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Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry., Comment: 119 pages, 63 figures, 37MB PDF

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

Machine Learning (ML) models have, in contrast to their usefulness in molecular dynamics studies, had limited success as surrogate potentials for reaction barrier search. It is due to the scarcity of training data in relevant transition state regions of chemical space. Currently, available datasets for training ML models on small molecular systems almost exclusively contain configurations at or near equilibrium. In this work, we present the dataset Transition1x containing 9.6 million Density Functional Theory (DFT) calculations of forces and energies of molecular configurations on and around reaction pathways at the wB97x/6-31G(d) level of theory. The data was generated by running Nudged Elastic Band (NEB) calculations with DFT on 10k reactions while saving intermediate calculations. We train state-of-the-art equivariant graph message-passing neural network models on Transition1x and cross-validate on the popular ANI1x and QM9 datasets. We show that ML models cannot learn features in transition-state regions solely by training on hitherto popular benchmark datasets. Transition1x is a new challenging benchmark that will provide an important step towards developing next-generation ML force fields that also work far away from equilibrium configurations and reactive systems.

Quantum mechanical methods like Density Functional Theory (DFT) are used with great success alongside efficient search algorithms for studying kinetics of reactive systems. However, DFT is prohibitively expensive for large scale exploration. Machine Learning (ML) models have turned out to be excellent emulators of small molecule DFT calculations and could possibly replace DFT in such tasks. For kinetics, success relies primarily on the models capability to accurately predict the Potential Energy Surface (PES) around transition-states and Minimal Energy Paths (MEPs). Previously this has not been possible due to scarcity of relevant data in the literature. In this paper we train state of the art equivariant Graph Neural Network (GNN)-based models on around 10.000 elementary reactions from the Transition1x dataset. We apply the models as potentials for the Nudged Elastic Band (NEB) algorithm and achieve a Mean Average Error (MAE) of 0.13+/-0.03 eV on barrier energies on unseen reactions. We compare the results against equivalent models trained on QM9 and ANI1x. We also compare with and outperform Density Functional based Tight Binding (DFTB) on both accuracy and computational resource. The implication is that ML models, given relevant data, are now at a level where they can be applied for downstream tasks in quantum chemistry transcending prediction of simple molecular features.

We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from $r_s=1$ to $r_s=100$, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ans\"{a}tze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high quality wave functions in computing the reduced single particle density matrix. This contribution establishes neural network models as flexible and high precision Ans\"{a}tze for periodic electronic systems, an important step towards applications to crystalline solids.

The interactions between water and hydroxyl species on Pt(111) surfaces have been intensely investigated due to their importance to fuel cell electrocatalysis. Here we present a room temperature molecular dynamics study of their structure and energetics using an ensemble of neural network potentials, which allow us to obtain unprecedented statistical sampling. We first study the energetics of hydroxyl formation, where we find a near-linear adsorption energy profile, which exhibits a soft and gradual increase in the differential adsorption energy at high hydroxyl coverages. This is strikingly different from the predictions of the conventional bilayer model, which displays a kink at 1/3ML OH coverage indicating a sizeable jump in differential adsorption energy, but within the statistical uncertainty of previously reported ab initio molecular dynamics studies. We then analyze the structure of the interface, where we provide evidence for the water-OH/Pt(111) interface being hydrophobic at high hydroxyl coverages. We furthermore explain the observed adsorption energetics by analyzing the hydrogen bonding in the water-hydroxyl adlayers, where we argue that the increase in differential adsorption energy at high OH coverage can be explained by a reduction in the number of hydrogen bonds from the adsorbed water molecules to the hydroxyls.

Data-driven methods based on machine learning have the potential to accelerate computational analysis of atomic structures. In this context, reliable uncertainty estimates are important for assessing confidence in predictions and enabling decision making. However, machine learning models can produce badly calibrated uncertainty estimates and it is therefore crucial to detect and handle uncertainty carefully. In this work we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. The method presented in this paper differs from previous work by considering both aleatoric and epistemic uncertainty in a unified framework, and by recalibrating the predictive distribution on unseen data. Through computer experiments, we show that our approach results in accurate models for predicting molecular formation energies with well calibrated uncertainty in and out of the training data distribution on two public molecular benchmark datasets, QM9 and PC9. The proposed method provides a general framework for training and evaluating neural network ensemble models that are able to produce accurate predictions of properties of molecules with well calibrated uncertainty estimates.

