Origins of structural and electronic transitions in disordered silicon.

Structurally disordered materials pose fundamental questions1-4, including how different disordered phases ('polyamorphs') can coexist and transform from one phase to another5-9. Amorphous silicon has been extensively studied; it forms a fourfold-coordinated, covalent network at ambient conditions and much-higher-coordinated, metallic phases under pressure10-12. However, a detailed mechanistic understanding of the structural transitions in disordered silicon has been lacking, owing to the intrinsic limitations of even the most advanced experimental and computational techniques, for example, in terms of the system sizes accessible via simulation. Here we show how atomistic machine learning models trained on accurate quantum mechanical computations can help to describe liquid-amorphous and amorphous-amorphous transitions for a system of 100,000 atoms (ten-nanometre length scale), predicting structure, stability and electronic properties. Our simulations reveal a three-step transformation sequence for amorphous silicon under increasing external pressure. First, polyamorphic low- and high-density amorphous regions are found to coexist, rather than appearing sequentially. Then, we observe a structural collapse into a distinct very-high-density amorphous (VHDA) phase. Finally, our simulations indicate the transient nature of this VHDA phase: it rapidly nucleates crystallites, ultimately leading to the formation of a polycrystalline structure, consistent with experiments13-15 but not seen in earlier simulations11,16-18. A machine learning model for the electronic density of states confirms the onset of metallicity during VHDA formation and the subsequent crystallization. These results shed light on the liquid and amorphous states of silicon, and, in a wider context, they exemplify a machine learning-driven approach to predictive materials modelling.

Dynamic Local Structure in Caesium Lead Iodide: Spatial Correlation and Transient Domains.

Metal halide perovskites are multifunctional semiconductors with tunable structures and properties. They are highly dynamic crystals with complex octahedral tilting patterns and strongly anharmonic atomic behavior. In the higher temperature, higher symmetry phases of these materials, several complex structural features are observed. The local structure can differ greatly from the average structure and there is evidence that dynamic 2D structures of correlated octahedral motion form. An understanding of the underlying complex atomistic dynamics is, however, still lacking. In this work, the local structure of the inorganic perovskite CsPbI3 is investigated using a new machine learning force field based on the atomic cluster expansion framework. Through analysis of the temporal and spatial correlation observed during large-scale simulations, it is revealed that the low frequency motion of octahedral tilts implies a double-well effective potential landscape, even well into the cubic phase. Moreover, dynamic local regions of lower symmetry are present within both higher symmetry phases. These regions are planar and the length and timescales of the motion are reported. Finally, the spatial arrangement of these features and their interactions are investigated and visualized, providing a comprehensive picture of local structure in the higher symmetry phases.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects.

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Toward transferable empirical valence bonds: Making classical force fields reactive.

The empirical valence bond technique allows classical force fields to model reactive processes. However, parametrization from experimental data or quantum mechanical calculations is required for each reaction present in the simulation. We show that the parameters present in the empirical valence bond method can be predicted using a neural network model and the SMILES strings describing a reaction. This removes the need for quantum calculations in the parametrization of the empirical valence bond technique. In doing so, we have taken the first steps toward defining a new procedure for enabling reactive atomistic simulations. This procedure would allow researchers to use existing classical force fields for reactive simulations, without performing additional quantum mechanical calculations.

Tensor-Reduced Atomic Density Representations.

Density-based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modeling, and the visualization and analysis of material datasets. The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. By exploiting symmetry, we recast this approach as tensor factorization of the standard neighbour-density-based descriptors and, using a new notation, identify connections to existing compression algorithms. In doing so, we form compact tensor-reduced representation of the local atomic environment whose size does not depend on the number of chemical elements, is systematically convergable, and therefore remains applicable to a wide range of data analysis and regression tasks.

Physics-Inspired Structural Representations for Molecules and Materials.

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

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.

Evaluation of the MACE force field architecture: From medicinal chemistry to materials science.

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation, and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems, from amorphous carbon, universal materials modeling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimization to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

Global analysis of energy landscapes for materials modeling: A test case for C60.

In this contribution, we employ computational tools from the energy landscape approach to test Gaussian Approximation Potentials (GAPs) for C60. In particular, we apply basin-hopping global optimization and explore the landscape starting from the low-lying minima using discrete path sampling. We exploit existing databases of minima and transition states harvested from previous work using tight-binding potentials. We explore the energy landscape for the full range of structures and pathways spanning from the buckminsterfullerene global minimum up to buckybowls. In the initial GAP model, the fullerene part of the landscape is reproduced quite well. However, there are extensive families of C1@C59 and C2@C58 structures that lie lower in energy. We succeeded in refining the potential to remove these artifacts by simply including two minima from the C2@C58 families found by global landscape exploration. We suggest that the energy landscape approach could be used systematically to test and improve machine learning interatomic potentials.

