Machine Learning Interatomic Potentials as Emerging Tools for Materials Science

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Learning Electronic Polarizations in Aqueous Systems

The polarization of periodically repeating systems is a discontinuous function of the atomic positions, a fact which seems at first to stymie attempts at their statistical learning. Two approaches to build models for bulk polarizations are compared: one in which a simple point charge model is used to preprocess the raw polarization to give a learning target that is a smooth function of atomic positions and the total polarization is learned as a sum of atom-centered dipoles and one in which instead the average position of Wannier centers around atoms is predicted. For a range of bulk aqueous systems, both of these methods perform perform comparatively well, with the former being slightly better but often requiring an extra effort to find a suitable point charge model. As a challenging test, we also analyze the performance of the models at the air-water interface. In this case, while the Wannier center approach delivers accurate predictions without further modifications, the preprocessing method requires augmentation with information from isolated water molecules to reach similar accuracy. Finally, we present a simple protocol to preprocess the polarizations in a data-driven way using a small number of derivatives calculated at a much lower level of theory, thus overcoming the need to find point charge models without appreciably increasing the computation cost. We believe that the training strategies presented here help the construction of accurate polarization models required for the study of the dielectric properties of realistic complex bulk systems and interfaces with ab initio accuracy.

Thermal conductivity of irregularly shaped nanoparticles from equilibrium molecular dynamics

The computation of thermal conductivity for finite nanoparticulate systems, particularly those of irregular shapes, poses significant challenges. The nonequilibrium molecular dynamics (NEMD) methods has been extensively utilized in numerous prior studies for the computation of thermal conductivity of nanoparticles. One of our recent works (Donget al2021Phys. Rev.B103035417) proposed that equilibrium molecular dynamics (EMD) methods can be used for the simulation of thermal conductivity of finite-scale systems and demonstrated their equivalence to NEMD methods. In this study, we investigated the application of the (EMD) approach for the computation of thermal conductivity in zero-dimensional nanoparticles. In our initial step, we merged both methodologies to substantiate the equivalence in thermal conductivity calculation for cube and cylinder nanoparticles. After filtering the data, we confirmed the usefulness of EMD for evaluating the thermal conductivity of zero-dimensional materials. The NEMD method faces challenges in accurately predicting thermal conductivity in nanoparticle systems with a varying cross-sectional area along the transport direction, whereas EMD methods can be utilized to estimate thermal conductivity when the volume is known. In a subsequent study, we used the state-of-the-art machine learning potential to calculate the thermal conductivity of spherical nanoparticles and compared the results with those obtained using the classical Tersoff potential. Ultimately, we predicted the thermal conductivity of nanoparticles with various geometries in all directions. Our findings collectively demonstrate the simplicity and effectiveness of employing EMD methods for calculating thermal conductivity in nanoparticle systems, thereby opening up new avenues for investigating thermal transport properties in particle systems as well as nanopders.

Experiment-Driven Atomistic Materials Modeling: A Case Study Combining X-Ray Photoelectron Spectroscopy and Machine Learning Potentials to Infer the Structure of Oxygen-Rich Amorphous Carbon

An important yet challenging aspect of atomistic materials modeling is reconciling experimental and computational results. Conventional approaches involve generating numerous configurations through molecular dynamics or Monte Carlo structure optimization and selecting the one with the closest match to experiment. However, this inefficient process is not guaranteed to succeed. We introduce a general method to combine atomistic machine learning (ML) with experimental observables that produces atomistic structures compatible with experiment by design. We use this approach in combination with grand-canonical Monte Carlo within a modified Hamiltonian formalism, to generate configurations that agree with experimental data and are chemically sound (low in energy). We apply our approach to understand the atomistic structure of oxygenated amorphous carbon (a-COx), an intriguing carbon-based material, to answer the question of how much oxygen can be added to carbon before it fully decomposes into CO and CO2. Utilizing an ML-based X-ray photoelectron spectroscopy (XPS) model trained from GW and density functional theory (DFT) data, in conjunction with an ML interatomic potential, we identify a-COx structures compliant with experimental XPS predictions that are also energetically favorable with respect to DFT. Employing a network analysis, we accurately deconvolve the XPS spectrum into motif contributions, both revealing the inaccuracies inherent to experimental XPS interpretation and granting us atomistic insight into the structure of a-COx. This method generalizes to multiple experimental observables and allows for the elucidation of the atomistic structure of materials directly from experimental data, thereby enabling experiment-driven materials modeling with a degree of realism previously out of reach.

Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a dataset of the melting points of 476 non-metallic crystalline binary compounds using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180 K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for TensorNet models, with performance gains ranging from 2× to 10× over previous, nonoptimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

Experimental and Computational Study Toward Identifying Active Sites of Supported SnOx Nanoparticles for Electrochemical CO2 Reduction Using Machine-Learned Interatomic Potentials

SnOx has received great attention as an electrocatalyst for CO2 reduction reaction (CO2RR), however; it still suffers from low activity. Moreover, the atomic-level SnOx structure and the nature of the active sites are still ambiguous due to the dynamism of surface structure and difficulty in structure characterization under electrochemical conditions. Herein, CO2RR performance is enhanced by supporting SnO2 nanoparticles on two common supports, vulcan carbon and TiO2. Then, electrolysis of CO2 at various temperatures in a neutral electrolyte reveals that the application window for this catalyst is between 12 and 30 °C. Furthermore, this study introduces a machine learning interatomic potential method for the atomistic simulation to investigate SnO2 reduction and establish a correlation between SnOx structures and their CO2RR performance. In addition, selectivity is analyzed computationally with density functional theory simulations to identify the key differences between the binding energies of *H and *CO2 -, where both are correlated with the presence of oxygen on the nanoparticle surface. This study offers in-depth insights into the rational design and application of SnOx-based electrocatalysts for CO2RR.

Hydrogen Embrittlement as a Conspicuous Material Challenge─Comprehensive Review and Future Directions

Hydrogen is considered a clean and efficient energy carrier crucial for shaping the net-zero future. Large-scale production, transportation, storage, and use of green hydrogen are expected to be undertaken in the coming decades. As the smallest element in the universe, however, hydrogen can adsorb on, diffuse into, and interact with many metallic materials, degrading their mechanical properties. This multifaceted phenomenon is generically categorized as hydrogen embrittlement (HE). HE is one of the most complex material problems that arises as an outcome of the intricate interplay across specific spatial and temporal scales between the mechanical driving force and the material resistance fingerprinted by the microstructures and subsequently weakened by the presence of hydrogen. Based on recent developments in the field as well as our collective understanding, this Review is devoted to treating HE as a whole and providing a constructive and systematic discussion on hydrogen entry, diffusion, trapping, hydrogen-microstructure interaction mechanisms, and consequences of HE in steels, nickel alloys, and aluminum alloys used for energy transport and storage. HE in emerging material systems, such as high entropy alloys and additively manufactured materials, is also discussed. Priority has been particularly given to these less understood aspects. Combining perspectives of materials chemistry, materials science, mechanics, and artificial intelligence, this Review aspires to present a comprehensive and impartial viewpoint on the existing knowledge and conclude with our forecasts of various paths forward meant to fuel the exploration of future research regarding hydrogen-induced material challenges.

Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations

Machine learning interatomic potential (MLIP) overcomes the challenges of high computational costs in density-functional theory and the relatively low accuracy in classical large-scale molecular dynamics, facilitating more efficient and precise simulations in materials research and design. In this review, the current state of the four essential stages of MLIP is discussed, including data generation methods, material structure descriptors, six unique machine learning algorithms, and available software. Furthermore, the applications of MLIP in various fields are investigated, notably in phase-change memory materials, structure searching, material properties predicting, and the pre-trained universal models. Eventually, the future perspectives, consisting of standard datasets, transferability, generalization, and trade-off between accuracy and complexity in MLIPs, are reported.

