was further analyzed carefully to translate the implicit "machine language" to chemical knowledge. The artificial neural network (ANN)-based model gave the most accurate results with a root-mean-square error of ∼11 K among the studied ML methods. More importantly, three potential PI candidates with desired Tg (DPIs) were designed according to the chemical insight of the key descriptors, which were then verified by experiments. The experimental and predicted Tg values of DPIs have an acceptable average deviation of ca. 3.66%. This accuracy has reached the level of the traditional molecular simulation, but the time consumption and hold-up computing resource are tremendously reduced. Furthermore, the current ML approach could offer a scalable and adaptable framework in future engineer plastics innovation.

Accelerating explicit solvent models of heterogeneous catalysts with machine learning interatomic potentials

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 ab initio 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 ab initio calculations. We envision that such simulations will pave the way towards detailed and realistic studies of solvated catalysts at large time- and length-scales.

MBX: A many-body energy and force calculator for data-driven many-body simulations

Many-Body eXpansion (MBX) is a C++ library that implements many-body potential energy functions (PEFs) within the "many-body energy" (MB-nrg) formalism. MB-nrg PEFs integrate an underlying polarizable model with explicit machine-learned representations of many-body interactions to achieve chemical accuracy from the gas to the condensed phases. MBX can be employed either as a stand-alone package or as an energy/force engine that can be integrated with generic software for molecular dynamics and Monte Carlo simulations. MBX is parallelized internally using Open Multi-Processing and can utilize Message Passing Interface when available in interfaced molecular simulation software. MBX enables classical and quantum molecular simulations with MB-nrg PEFs, as well as hybrid simulations that combine conventional force fields and MB-nrg PEFs, for diverse systems ranging from small gas-phase clusters to aqueous solutions and molecular fluids to biomolecular systems and metal-organic frameworks.

Spin Glass Behavior in Amorphous Cr2 Ge2 Te6 Phase-Change Alloy

The layered crystal structure of Cr2 Ge2 Te6 shows ferromagnetic ordering at the two-dimensional limit, which holds promise for spintronic applications. However, external voltage pulses can trigger amorphization of the material in nanoscale electronic devices, and it is unclear whether the loss of structural ordering leads to a change in magnetic properties. Here, it is demonstrated that Cr2 Ge2 Te6 preserves the spin-polarized nature in the amorphous phase, but undergoes a magnetic transition to a spin glass state below 20 K. Quantum-mechanical computations reveal the microscopic origin of this transition in spin configuration: it is due to strong distortions of the CrTeCr bonds, connecting chromium-centered octahedra, and to the overall increase in disorder upon amorphization. The tunable magnetic properties of Cr2 Ge2 Te6 can be exploited for multifunctional, magnetic phase-change devices that switch between crystalline and amorphous states.

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

Machine-learned acceleration for molecular dynamics in CASTEP

Machine learning (ML) methods are of rapidly growing interest for materials modeling, and yet, the use of ML interatomic potentials for new systems is often more demanding than that of established density-functional theory (DFT) packages. Here, we describe computational methodology to combine the CASTEP first-principles simulation software with the on-the-fly fitting and evaluation of ML interatomic potential models. Our approach is based on regular checking against DFT reference data, which provides a direct measure of the accuracy of the evolving ML model. We discuss the general framework and the specific solutions implemented, and we present an example application to high-temperature molecular-dynamics simulations of carbon nanostructures. The code is freely available for academic research.

Review: understanding the properties of amorphous materials with high-performance computing methods

Amorphous materials have no long-range order in their atomic structure. This makes much of the formalism for the study of crystalline materials irrelevant, and so elucidating their structure and properties is challenging. The use of computational methods is a powerful complement to experimental studies, and in this paper we review the use of high-performance computing methods in the simulation of amorphous materials. Five case studies are presented to showcase the wide range of materials and computational methods available to practitioners in this field. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Reactivity of Single-Atom Alloy Nanoparticles: Modeling the Dehydrogenation of Propane

