Realistic Atomistic Structure of Amorphous Silicon from Machine-Learning-Driven Molecular Dynamics

Prediction rigidities for data-driven chemistry

The widespread application of machine learning (ML) to the chemical sciences is making it very important to understand how the ML models learn to correlate chemical structures with their properties, and what can be done to improve the training efficiency whilst guaranteeing interpretability and transferability. In this work, we demonstrate the wide utility of prediction rigidities, a family of metrics derived from the loss function, in understanding the robustness of ML model predictions. We show that the prediction rigidities allow the assessment of the model not only at the global level, but also on the local or the component-wise level at which the intermediate (e.g. atomic, body-ordered, or range-separated) predictions are made. We leverage these metrics to understand the learning behavior of different ML models, and to guide efficient dataset construction for model training. We finally implement the formalism for a ML model targeting a coarse-grained system to demonstrate the applicability of the prediction rigidities to an even broader class of atomistic modeling problems.

Establishing coherent momentum-space electronic states in locally ordered materials

Rich momentum-dependent electronic structure naturally arises in solids with long-range crystalline symmetry. Reliable and scalable quantum technologies rely on materials that are either not perfect crystals or non-crystalline, breaking translational symmetry. This poses the fundamental questions of whether coherent momentum-dependent electronic states can arise without long-range order, and how they can be characterized. Here we investigate Bi2Se3, which exists in crystalline, nanocrystalline, and amorphous forms, allowing direct comparisons between varying degrees of spatial ordering. Through angle-resolved photoemission spectroscopy, we show for the first time momentum-dependent band structure with Fermi surface repetitions in an amorphous solid. The experimental data is complemented by a model that accurately reproduces the vertical, dispersive features as well as the replication at higher momenta in the amorphous form. These results reveal that well-defined real-space length scales are sufficient to produce dispersive band structures, and that photoemission can expose the imprint of these length scales on the electronic structure.

Evaluating the Physicochemical Properties-Activity Relationship and Discovering New 1,2-Dihydropyridine Derivatives as Promising Inhibitors for PIM1-Kinase: Evidence from Principal Component Analysis, Molecular Docking, and Molecular Dynamics Studies

In this study, we evaluated the physicochemical properties related to the previously reported anticancer activity of a dataset comprising thirty 1,2-dihydropyridine derivatives. We utilized Principal Component Analysis (PCA) to identify the most significant influencing factors. The PCA analysis showed that the first two principal components accounted for 59.91% of the total variance, indicating a strong correlation between the molecules and specific descriptors. Among the 239 descriptors analyzed, 18 were positively correlated with anticancer activity, clustering with the 12 most active compounds based on their IC50 values. Six of these variables-LogP, Csp3, b_1rotN, LogS, TPSA, and lip_don-are related to drug-likeness potential. Thus, we then ranked the 12 compounds according to these six variables and excluded those violating the drug-likeness criteria, resulting in a shortlist of nine compounds. Next, we investigated the binding affinity of these nine shortlisted compounds with the use of molecular docking towards the PIM-1 Kinase enzyme (PDB: 2OBJ), which is overexpressed in various cancer cells. Compound 6 exhibited the best docking score among the docked compounds, with a docking score of -11.77 kcal/mol, compared to -12.08 kcal/mol for the reference PIM-1 kinase inhibitor, 6-(5-bromo-2-hydroxyphenyl)-2-oxo-4-phenyl-1,2-dihydropyridine-3-carbonitrile. To discover new PIM-1 kinase inhibitors, we designed nine novel compounds featuring hybrid structures of compound 6 and the reference inhibitor. Among these, compound 31 displayed the best binding affinity, with a docking score of -13.11 kcal/mol. Additionally, we performed PubChem database mining using the structure of compound 6 and the similarity search tool, identifying 16 structurally related compounds with various reported biological properties. Among these, compound 52 exhibited the best binding affinity, with a docking score of -13.03 kcal/mol. Finally, molecular dynamics (MD) studies were conducted to confirm the stability of the protein-ligand complexes obtained from docking the studied compounds to PIM-1 kinase, validating the potential of these compounds as PIM-1 kinase inhibitors.