Two-Step Growth Mechanism of the Solid Electrolyte Interphase in Argyrodyte/Li-Metal Contacts

The structure and growth of the solid electrolyte interphase (SEI) region between an electrolyte and an electrode is one of the most fundamental yet less well-understood phenomena in solid-state batteries. We present an atomistic simulation of the SEI growth for one of the currently promising solid electrolytes (Li6PS5Cl), based on ab initio-trained machine learning interatomic potentials, for over 30,000 atoms during 10 ns, well beyond the capabilities of conventional molecular dynamics. This unveils a two-step growth mechanism: a Li-argyrodite chemical reaction leading to the formation of an amorphous phase, followed by a kinetically slower crystallization of the reaction products into a 5Li2S·Li3P·LiCl solid solution. The simulation results support the recent, experimentally founded hypothesis of an indirect pathway of electrolyte reduction. These findings shed light on the intricate processes governing SEI evolution, providing a valuable foundation for the design and optimization of next-generation solid-state batteries.

Data-driven interpretable analysis for polysaccharide yield prediction

Cornstalks show promise as a raw material for polysaccharide production through xylanase. Rapid and accurate prediction of polysaccharide yield can facilitate process optimization, eliminating the need for extensive experimentation in actual production to refine reaction conditions, thereby saving time and costs. However, the intricate interplay of enzymatic factors poses challenges in predicting and optimizing polysaccharide yield accurately. Here, we introduce an innovative data-driven approach leveraging multiple artificial intelligence techniques to enhance polysaccharide production. We propose a machine learning framework to identify highly accurate polysaccharide yield prediction modeling methods and uncover optimal enzymatic parameter combinations. Notably, Random Forest (RF) and eXtreme Gradient Boost (XGB) demonstrate robust performance, achieving prediction accuracies of 93.0% and 95.6%, respectively, while an independently developed deep neural network (DNN) model achieves 91.1% accuracy. A feature importance analysis of XGB reveals the enzyme solution volume's dominant role (43.7%), followed by time (20.7%), substrate concentration (15%), temperature (15%), and pH (5.6%). Further interpretability analysis unveils complex parameter interactions and potential optimization strategies. This data-driven approach, incorporating machine learning, deep learning, and interpretable analysis, offers a viable pathway for polysaccharide yield prediction and the potential recovery of various agricultural residues.

Expanding the Horizons of Machine Learning in Nanomaterials to Chiral Nanostructures

Machine learning holds significant research potential in the field of nanotechnology, enabling nanomaterial structure and property predictions, facilitating materials design and discovery, and reducing the need for time-consuming and labor-intensive experiments and simulations. In contrast to their achiral counterparts, the application of machine learning for chiral nanomaterials is still in its infancy, with a limited number of publications to date. This is despite the great potential of machine learning to advance the development of new sustainable chiral materials with high values of optical activity, circularly polarized luminescence, and enantioselectivity, as well as for the analysis of structural chirality by electron microscopy. In this review, an analysis of machine learning methods used for studying achiral nanomaterials is provided, subsequently offering guidance on adapting and extending this work to chiral nanomaterials. An overview of chiral nanomaterials within the framework of synthesis-structure-property-application relationships is presented and insights on how to leverage machine learning for the study of these highly complex relationships are provided. Some key recent publications are reviewed and discussed on the application of machine learning for chiral nanomaterials. Finally, the review captures the key achievements, ongoing challenges, and the prospective outlook for this very important research field.

Global machine learning potentials for molecular crystals

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

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

Effect of Interlayer Bonding on Superlubric Sliding of Graphene Contacts: A Machine-Learning Potential Study

Surface defects and their mutual interactions are anticipated to affect the superlubric sliding of incommensurate layered material interfaces. Atomistic understanding of this phenomenon is limited due to the high computational cost of ab initio simulations and the absence of reliable classical force-fields for molecular dynamics simulations of defected systems. To address this, we present a machine-learning potential (MLP) for bilayer defected graphene, utilizing state-of-the-art graph neural networks trained against many-body dispersion corrected density functional theory calculations under iterative configuration space exploration. The developed MLP is utilized to study the impact of interlayer bonding on the friction of bilayer defected graphene interfaces. While a mild effect on the sliding dynamics of aligned graphene interfaces is observed, the friction coefficients of incommensurate graphene interfaces are found to significantly increase due to interlayer bonding, nearly pushing the system out of the superlubric regime. The methodology utilized herein is of general nature and can be adapted to describe other homogeneous and heterogeneous defected layered material interfaces.