Physical catalysts often have multiple sites where reactions can take place. One prominent example is single-atom alloys, where the reactive dopant atoms can preferentially locate in the bulk or at different sites on the surface of the nanoparticle. However, ab initio modeling of catalysts usually only considers one site of the catalyst, neglecting the effects of multiple sites. Here, nanoparticles of copper doped with single-atom rhodium or palladium are modeled for the dehydrogenation of propane. Single-atom alloy nanoparticles are simulated at 400-600 K, using machine learning potentials trained on density functional theory calculations, and then the occupation of different single-atom active sites is identified using a similarity kernel. Further, the turnover frequency for all possible sites is calculated for propane dehydrogenation to propene through microkinetic modeling using density functional theory calculations. The total turnover frequencies of the whole nanoparticle are then described from both the population and the individual turnover frequency of each site. Under operating conditions, rhodium as a dopant is found to almost exclusively occupy (111) surface sites while palladium as a dopant occupies a greater variety of facets. Undercoordinated dopant surface sites are found to tend to be more reactive for propane dehydrogenation compared to the (111) surface. It is found that considering the dynamics of the single-atom alloy nanoparticle has a profound effect on the calculated catalytic activity of single-atom alloys by several orders of magnitude.

Lifelong Machine Learning Potentials

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs have been trained from scratch because learning additional data typically requires retraining on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs), which combine structural properties and element information from the periodic table. These eeACSFs are key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pretrained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

Machine learning facilitating the rational design of nanozymes

As a component substitute for natural enzymes, nanozymes have the advantages of easy synthesis, convenient modification, low cost, and high stability, and are widely used in many fields. However, their application is seriously restricted by the difficulty of rapidly creating high-performance nanozymes. The use of machine learning techniques to guide the rational design of nanozymes holds great promise to overcome this difficulty. In this review, we introduce the recent progress of machine learning in assisting the design of nanozymes. Particular attention is given to the successful strategies of machine learning in predicting the activity, selectivity, catalytic mechanisms, optimal structures and other features of nanozymes. The typical procedures and approaches for conducting machine learning in the study of nanozymes are also highlighted. Moreover, we discuss in detail the difficulties of machine learning methods in dealing with the redundant and chaotic nanozyme data and provide an outlook on the future application of machine learning in the nanozyme field. We hope that this review will serve as a useful handbook for researchers in related fields and promote the utilization of machine learning in nanozyme rational design and related topics.

Machine Learning Electron Density Prediction Using Weighted Smooth Overlap of Atomic Positions

Having access to accurate electron densities in chemical systems, especially for dynamical systems involving chemical reactions, ion transport, and other charge transfer processes, is crucial for numerous applications in materials chemistry. Traditional methods for computationally predicting electron density data for such systems include quantum mechanical (QM) techniques, such as density functional theory. However, poor scaling of these QM methods restricts their use to relatively small system sizes and short dynamic time scales. To overcome this limitation, we have developed a deep neural network machine learning formalism, which we call deep charge density prediction (DeepCDP), for predicting charge densities by only using atomic positions for molecules and condensed phase (periodic) systems. Our method uses the weighted smooth overlap of atomic positions to fingerprint environments on a grid-point basis and map it to electron density data generated from QM simulations. We trained models for bulk systems of copper, LiF, and silicon; for a molecular system, water; and for two-dimensional charged and uncharged systems, hydroxyl-functionalized graphane, with and without an added proton. We showed that DeepCDP achieves prediction R2 values greater than 0.99 and mean squared error values on the order of 10-5e2 Å-6 for most systems. DeepCDP scales linearly with system size, is highly parallelizable, and is capable of accurately predicting the excess charge in protonated hydroxyl-functionalized graphane. We demonstrate how DeepCDP can be used to accurately track the location of charges (protons) by computing electron densities at a few selected grid points in the materials, thus significantly reducing the computational cost. We also show that our models can be transferable, allowing prediction of electron densities for systems on which it has not been trained but that contain a subset of atomic species on which it has been trained. Our approach can be used to develop models that span different chemical systems and train them for the study of large-scale charge transport and chemical reactions.