Deciphering diffuse scattering with machine learning and the equivariant foundation model: the case of molten FeO

Bridging the gap between diffuse x-ray or neutron scattering measurements and predicted structures derived from atom-atom pair potentials in disordered materials, has been a longstanding challenge in condensed matter physics. This perspective gives a brief overview of the traditional approaches employed over the past several decades. Namely, the use of approximate interatomic pair potentials that relate three-dimensional structural models to the measured structure factor and its' associated pair distribution function. The use of machine learned interatomic potentials has grown in the past few years, and has been particularly successful in the cases of ionic and oxide systems. Recent advances in large scale sampling, along with a direct integration of scattering measurements into the model development, has provided improved agreement between experiments and large-scale models calculated with quantum mechanical accuracy. However, details of local polyhedral bonding and connectivity in meta-stable disordered systems still require improvement. Here we leverage MACE-MP-0; a newly introduced equivariant foundation model and validate the results against high-quality experimental scattering data for the case of molten iron(II) oxide (FeO). These preliminary results suggest that the emerging foundation model has the potential to surpass the traditional limitations of classical interatomic potentials.

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.

Understanding Defects in Amorphous Silicon with Million-Atom Simulations and Machine Learning

The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone.

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.

Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models

While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many independent variables, such as X-ray/neutron scattering patterns and electromagnetic spectra. To address this challenge, we employ local Gaussian process (LGP) surrogate models to accelerate Bayesian optimization over these complex thermophysical properties. The time-complexity of the LGPs scales linearly in the number of independent variables, in stark contrast to the computationally expensive cubic scaling of conventional Gaussian processes. To illustrate the method, we trained a LGP surrogate model on the radial distribution function of liquid neon and observed a 1,760,000-fold speed-up compared to molecular dynamics simulation, beating a conventional GP by three orders-of-magnitude. We conclude that LGPs are robust and efficient surrogate models poised to expand the application of Bayesian inference in molecular simulations to a broad spectrum of experimental data.

Unravelling the structure of CO2 in silica adsorbents: an NMR and computational perspective

This comprehensive review describes recent advancements in the use of solid-state NMR-assisted methods and computational modeling strategies to unravel gas adsorption mechanisms and CO2 speciation in porous CO2-adsorbent silica materials at the atomic scale. This work provides new perspectives for the innovative modifications of these materials rendering them more amenable to the use of advanced NMR methods.

Modelling atomic and nanoscale structure in the silicon-oxygen system through active machine learning

Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well-known silicon dioxide, there are phases with different stoichiometric composition and nanostructured composites. One of the key challenges in understanding the Si-O system is therefore to accurately account for its nanoscale heterogeneity beyond the length scale of individual atoms. Here we show that a unified computational description of the full Si-O system is indeed possible, based on atomistic machine learning coupled to an active-learning workflow. We showcase applications to very-high-pressure silica, to surfaces and aerogels, and to the structure of amorphous silicon monoxide. In a wider context, our work illustrates how structural complexity in functional materials beyond the atomic and few-nanometre length scales can be captured with active machine learning.

Combined Experimental and Computational Insight into the Role of Substrate in the Synthesis of Two-Dimensional WSe2

Synthesis of large-area transition-metal dichalcogenides (TMDs) with controlled orientation is a significant challenge to their industrial applications. Substrate plays a vital role in determining the final quality of monolayer materials grown via the chemical vapor deposition process by controlling their orientation, crystal structure, and grain boundary. This study determined the binding energy and equilibrium distance for tungsten diselenide (WSe2) monolayers on crystalline and amorphous silicon dioxide and aluminum dioxide substrates. Differently oriented WSe2 monolayers are considered to investigate the role of the substrate in the orientation, binding strength, and equilibrium distance. This study can pave the way to synthesizing high-quality two-dimensional (2D) materials for electronic and chemical applications.

Microscopic mechanisms of pressure-induced amorphous-amorphous transitions and crystallisation in silicon

Some low-coordination materials, including water, silica, and silicon, exhibit polyamorphism, having multiple amorphous forms. However, the microscopic mechanism and kinetic pathway of amorphous-amorphous transition (AAT) remain largely unknown. Here, we use a state-of-the-art machine-learning potential and local structural analysis to investigate the microscopic kinetics of AAT in silicon after a rapid pressure change. We find that the transition from low-density-amorphous (LDA) to high-density-amorphous (HDA) occurs through nucleation and growth, resulting in non-spherical interfaces that underscore the mechanical nature of AAT. In contrast, the reverse transition occurs through spinodal decomposition. Further pressurisation transforms LDA into very-high-density amorphous (VHDA), with HDA serving as an intermediate state. Notably, the final amorphous states are inherently unstable, transitioning into crystals. Our findings demonstrate that AAT and crystallisation are driven by joint thermodynamic and mechanical instabilities, assisted by preordering, occurring without diffusion. This unique mechanical and diffusion-less nature distinguishes AAT from liquid-liquid transitions.

Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope

As the sophistication of machine learning force fields (MLFF) increases to match the complexity of extended molecules and materials, so does the need for tools to properly analyze and assess the practical performance of MLFFs. To go beyond average error metrics and into a complete picture of a model's applicability and limitations, we developed FFAST (force field analysis software and tools): a cross-platform software package designed to gain detailed insights into a model's performance and limitations, complete with an easy-to-use graphical user interface. The software allows the user to gauge the performance of any molecular force field,─such as popular state-of-the-art MLFF models, ─ on various popular data set types, providing general prediction error overviews, outlier detection mechanisms, atom-projected errors, and more. It has a 3D visualizer to find and picture problematic configurations, atoms, or clusters in a large data set. In this paper, the example of the MACE and NequIP models is used on two data sets of interest [stachyose and docosahexaenoic acid (DHA)]─to illustrate the use cases of the software. With this, it was found that carbons and oxygens involved in or near glycosidic bonds inside the stachyose molecule present increased prediction errors. In addition, prediction errors on DHA rise as the molecule folds, especially for the carboxylic group at the edge of the molecule. We emphasize the need for a systematic assessment of MLFF models for ensuring their successful application to the study of dynamics of molecules and materials.

Velocity-Gauge Real-Time Time-Dependent Density Functional Tight-Binding for Large-Scale Condensed Matter Systems

We present a new velocity-gauge real-time, time-dependent density functional tight-binding (VG-rtTDDFTB) implementation in the open-source DFTB+ software package (https://dftbplus.org) for probing electronic excitations in large, condensed matter systems. Our VG-rtTDDFTB approach enables real-time electron dynamics simulations of large, periodic, condensed matter systems containing thousands of atoms with a favorable computational scaling as a function of system size. We provide computational details and benchmark calculations to demonstrate its accuracy and computational parallelizability on a variety of large material systems. As a representative example, we calculate laser-induced electron dynamics in a 512-atom amorphous silicon supercell to highlight the large periodic systems that can be examined with our implementation. Taken together, our VG-rtTDDFTB approach enables new electron dynamics simulations of complex systems that require large periodic supercells, such as crystal defects, complex surfaces, nanowires, and amorphous materials.

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'.

Structure and Bonding in Amorphous Red Phosphorus

Amorphous red phosphorus (a-P) is one of the remaining puzzling cases in the structural chemistry of the elements. Here, we elucidate the structure, stability, and chemical bonding in a-P from first principles, combining machine-learning and density-functional theory (DFT) methods. We show that a-P structures exist with a range of energies slightly higher than those of phosphorus nanorods, to which they are closely related, and that the stability of a-P is linked to the degree of structural relaxation and medium-range order. We thus complete the stability range of phosphorus allotropes [Angew. Chem. Int. Ed. 2014, 53, 11629] by now including the previously poorly understood amorphous phase, and we quantify the covalent and van der Waals interactions in all main phases of phosphorus. We also study the electronic densities of states, including those of hydrogenated a-P. Beyond the present study, our structural models are expected to enable wider-ranging first-principles investigations-for example, of a-P-based battery materials.

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.

Modelling amorphous materials via a joint solid-state NMR and X-ray absorption spectroscopy and DFT approach: application to alumina

Understanding a material's electronic structure is crucial to the development of many functional devices from semiconductors to solar cells and Li-ion batteries. A material's properties, including electronic structure, are dependent on the arrangement of its atoms. However, structure determination (the process of uncovering the atomic arrangement), is impeded, both experimentally and computationally, by disorder. The lack of a verifiable atomic model presents a huge challenge when designing functional amorphous materials. Such materials may be characterised through their local atomic environments using, for example, solid-state NMR and XAS. By using these two spectroscopy methods to inform the sampling of configurations from ab initio molecular dynamics we devise and validate an amorphous model, choosing amorphous alumina to illustrate the approach due to its wide range of technological uses. Our model predicts two distinct geometric environments of AlO₅ coordination polyhedra and determines the origin of the pre-edge features in the Al K-edge XAS. From our model we construct an average electronic density of states for amorphous alumina, and identify localized states at the conduction band minimum (CBM). We show that the presence of a pre-edge peak in the XAS is a result of transitions from the Al 1s to Al 3s states at the CBM. Deconvoluting this XAS by coordination geometry reveals contributions from both AlO₄ and AlO₅ geometries at the CBM give rise to the pre-edge, which provides insight into the role of AlO₅ in the electronic structure of alumina. This work represents an important advance within the field of solid-state amorphous modelling, providing a method for developing amorphous models through the comparison of experimental and computationally derived spectra, which may then be used to determine the electronic structure of amorphous materials.