Temperature-transferable tight-binding model using a hybrid-orbital basis

Finite-temperature calculations are relevant for rationalizing material properties, yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many explicit first-principles calculations, tight-binding and machine-learning models for the electronic structure emerged as promising alternatives, but transferability of such methods to elevated temperatures in a data-efficient way remains a great challenge. In this work, we suggest a tight-binding model for efficient and accurate calculations of temperature-dependent properties of semiconductors. Our approach utilizes physics-informed modeling of the electronic structure in the form of hybrid-orbital basis functions and numerically integrating atomic orbitals for the distance dependence of matrix elements. We show that these design choices lead to a tight-binding model with a minimal amount of parameters that are straightforwardly optimized using density functional theory or alternative electronic-structure methods. The temperature transferability of our model is tested by applying it to existing molecular-dynamics trajectories without explicitly fitting temperature-dependent data and comparison with density functional theory. We utilize it together with machine-learning molecular dynamics and hybrid density functional theory for the prototypical semiconductor gallium arsenide. We find that including the effects of thermal expansion on the onsite terms of the tight-binding model is important in order to accurately describe electronic properties at elevated temperatures in comparison with experiment.

Surface Segregation Studies in Ternary Noble Metal Alloys: Comparing DFT and Machine Learning with Experimental Data

Surface segregation, whereby the surface composition of an alloy differs systematically from the bulk, has historically been hard to study, because it requires experimental and modeling methods that span alloy composition space. In this work, we study surface segregation in catalytically relevant noble and platinum-group metal alloys with a focus on three ternary systems: AgAuCu, AuCuPd, and CuPdPt. We develop a data set of 2478 fcc slabs with those compositions including all three low-index crystallographic orientations relaxed with Density Functional Theory using the PBEsol functional with D3 dispersion corrections. We fine-tune a machine learning model on this data and use the model in a series of 1800 Monte Carlo simulations spanning ternary composition space for each surface orientation and ternary chemical system. The results of these simulations are validated against prior experimental surface segregation data collected using composition spread alloy films for AgAuCu and AuCuPd. Our findings reveal that simulations conducted using the (110) orientation most closely match experimentally observed surface segregation trends, and while predicted trends qualitatively match observation, biases in the PBEsol functional limit numeric accuracy. This study advances understanding of surface segregation and the utility of computational studies and highlights the need for further improvements in simulation accuracy.

Accelerating the prediction of inorganic surfaces with machine learning interatomic potentials

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the material's synthesis or operating conditions. These conditions dictate thermodynamic driving forces and kinetic rates responsible for yielding the observed surface structure and morphology. Computational surface science methods have long been applied to connect thermochemical conditions to surface phase stability, particularly in the heterogeneous catalysis and thin film growth communities. This review provides a brief introduction to first-principles approaches to compute surface phase diagrams before introducing emerging data-driven approaches. The remainder of the review focuses on the application of machine learning, predominantly in the form of learned interatomic potentials, to study complex surfaces. As machine learning algorithms and large datasets on which to train them become more commonplace in materials science, computational methods are poised to become even more predictive and powerful for modeling the complexities of inorganic surfaces at the nanoscale.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

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.

Advances of LiCoO2 in Cathode of Aqueous Lithium-Ion Batteries

Aqueous lithium-ion batteries offer promising advantages such as low cost, enhanced safety, high rate capability, and the ability to deliver considerable capacity at 1.8 V, making them ideal candidates for large-scale reserve power sources for renewable energy. However, the practical application of aqueous lithium-ion batteries has been hindered by the poor cycle stability of layered cathode materials, including LiCoO2 , in neutral aqueous electrolytes. This review examines the working principles, material limitations, and research progress of aqueous lithium-ion batteries. The types and characteristics of materials used in the cathode of aqueous lithium-ion batteries are summarized, with a primary focus on the attenuation mechanisms of LiCoO2 when used as the cathode material in aqueous electrolytes. Furthermore, this review explores the advancements in utilizing LiCoO2 in the cathode of aqueous lithium-ion batteries, as well as the combination with machine learning. By addressing these critical aspects, this review aims to provide a comprehensive understanding of aqueous lithium-ion batteries and shed light on future development and application prospects.

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.