Combining Machine Learning with Physical Knowledge in Thermodynamic Modeling of Fluid Mixtures

Thermophysical properties of fluid mixtures are important in many fields of science and engineering. However, experimental data are scarce in this field, so prediction methods are vital. Different types of physical prediction methods are available, ranging from molecular models over equations of state to models of excess properties. These well-established methods are currently being complemented by new methods from the field of machine learning (ML). This review focuses on the rapidly developing interface between these two approaches and gives a structured overview of how physical modeling and ML can be combined to yield hybrid models. We illustrate the different options with examples from recent research and give an outlook on future developments.

Unraveling Thermal Transport Correlated with Atomistic Structures in Amorphous Gallium Oxide via Machine Learning Combined with Experiments

Thermal transport properties of amorphous materials are crucial for their emerging applications in energy and electronic devices. However, understanding and controlling thermal transport in disordered materials remains an outstanding challenge, owing to the intrinsic limitations of computational techniques and the lack of physically intuitive descriptors for complex atomistic structures. Here, it is shown how combining machine-learning-based models and experimental observations can help to accurately describe realistic structures, thermal transport properties, and structure-property maps for disordered materials, which is illustrated by a practical application on gallium oxide. First, the experimental evidence is reported to demonstrate that machine-learning interatomic potentials, generated in a self-guided fashion with minimum quantum-mechanical computations, enable the accurate modeling of amorphous gallium oxide and its thermal transport properties. The atomistic simulations then reveal the microscopic changes in the short-range and medium-range order with density and elucidate how these changes can reduce localization modes and enhance coherences' contribution to heat transport. Finally, a physics-inspired structural descriptor for disordered phases is proposed, with which the underlying relationship between structures and thermal conductivities is predicted in a linear form. This work may shed light on the future accelerated exploration of thermal transport properties and mechanisms in disordered functional materials.

A fully quantum-mechanical treatment for kaolinite

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculations that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate the static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included, the dynamic properties of the material change substantially.

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

Two-dimensional materials (2DMs) continue to attract a lot of attention, particularly for their extreme flexibility and superior thermal properties. Molecular dynamics simulations are among the most powerful methods for computing these properties, but their reliability depends on the accuracy of interatomic interactions. While first principles approaches provide the most accurate description of interatomic forces, they are computationally expensive. In contrast, classical force fields are computationally efficient, but have limited accuracy in interatomic force description. Machine learning interatomic potentials, such as Gaussian Approximation Potentials, trained on density functional theory (DFT) calculations offer a compromise by providing both accurate estimation and computational efficiency. In this work, we present a systematic procedure to develop Gaussian approximation potentials for selected 2DMs, graphene, buckled silicene, and h-XN (X = B, Al, and Ga, as binary compounds) structures. We validate our approach through calculations that require various levels of accuracy in interatomic interactions. The calculated phonon dispersion curves and lattice thermal conductivity, obtained through harmonic and anharmonic force constants (including fourth order) are in excellent agreement with DFT results. HIPHIVE calculations, in which the generated GAP potentials were used to compute higher-order force constants instead of DFT, demonstrated the first-principles level accuracy of the potentials for interatomic force description. Molecular dynamics simulations based on phonon density of states calculations, which agree closely with DFT-based calculations, also show the success of the generated potentials in high-temperature simulations.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

A Perspective on Explanations of Molecular Prediction Models

Chemists can be skeptical in using deep learning (DL) in decision making, due to the lack of interpretability in "black-box" models. Explainable artificial intelligence (XAI) is a branch of artificial intelligence (AI) which addresses this drawback by providing tools to interpret DL models and their predictions. We review the principles of XAI in the domain of chemistry and emerging methods for creating and evaluating explanations. Then, we focus on methods developed by our group and their applications in predicting solubility, blood-brain barrier permeability, and the scent of molecules. We show that XAI methods like chemical counterfactuals and descriptor explanations can explain DL predictions while giving insight into structure-property relationships. Finally, we discuss how a two-step process of developing a black-box model and explaining predictions can uncover structure-property relationships.