Gaussian approximation potentials: Theory, software implementation and application examples.

Gaussian Approximation Potentials (GAPs) are a class of Machine Learned Interatomic Potentials routinely used to model materials and molecular systems on the atomic scale. The software implementation provides the means for both fitting models using ab initio data and using the resulting potentials in atomic simulations. Details of the GAP theory, algorithms and software are presented, together with detailed usage examples to help new and existing users. We review some recent developments to the GAP framework, including Message Passing Interface parallelisation of the fitting code enabling its use on thousands of central processing unit cores and compression of descriptors to eliminate the poor scaling with the number of different chemical elements.

wfl Python toolkit for creating machine learning interatomic potentials and related atomistic simulation workflows.

Predictive atomistic simulations are increasingly employed for data intensive high throughput studies that take advantage of constantly growing computational resources. To handle the sheer number of individual calculations that are needed in such studies, workflow management packages for atomistic simulations have been developed for a rapidly growing user base. These packages are predominantly designed to handle computationally heavy ab initio calculations, usually with a focus on data provenance and reproducibility. However, in related simulation communities, e.g., the developers of machine learning interatomic potentials (MLIPs), the computational requirements are somewhat different: the types, sizes, and numbers of computational tasks are more diverse and, therefore, require additional ways of parallelization and local or remote execution for optimal efficiency. In this work, we present the atomistic simulation and MLIP fitting workflow management package wfl and Python remote execution package ExPyRe to meet these requirements. With wfl and ExPyRe, versatile atomic simulation environment based workflows that perform diverse procedures can be written. This capability is based on a low-level developer-oriented framework, which can be utilized to construct high level functionality for user-friendly programs. Such high level capabilities to automate machine learning interatomic potential fitting procedures are already incorporated in wfl, which we use to showcase its capabilities in this work. We believe that wfl fills an important niche in several growing simulation communities and will aid the development of efficient custom computational tasks.

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.

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.

Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions" [J. Chem. Phys. 156, 034302 (2022)].

The "quasi-constant" smooth overlap of atomic position and atom-centered symmetry function fingerprint manifolds recently discovered by Parsaeifard and Goedecker [J. Chem. Phys. 156, 034302 (2022)] are closely related to the degenerate pairs of configurations, which are known shortcomings of all low-body-order atom-density correlation representations of molecular structures. Configurations that are rigorously singular-which we demonstrate can only occur in finite, discrete sets and not as a continuous manifold-determine the complete failure of machine-learning models built on this class of descriptors. The "quasi-constant" manifolds, on the other hand, exhibit low but non-zero sensitivity to atomic displacements. As a consequence, for any such manifold, it is possible to optimize model parameters and the training set to mitigate their impact on learning even though this is often impractical and it is preferable to use descriptors that avoid both exact singularities and the associated numerical instability.

Mapping Materials and Molecules.

The visualization of data is indispensable in scientific research, from the early stages when human insight forms to the final step of communicating results. In computational physics, chemistry and materials science, it can be as simple as making a scatter plot or as straightforward as looking through the snapshots of atomic positions manually. However, as a result of the "big data" revolution, these conventional approaches are often inadequate. The widespread adoption of high-throughput computation for materials discovery and the associated community-wide repositories have given rise to data sets that contain an enormous number of compounds and atomic configurations. A typical data set contains thousands to millions of atomic structures, along with a diverse range of properties such as formation energies, band gaps, or bioactivities.It would thus be desirable to have a data-driven and automated framework for visualizing and analyzing such structural data sets. The key idea is to construct a low-dimensional representation of the data, which facilitates navigation, reveals underlying patterns, and helps to identify data points with unusual attributes. Such data-intensive maps, often employing machine learning methods, are appearing more and more frequently in the literature. However, to the wider community, it is not always transparent how these maps are made and how they should be interpreted. Furthermore, while these maps undoubtedly serve a decorative purpose in academic publications, it is not always apparent what extra information can be garnered from reading or making them.This Account attempts to answer such questions. We start with a concise summary of the theory of representing chemical environments, followed by the introduction of a simple yet practical conceptual approach for generating structure maps in a generic and automated manner. Such analysis and mapping is made nearly effortless by employing the newly developed software tool ASAP. To showcase the applicability to a wide variety of systems in chemistry and materials science, we provide several illustrative examples, including crystalline and amorphous materials, interfaces, and organic molecules. In these examples, the maps not only help to sift through large data sets but also reveal hidden patterns that could be easily missed using conventional analyses.The explosion in the amount of computed information in chemistry and materials science has made visualization into a science in itself. Not only have we benefited from exploiting these visualization methods in previous works, we also believe that the automated mapping of data sets will in turn stimulate further creativity and exploration, as well as ultimately feed back into future advances in the respective fields.