Plasma Oxidation of Copper: Molecular Dynamics Study with Neural Network Potentials

The formation of thin oxide films is of significant scientific and practical interest. In particular, the semiconductor industry is interested in developing a plasma atomic layer etching process to pattern copper, replacing the dual Damascene process. Using a nonthermal oxygen plasma to convert the metallic copper into copper oxide, followed by a formic acid organometallic reaction to etch the copper oxide, this process has shown great promise. However, the current process is not optimal because the plasma oxidation step is not self-limiting, hampering the degree of thickness control. In the present study, a neural network potential for the binary interaction between copper and oxygen is developed and validated against first-principles calculations. This potential covers the entire range of potential energy surfaces of metallic copper, copper oxides, atomic oxygen, and molecular oxygen. The usable kinetic energy ranges from 0 to 20 eV. Using this potential, the plasma oxidation of copper surfaces was studied with large-scale molecular dynamics at atomic resolution, with an accuracy approaching that of the first principle calculations. An amorphous layer of CuO is formed on Cu, with thicknesses reaching 2.5 nm. Plasma is found to create an intense local heating effect that rapidly dissipates across the thickness of the film. The range of this heating effect depends on the kinetic energy of the ions. A higher ion energy leads to a longer range, which sustains faster-than-thermal rates for longer periods of time for the oxide growth. Beyond the range of this agitation, the growth is expected to be limited to the thermally activated rate. High-frequency, repeated ion impacts result in a microannealing effect that leads to a quasicrystalline oxide beneath the amorphized layer. The crystalline layer slows down oxide growth. Growth rate is fitted to the temperature gradient due to ion-induced thermal agitations, to obtain an apparent activation energy of 1.0 eV. A strategy of lowering the substrate temperature and increasing plasma power is proposed as being favorable for more self-limited oxidation.

Quantum Chemical Roots of Machine-Learning Molecular Similarity Descriptors

In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth overlap of atomic positions (SOAP). We adopt a basic framework that allows us to connect both descriptors to electronic structure theory. This framework enables us to then define two new descriptors that are more closely related to electronic structure theory, which we call Coulomb lists and smooth overlap of electron densities (SOED). By investigating their usefulness as molecular similarity descriptors, we gain new insights into how and why Coulomb matrix and SOAP work. Moreover, Coulomb lists avoid the somewhat mysterious diagonalization step of the Coulomb matrix and might provide a direct means to extract subsystem information that can be compared across Born-Oppenheimer surfaces of varying dimension. For the electron density, we derive the necessary formalism to create the SOED measure in close analogy to SOAP. Because this formalism is more involved than that of SOAP, we review the essential theory as well as introduce a set of approximations that eventually allow us to work with SOED in terms of the same implementation available for the evaluation of SOAP. We focus our analysis on elementary reaction steps, where transition state structures are more similar to either reactant or product structures than the latter two are with respect to one another. The prediction of electronic energies of transition state structures can, however, be more difficult than that of stable intermediates due to multi-configurational effects. The question arises to what extent molecular similarity descriptors rooted in electronic structure theory can resolve these intricate effects.

Indirect learning and physically guided validation of interatomic potential models

Machine learning (ML) based interatomic potentials are emerging tools for material simulations, but require a trade-off between accuracy and speed. Here, we show how one can use one ML potential model to train another: we use an accurate, but more computationally expensive model to generate reference data (locations and labels) for a series of much faster potentials. Without the need for quantum-mechanical reference computations at the secondary stage, extensive reference datasets can be easily generated, and we find that this improves the quality of fast potentials with less flexible functional forms. We apply the technique to disordered silicon, including a simulation of vitrification and polycrystalline grain formation under pressure with a system size of a million atoms. Our work provides conceptual insight into the ML of interatomic potential models and suggests a route toward accelerated simulations of condensed-phase systems.