Open access to research data is increasingly important for accelerating research. Grant authorities therefore request detailed plans for how data is managed in the projects they finance. We have recently developed such a plan for the EU-H2020 BIG-MAP project - a cross-disciplinary project targeting disruptive battery-material discoveries. Essential for reaching the goal is extensive sharing of research data across scales, disciplines and stakeholders, not limited to BIG-MAP and the European BATTERY 2030+ initiative but within the entire battery community. The key challenges faced in developing the data management plan for such a large and complex project were to generate an overview of the enormous amount of data that will be produced, to build an understanding of the data flow within the project and to agree on a roadmap for making all data FAIR. This paper describes the process we followed and how we structured the plan., Comment: 12 pages, 4 figures; the full DMP is published as Supporting Information

Stable and fast ionic conductors for magnesium cathode materials have the prospect of enabling high energy density batteries beyond current Lithium-ion technologies. So far, only a few candidate materials have been identified leading to data only being scarcely available to the community. Here, we present a systematic study, in the framework of Density Functional Theory, including the estimation of the diffusion barrier for 16 materials through employing Nudged Elastic Band (NEB) calculations. By introducing a path finder algorithm based on the idea of Voronoi tessellations, we show that an estimate of the transition state configuration can be extracted automatically prior to running NEB-calculations. Using geometrical descriptors in combination with a principal component analysis it is possible to further sub-group the diffusion paths. This approach also extends to materials which are not part of the study, making it a viable approach to more efficiently explore crystal structures with distinguishable diffusion characteristics., Comment: 19 pages, 4 figures

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented as a function of the elements of a skew-Hermitian matrix that can be optimized directly using unconstrained minimization methods. An implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and a preconditioner is presented and the performance compared with that of the commonly used self-consistent field approach. Results are presented for the G2 set of 148 molecules, liquid water configurations with up to 576 molecules and some insulating crystals. A general preconditioner is presented that is applicable to systems with fractional orbital occupation as is, for example, needed in the k-point sampling for periodic systems. This exponential transformation direct minimization approach is found to outperform the standard implementation of the self-consistent field approach in that all the calculations converge with the same set of parameter values and it requires less computational effort on average. The formulation of the exponential transformation and the gradients of the energy presented here are quite general and can be applied to energy functionals that are not unitary invariant such as self-interaction corrected functionals.

One-dimensional inorganic nanotubes hold promise for technological applications due to their distinct physical/chemical properties, but so far advancements have been hampered by difficulties in producing single-wall nanotubes with a well-defined radius. In this work we investigate, based on Density Functional Theory (DFT), the formation mechanism of 135 different inorganic nanotubes formed by the intrinsic self-rolling driving force found in asymmetric 2D Janus sheets. We show that for isovalent Janus sheets, the lattice mismatch between inner and outer atomic layers is the driving force behind the nanotube formation, while in the non-isovalent case it is governed by the difference in chemical bond strength of the inner and outer layer leading to steric effects. From our pool of candidate structures we have identified more than 100 tubes with a preferred radius below 35 {\AA}, which we hypothesize can display unique properties compared to their parent 2D monolayers. Simple descriptors have been identified to accelerate the discovery of small-radius tubes and a Bayesian regression approach has been implemented to assess the uncertainty in our predictions on the radius., Comment: 26 pages, 8 figures

Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our methods allow us to derive closed form expressions for herd immunity thresholds as a function of initial susceptibility distributions and suggests an intuitively satisfying approach to inoculation when only a fraction of the population is accessible to such intervention. Of particular interest, if we assume static susceptibility of individuals in the susceptible pool, ignoring susceptibility diversity {\em always} results in overestimation of the herd immunity threshold and that difference can be dramatic. Therefore, we should develop robust measures of susceptibility variation as part of public health strategies for handling pandemics., Comment: 12 pages, 2 figures

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility. We show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. Intriguingly, we find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions often tend towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak.

Magnesium hydride owns the largest share of publications on solid materials for hydrogen storage. The Magnesium group of international experts contributing to IEA Task 32 Hydrogen Based Energy Storage recently published two review papers presenting the activities of the group focused on magnesium hydride based materials and on Mg based compounds for hydrogen and energy storage. This review article not only overviews the latest activities on both fundamental aspects of Mg-based hydrides and their applications, but also presents a historic overview on the topic and outlines projected future developments. Particular attention is paid to the theoretical and experimental studies of Mg-H system at extreme pressures, kinetics and thermodynamics of the systems based on MgH2,nanostructuring, new Mg-based compounds and novel composites, and catalysis in the Mg based H storage systems. Finally, thermal energy storage and upscaled H storage systems accommodating MgH2 are presented.

Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large configurational space, which makes it practically impossible to be explored manually using first-principles calculations such as density functional theory (DFT) due to the high computational costs. Consequently, the use of methods such as cluster expansion (CE) is vital in enhancing our understanding of the disordered materials. CE dramatically reduces the computational cost by mapping the first-principles calculation results on to a Hamiltonian which is much faster to evaluate. In this work, we present our implementation of the CE method, which is integrated as a part of the Atomic Simulation Environment (ASE) open-source package. The versatile and user-friendly code automates the complex set up and construction procedure of CE while giving the users the flexibility to tweak the settings and to import their own structures and previous calculation results. Recent advancements such as regularization techniques from machine learning are implemented in the developed code. The code allows the users to construct CE on any bulk lattice structure, which makes it useful for a wide range of applications involving complex materials. We demonstrate the capabilities of our implementation by analyzing the two example materials with varying complexities: a binary metal alloy and a disordered lithium chromium oxyfluoride.