Algorithmic Graph Theory, Reinforcement Learning and Game Theory in MD Simulations: From 3D Structures to Topological 2D-Molecular Graphs (2D-MolGraphs) and Vice Versa

This paper reviews graph-theory-based methods that were recently developed in our group for post-processing molecular dynamics trajectories. We show that the use of algorithmic graph theory not only provides a direct and fast methodology to identify conformers sampled over time but also allows to follow the interconversions between the conformers through graphs of transitions in time. Examples of gas phase molecules and inhomogeneous aqueous solid interfaces are presented to demonstrate the power of topological 2D graphs and their versatility for post-processing molecular dynamics trajectories. An even more complex challenge is to predict 3D structures from topological 2D graphs. Our first attempts to tackle such a challenge are presented with the development of game theory and reinforcement learning methods for predicting the 3D structure of a gas-phase peptide.

Machine Learning Interatomic Potentials and Long-Range Physics

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Simulations in the era of exascale computing

Exascale computers - supercomputers that can perform 1018 floating point operations per second - started coming online in 2022: in the United States, Frontier launched as the first public exascale supercomputer and Aurora is due to open soon; OceanLight and Tianhe-3 are operational in China; and JUPITER is due to launch in 2023 in Europe. Supercomputers offer unprecedented opportunities for modelling complex materials. In this Viewpoint, five researchers working on different types of materials discuss the most promising directions in computational materials science.

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

Size and Quality of Quantum Mechanical Data Set for Training Neural Network Force Fields for Liquid Water

Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT) and thus is limited to small systems and a relatively short simulation time. In this scenario, Neural Network Force Fields (NNFFs) have an important role, since they provide a way to circumvent these caveats. In this work, we investigate NNFFs designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data set considered. We show that structural properties are less dependent on the size of the training data set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for the training process) can lead to a small sample with good precision.

A first-principles exploration of the conformational space of sodiated pyranose assisted by neural network potentials

Sampling the conformational space of monosaccharides using the first-principles methods is important and as a database of local minima provides a solid base for interpreting experimental measurements such as infrared photo-dissociation (IRPD) spectroscopy or collision-induced dissociation (CID). IRPD emphasizes low-energy conformers and CID can distinguish conformers with distinct reaction pathways. A typical computational approach is to engage empirical or semi-empirical methods to sample the conformational space first, and only selected minima are reoptimized at first-principles levels. In this work, we propose a computational scheme to explore the configurational space of 12 types of sodiated pyranoses with the assistance of a neural network potential (NNP). We demonstrated that it is possible to train an NNP based on the density functional calculations extracted from a previous study on sodiated glucose (Glc), galactose (Gal), and mannose (Man). This NNP yields a better description of the other five types of aldohexoses than the four types of ketohexoses. We further show that such a discrepancy in the accuracy of NNP can be resolved by an active learning scheme where the NNP model is engaged in generating the data and has itself updated. Through this iterative process, we can locate more than 17 000 distinct local minima at the B3LYP/6-311+G(d,p) level and an NNP with an accuracy of 1 kJ mol^-1 was created, which can be used for further studies.

Using Machine Learning Potentials to Explore Interdiffusion at Metal-Chalcogenide Interfaces

Chalcogenide alloys are key materials for selector and memory elements used in next-generation nonvolatile memory cells. However, the high electric fields and Joule heating experienced during operation can promote interdiffusion at the interfaces that degrade device performance over time. A clear atomic scale understanding of how chalcogenide alloys interact with electrodes could aid in identifying ways to improve long-term device endurance. In this work, we develop a robust set of moment tensor potentials (MTPs) to examine interactions between Ge-Se alloys and Ti electrodes. Previous works have shown evidence of strong interactions between Ti and chalcogenide alloys. This system offers an important first test in the use of ML empirical potentials to understand the role of interfaces in endurance in memory elements and broader nanoscale devices. The empirical potentials are constructed using an active learning moment tensor potential framework that leverages a broad data set of first-principles calculations for Ti, Ge, and Se compounds. Long-term simulations (>1 ns) show significant interdiffusion at the Ti|Ge-Se interface with Ti and Se both actively moving across the original interface. The strong chemical affinity of Ti and Se leads to a well-defined Ti-Se region and a severely Se-depleted central Ge-Se region with unfavorable selector characteristics. The evolution of the Ti-Se layer can be described using a self-limited growth model. By comparing effective Ti-Se diffusion constants for simulations at different temperatures, we find a low activation energy of 0.1 eV for Ti-Se layer interdiffusion.

Liquid-Liquid Transition in Water from First Principles

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.