Attention-wise masked graph contrastive learning for predicting molecular property

MOTIVATION

Accurate and efficient prediction of the molecular property is one of the fundamental problems in drug research and development. Recent advancements in representation learning have been shown to greatly improve the performance of molecular property prediction. However, due to limited labeled data, supervised learning-based molecular representation algorithms can only search limited chemical space and suffer from poor generalizability.

RESULTS

In this work, we proposed a self-supervised learning method, ATMOL, for molecular representation learning and properties prediction. We developed a novel molecular graph augmentation strategy, referred to as attention-wise graph masking, to generate challenging positive samples for contrastive learning. We adopted the graph attention network as the molecular graph encoder, and leveraged the learned attention weights as masking guidance to generate molecular augmentation graphs. By minimization of the contrastive loss between original graph and augmented graph, our model can capture important molecular structure and higher order semantic information. Extensive experiments showed that our attention-wise graph mask contrastive learning exhibited state-of-the-art performance in a couple of downstream molecular property prediction tasks. We also verified that our model pretrained on larger scale of unlabeled data improved the generalization of learned molecular representation. Moreover, visualization of the attention heatmaps showed meaningful patterns indicative of atoms and atomic groups important to specific molecular property.

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Modelling and understanding properties of materials from first principles require knowledge of the underlyingatomistic structure. This entails knowing the individual chemical identity and position of all atoms involved.Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, andbulk phases of amorphous and solid materials represents a difficult high-dimensional global optimizationproblem. The rise of machine learning techniques in materials science has, however, led to many compellingdevelopments that may speed up structure searches. The complexity of such new methods has prompted aneed for an efficient way of assembling them into global optimization algorithms that can be experimentedwith. In this paper, we introduce the Atomistic Global Optimization X (AGOX) framework and code, asa customizable approach that enables efficient building and testing of global optimization algorithms. Amodular way of expressing global optimization algorithms is described and modern programming practicesare used to enable that modularity in the freely available AGOX python package. A number of examplesof global optimization approaches are implemented and analyzed. This ranges from random search andbasin-hopping to machine learning aided approaches with on-the-fly learnt surrogate energy landscapes. Themethods are show-cased on problems ranging from supported clusters over surface reconstructions to largecarbon clusters and metal-nitride clusters incorporated into graphene sheets.

Topological descriptor of thermal conductivity in amorphous Si

Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a longstanding problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence of a medium-range order (MRO) has been intensively discussed. However, the specific atomic arrangement corresponding to the MRO and its relationship with physical properties, such as thermal conductivity, remains elusive. We solved this problem by combining topological data analysis, machine learning, and molecular dynamics simulations. Using persistent homology, we constructed a topological descriptor that can predict thermal conductivity. Moreover, from the inverse analysis of the descriptor, we determined the typical ring features correlated with both the thermal conductivity and MRO. The results could provide an avenue for controlling material characteristics through the topology of the nanostructures.

Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network - a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions - and demonstrate its utility by modeling liquid water with and without applied fields.

Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides

The application of machine learning to theoretical chemistry has made it possible to combine the accuracy of quantum chemical energetics with the thorough sampling of finite-temperature fluctuations. To reach this goal, a diverse set of methods has been proposed, ranging from simple linear models to kernel regression and highly nonlinear neural networks. Here we apply two widely different approaches to the same, challenging problem: the sampling of the conformational landscape of polypeptides at finite temperature. We develop a local kernel regression (LKR) coupled with a supervised sparsity method and compare it with a more established approach based on Behler-Parrinello type neural networks. In the context of the LKR, we discuss how the supervised selection of the reference pool of environments is crucial to achieve accurate potential energy surfaces at a competitive computational cost and leverage the locality of the model to infer which chemical environments are poorly described by the DFTB baseline. We then discuss the relative merits of the two frameworks and perform Hamiltonian-reservoir replica-exchange Monte Carlo sampling and metadynamics simulations, respectively, to demonstrate that both frameworks can achieve converged and transferable sampling of the conformational landscape of complex and flexible biomolecules with comparable accuracy and computational cost.