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.

Incompleteness of Atomic Structure Representations.

Many-body descriptors are widely used to represent atomic environments in the construction of machine-learned interatomic potentials and more broadly for fitting, classification, and embedding tasks on atomic structures. There is a widespread belief in the community that three-body correlations are likely to provide an overcomplete description of the environment of an atom. We produce several counterexamples to this belief, with the consequence that any classifier, regression, or embedding model for atom-centered properties that uses three- (or four)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centered contributions mitigates the impact of this fundamental deficiency-explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.

A machine learning based intramolecular potential for a flexible organic molecule.

Quantum mechanical predictive modelling in chemistry and biology is often hindered by the long time scales and large system sizes required of the computational model. Here, we employ the kernel regression machine learning technique to construct an analytical potential, using the Gaussian Approximation Potential software and framework, that reproduces the quantum mechanical potential energy surface of a small, flexible, drug-like molecule, 3-(benzyloxy)pyridin-2-amine. Challenges linked to the high dimensionality of the configurational space of the molecule are overcome by developing an iterative training protocol and employing a representation that separates short and long range interactions. The analytical model is connected to the MCPRO simulation software, which allows us to perform Monte Carlo simulations of the small molecule bound to two proteins, p38 MAP kinase and leukotriene A4 hydrolase, as well as in water. We demonstrate that our machine learning based intramolecular model is transferable to the condensed phase, and demonstrate that the use of a faithful representation of the quantum mechanical potential energy surface can result in corrections to absolute protein-ligand binding free energies of up to 2 kcal mol-1 in the example studied here.

Copper Transporter ATP7A (Copper-Transporting P-Type ATPase/Menkes ATPase) Limits Vascular Inflammation and Aortic Aneurysm Development: Role of MicroRNA-125b.

OBJECTIVE: Copper (Cu) is essential micronutrient, and its dysregulation is implicated in aortic aneurysm (AA) development. The Cu exporter ATP7A (copper-transporting P-type ATPase/Menkes ATPase) delivers Cu via the Cu chaperone Atox1 (antioxidant 1) to secretory Cu enzymes, such as lysyl oxidase, and excludes excess Cu. Lysyl oxidase is shown to protect against AA formation. However, the role and mechanism of ATP7A in AA pathogenesis remain unknown. Approach and Results: Here, we show that Cu chelator markedly inhibited Ang II (angiotensin II)-induced abdominal AA (AAA) in which ATP7A expression was markedly downregulated. Transgenic ATP7A overexpression prevented Ang II-induced AAA formation. Conversely, Cu transport dysfunctional ATP7Amut/+/ApoE-/- mice exhibited robust AAA formation and dissection, excess aortic Cu accumulation as assessed by X-ray fluorescence microscopy, and reduced lysyl oxidase activity. In contrast, AAA formation was not observed in Atox1-/-/ApoE-/- mice, suggesting that decreased lysyl oxidase activity, which depends on both ATP7A and Atox1, was not sufficient to develop AAA. Bone marrow transplantation suggested importance of ATP7A in vascular cells, not bone marrow cells, in AAA development. MicroRNA (miR) array identified miR-125b as a highly upregulated miR in AAA from ATP7Amut/+/ApoE-/- mice. Furthermore, miR-125b target genes (histone methyltransferase Suv39h1 and the NF-κB negative regulator TNFAIP3 [tumor necrosis factor alpha induced protein 3]) were downregulated, which resulted in increased proinflammatory cytokine expression, aortic macrophage recruitment, MMP (matrix metalloproteinase)-2/9 activity, elastin fragmentation, and vascular smooth muscle cell loss in ATP7Amut/+/ApoE-/- mice and reversed by locked nucleic acid-anti-miR-125b infusion. CONCLUSIONS: ATP7A downregulation/dysfunction promotes AAA formation via upregulating miR-125b, which augments proinflammatory signaling in a Cu-dependent manner. Thus, ATP7A is a potential therapeutic target for inflammatory vascular disease.

Functional movements of the GABA type A receptor.

We have performed a parallel tempering crankshaft motion Monte Carlo simulation on a model of the GABA type A receptor with the aim of exploring a wide variety of local conformational space. We develop a novel method to analyse the protein movements in terms of a correlation tensor and use this to explore the gating process, that is, how agonist binding could cause ion channel opening. We find that simulated binding impulses to varying clusters of GABA binding site residues produce channel opening, and that equivalent impulses to single GABA sites produce partial opening.