Cluster Fragments in Amorphous Phosphorus and their Evolution under Pressure

Amorphous phosphorus (a-P) has long attracted interest because of its complex atomic structure, and more recently as an anode material for batteries. However, accurately describing and understanding a-P at the atomistic level remains a challenge. Here, it is shown that large-scale molecular-dynamics simulations, enabled by a machine-learning (ML)-based interatomic potential for phosphorus, can give new insights into the atomic structure of a-P and how this structure changes under pressure. The structural model so obtained contains abundant five-membered rings, as well as more complex seven- and eight-atom clusters. Changes in the simulated first sharp diffraction peak during compression and decompression indicate a hysteresis in the recovery of medium-range order. An analysis of cluster fragments, large rings, and voids suggests that moderate pressure (up to about 5 GPa) does not break the connectivity of clusters, but higher pressure does. The work provides a starting point for further computational studies of the structure and properties of a-P, and more generally it exemplifies how ML-driven modeling can accelerate the understanding of disordered functional materials.

Structural Transformation of Heterogeneous Materials for Electrocatalytic Oxygen Evolution Reaction

Electrochemical water splitting for hydrogen generation is a promising pathway for renewable energy conversion and storage. One of the most important issues for efficient water splitting is to develop cost-effective and highly efficient electrocatalysts to drive sluggish oxygen-evolution reaction (OER) at the anode side. Notably, structural transformation such as surface oxidation of metals or metal nonoxide compounds and surface amorphization of some metal oxides during OER have attracted growing attention in recent years. The investigation of structural transformation in OER will contribute to the in-depth understanding of accurate catalytic mechanisms and will finally benefit the rational design of catalytic materials with high activity. In this Review, we provide an overview of heterogeneous materials with obvious structural transformation during OER electrocatalysis. To gain insight into the essence of structural transformation, we summarize the driving forces and critical factors that affect the transformation process. In addition, advanced techniques that are used to probe chemical states and atomic structures of transformed surfaces are also introduced. We then discuss the structure of active species and the relationship between catalytic performance and structural properties of transformed materials. Finally, the challenges and prospects of heterogeneous OER electrocatalysis are presented.

Computational UV spectra for amorphous solids of small molecules

Ices in the interstellar medium largely exist as amorphous solids composed of small molecules including ammonia, water, and carbon dioxide. Describing gas-phase molecules can be readily accomplished with current high-level quantum chemical calculations with the description of crystalline solids becoming more readily accomplished. Differently, amorphous solids require more novel approaches. The present work describes a method for generating amorphous structures and constructing electronic spectra through a combination of quantum chemical calculations and statistical mechanics. The structures are generated through a random positioning program and DFT methods, such as ωB97-XD and CAM-B3LYP. A Boltzmann distribution weights the excitations to compile a final spectrum from a sampling of molecular clusters. Three ice analogs are presented herein consisting of ammonia, carbon dioxide, and water. Ammonia and carbon dioxide provide semi-quantitative agreement with experiment for CAM-B3LYP/6-311++G(2d,2p) from 30 clusters of 8 molecules. Meanwhile, the amorphous water description improves when the sample size is increased in cluster size and count to as many as 105 clusters of 32 water molecules. The described methodology can produce highly comparative descriptions of electronic spectra for ice analogs and can be used to predict electronic spectra for other ice analogs.

Tension-compression asymmetry in amorphous silicon

Hard and brittle materials usually exhibit a much lower strength when loaded in tension than in compression. However, this common-sense behaviour may not be intrinsic to these materials, but arises from their higher flaw sensitivity to tensile loading. Here, we demonstrate a reversed and unusually pronounced tension-compression asymmetry (tensile strength exceeds compressive strength by a large margin) in submicrometre-sized samples of isotropic amorphous silicon. The abnormal asymmetry in the yield strength and anelasticity originates from the reduction in shear modulus and the densification of the shear-activated configuration under compression, altering the magnitude of the activation energy barrier for elementary shear events in amorphous Si. In situ coupled electrical tests corroborate that compressive strains indeed cause increased atomic coordination (metallization) by transforming some local structures from sp³-bonded semiconducting motifs to more metallic-like sites, lending credence to the mechanism we propose. This finding opens up an unexplored regime of intrinsic tension-compression asymmetry in materials.

Anisotropic Disorder and Thermal Stability of Silicane

Atomically thin silicon nanosheets (SiNSs), such as silicane, have potential for next-generation computing paradigms, such as integrated photonics, owing to their efficient photoluminescence emission and complementary-metal-oxide-semiconductor (CMOS) compatibility. To be considered as a viable material for next-generation photonics, the SiNSs must retain their structural and optical properties at operating temperatures. However, the intersheet disorder of SiNSs and their nanoscale structure makes structural characterization difficult. Here, we use synchrotron X-ray diffraction and atomic pair distribution function (PDF) analysis to characterize the anisotropic disorder within SiNSs, demonstrating they exhibit disorder within the intersheet spacing, but have little translational or rotational disorder among adjacent SiNSs. Furthermore, we identify changes in their structural, chemical, and optical properties after being heated in an inert atmosphere up to 475 °C. We characterized changes of the annealed SiNSs using synchrotron-based total X-ray scattering, infrared spectroscopy, X-ray photoelectron spectroscopy, scanning electron microscopy, electron paramagnetic resonance, absorbance, photoluminescence, and excited-state lifetime. We find that the silicon framework is robust, with an onset of amorphization at ∼300 °C, which is well above the required operating temperatures of photonic devices. Above ∼300 °C, we demonstrate that the SiNSs begin to coalesce while keeping their translational alignment to yield amorphous silicon nanosheets. In addition, our DFT results provide information on the structure, energetics, band structures, and vibrational properties of 11 distinct oxygen-containing SiNSs. Overall, these results provide critical information for the implementation of atomically thin silicon nanosheets in next-generation CMOS-compatible integrated photonic devices.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α)≡dΔ(α)/dα, the first derivative of the optimal gap-to-midgap ratio Δ(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, S_{QWS}(α). Even more surprisingly, the values of S(α) for our disordered networks converge to S_{QWS}(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.

Machine-learned potentials for next-generation matter simulations

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

Automated Development of Molten Salt Machine Learning Potentials: Application to LiCl

The in silico modeling of molten salts is critical for emerging "carbon-free" energy applications but is inhibited by the cost of quantum mechanically treating the high polarizabilities of molten salts. Here, we integrate configurational sampling using classical force fields with active learning to automate and accelerate the generation of Gaussian approximation potentials (GAP) for molten salts. This methodology reduces the number of expensive ab initio evaluations required for training set generation to O(100), enabling the facile parametrization of a molten LiCl GAP model that exhibits a 19 000-fold speedup relative to AIMD. The developed molten LiCl GAP model is applied to sample extended spatiotemporal scales, permitting new physical insights into molten LiCl's coordination structure as well as experimentally validated predictions of structures, densities, self-diffusion constants, and ionic conductivities. The developed methodology significantly lowers the barrier to the in silico understanding and design of molten salts across the periodic table.

Inverse Design of Fe-Based Bulk Metallic Glasses Using Machine Learning

Fe-based bulk metallic glasses (BMGs) are a unique class of materials that are attracting attention in a wide variety of applications owing to their physical properties. Several studies have investigated and designed the relationships between alloy composition and thermal properties of BMGs using an artificial neural network (ANN). The limitation of the wide-scale use of these models is that the required composition is yet to be found despite numerous case studies. To address this issue, we trained an ANN to design Fe-based BMGs that predict the thermal properties. Models were trained using only the composition of the alloy as input and were created from a database of more than 150 experimental data of Fe-based BMGs from relevant literature. We adopted these ANN models to design BMGs with thermal properties to satisfy the intended purpose using particle swarm optimization. A melt spinner was employed to fabricate the designed alloys. X-ray diffraction and differential thermal analysis tests were used to evaluate the specimens.

Experimentally Driven Automated Machine-Learned Interatomic Potential for a Refractory Oxide

Understanding the structure and properties of refractory oxides is critical for high temperature applications. In this work, a combined experimental and simulation approach uses an automated closed loop via an active learner, which is initialized by x-ray and neutron diffraction measurements, and sequentially improves a machine-learning model until the experimentally predetermined phase space is covered. A multiphase potential is generated for a canonical example of the archetypal refractory oxide, HfO_{2}, by drawing a minimum number of training configurations from room temperature to the liquid state at ∼2900 °C. The method significantly reduces model development time and human effort.

Distilling nanoscale heterogeneity of amorphous silicon using tip-enhanced Raman spectroscopy (TERS) via multiresolution manifold learning

Accurately identifying the local structural heterogeneity of complex, disordered amorphous materials such as amorphous silicon is crucial for accelerating technology development. However, short-range atomic ordering quantification and nanoscale spatial resolution over a large area on a-Si have remained major challenges and practically unexplored. We resolve phonon vibrational modes of a-Si at a lateral resolution of <60 nm by tip-enhanced Raman spectroscopy. To project the high dimensional TERS imaging to a two-dimensional manifold space and categorize amorphous silicon structure, we developed a multiresolution manifold learning algorithm. It allows for quantifying average Si-Si distortion angle and the strain free energy at nanoscale without a human-specified physical threshold. The multiresolution feature of the multiresolution manifold learning allows for distilling local defects of ultra-low abundance (< 0.3%), presenting a new Raman mode at finer resolution grids. This work promises a general paradigm of resolving nanoscale structural heterogeneity and updating domain knowledge for highly disordered materials.

Measuring transferability issues in machine-learning force fields: the example of gold–iron interactions with linearized potentials

Machine-learning force fields have been increasingly employed in order to extend the possibility of current first-principles calculations. However, the transferability of the obtained potential cannot always be guaranteed in situations that are outside the original database. To study such limitation, we examined the very difficult case of the interactions in gold–iron nanoparticles. For the machine-learning potential, we employed a linearized formulation that is parameterized using a penalizing regression scheme which allows us to control the complexity of the obtained potential. We showed that while having a more complex potential allows for a better agreement with the training database, it can also lead to overfitting issues and a lower accuracy in untrained systems.

Can we predict materials that can be synthesised?

The discovery of materials is an important element in the development of new technologies and abilities that can help humanity tackle many challenges. Materials discovery is frustratingly slow, with the large time and resource cost often providing only small gains in property performance. Furthermore, researchers are unwilling to take large risks that they will only know the outcome of months or years later. Computation is playing an increasing role in allowing rapid screening of large numbers of materials from vast search space to identify promising candidates for laboratory synthesis and testing. However, there is a problem, in that many materials computationally predicted to have encouraging properties cannot be readily realised in the lab. This minireview looks at how we can tackle the problem of confirming that hypothetical materials are synthetically realisable, through consideration of all the stages of the materials discovery process, from obtaining the components, reacting them to a material in the correct structure, through to processing into a desired form. In an ideal world, a material prediction would come with an associated 'recipe' for the successful laboratory preparation of the material. We discuss the opportunity to thus prevent wasted effort in experimental discovery programmes, including those using automation, to accelerate the discovery of novel materials.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

Acceleration of PDE-Based Biological Simulation Through the Development of Neural Network Metamodels

PURPOSE OF REVIEW

Partial differential equation (PDE) mathematical models of biological systems and the simulation approaches used to solve them are widely used to test hypotheses and infer regulatory interactions based on optimization of the PDE model against the observed data. In this review, we discuss the ability of powerful machine learning methods to accelerate the parametric screening of biophysical informed- PDE systems.

RECENT FINDINGS

A major shortcoming in more broad adaptation of PDE-based models is the high computational complexity required to solve and optimize the models and it requires many simulations to traverse the very high-dimensional parameter spaces during model calibration and inference tasks. For instance, when scaling up to tens of millions of simulations for optimization and sensitivity analysis of the PDE models, compute times quickly extend from months to years for sufficient coverage to solve the problems. For many systems, this brute-force approach is simply not feasible. Recently, neural network metamodels have been shown to be an efficient way to accelerate PDE model calibration and here we look at the benefits and limitations in extending the PDE acceleration methods to improve optimization and sensitivity analysis.

SUMMARY

We use an example simulation to quantitatively and qualitatively show how neural network metamodels can be accurate and fast and demonstrate their potential for optimization of complex spatiotemporal problems in biology. We expect these approaches will be broadly applied to speed up scientific research and discovery in biology and other systems that can be described by complex PDE systems.

Recent advances in bioelectronics chemistry

Research in bioelectronics is highly interdisciplinary, with many new developments being based on techniques from across the physical and life sciences. Advances in our understanding of the fundamental chemistry underlying the materials used in bioelectronic applications have been a crucial component of many recent discoveries. In this review, we highlight ways in which a chemistry-oriented perspective may facilitate novel and deep insights into both the fundamental scientific understanding and the design of materials, which can in turn tune the functionality and biocompatibility of bioelectronic devices. We provide an in-depth examination of several developments in the field, organized by the chemical properties of the materials. We conclude by surveying how some of the latest major topics of chemical research may be further integrated with bioelectronics.