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Register a new userOn the Completeness of Atomic Structure Representations
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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. It was generally believed that 3-body descriptors uniquely specify the environment of an atom, up to a rotation and permutation of like atoms. We produce several counterexamples to this belief, with the consequence that any classifier, regression or embedding model for atom-centred properties that uses 3 (or 4)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centred contributions mitigates, but does not eliminate, 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.
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Quantum-chemical processes in liquid environments impact broad areas of science, from molecular biology to geology to electrochemistry. While density-functional theory (DFT) has enabled efficient quantum-mechanical calculations which profoundly impact understanding of atomic-scale phenomena, realistic description of the liquid remains a challenge. Here, we present an approach based on joint density-functional theory (JDFT) which addresses this challenge by leveraging the DFT approach not only for the quantum mechanics of the electrons in a solute, but also simultaneously for the statistical mechanics of the molecules in a surrounding equilibrium liquid solvent. Specifically, we develop a new universal description for the interaction of electrons with an arbitrary liquid, providing the missing link to finally transform JDFT into a practical tool for the realistic description of chemical processes in solution. This approach predicts accurate solvation free energies and surrounding atomic-scale liquid structure for molecules and surfaces in multiple solvents without refitting, all at a fraction of the computational cost of methods of comparable detail and accuracy. To demonstrate the potential impact of this method, we determine the structure of the solid/liquid interface, offering compelling agreement with more accurate (but much more computationally intensive) theories and with X-ray reflectivity measurements.
Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict the properties of both materials and molecules as well as to explore and visualize the chemical compound and configuration space. Recently, it has become clear that many of the most effective representations share a fundamental formal connection: that they can all be expressed as a discretization of N-body correlation functions of the local atom density, suggesting the opportunity of standardizing and, more importantly, optimizing the calculation of such representations. We present an implementation, named librascal, whose modular design lends itself both to developing refinements to the density-based formalism and to rapid prototyping for new developments of rotationally equivariant atomistic representations. As an example, we discuss SOAP features, perhaps the most widely used member of this family of representations, to show how the expansion of the local density can be optimized for any choice of radial basis set. We discuss the representation in the context of a kernel ridge regression model, commonly used with SOAP features, and analyze how the computational effort scales for each of the individual steps of the calculation. By applying data reduction techniques in feature space, we show how to further reduce the total computational cost by at up to a factor of 4 or 5 without affecting the models symmetry properties and without significantly impacting its accuracy.
Rechargeable lithium ion batteries are an attractive alternative power source for a wide variety of applications. To optimize their performances, a complete description of the solvation properties of the ion in the electrolyte is crucial. A comprehensive understanding at the nanoscale of the solvation structure of lithium ions in nonaqueous carbonate electrolytes is, however, still unclear. We have measured by femtosecond vibrational spectroscopy the orientational correlation time of the CO stretching mode of Li+-bound and Li+-unbound ethylene carbonate molecules, in LiBF4, LiPF6, and LiClO4 ethylene carbonate solutions with different concentrations. Surprisingly, we have found that the coordination number of ethylene carbonate in the first solvation shell of Li+ is only two, in all solutions with concentrations higher than 0.5 M. Density functional theory calculations indicate that the presence of anions in the first coordination shell modifies the generally accepted tetrahedral structure of the complex, allowing only two EC molecules to coordinate to Li+ directly. Our results demonstrate for the first time, to the best of our knowledge, the anion influence on the overall structure of the first solvation shell of the Li+ ion. The formation of such a cation/solvent/anion complex provides a rational explanation for the ionic conductivity drop of lithium/carbonate electrolyte solutions at high concentrations.
A major goal of energy research is to use visible light to cleave water directly, without an applied voltage, into hydrogen and oxygen. Since the initial reports of the ultraviolet (UV) activity of TiO2 and SrTiO3 in the 1970s, researchers have pursued a fundamental understanding of the mechanistic and molecular-level phenomena involved in photo-catalysis. Although it requires UV light, after four decades SrTiO3 is still the gold standard for splitting water. It is chemically stable and catalyzes both the hydrogen and the oxygen reactions without applied bias. While ultrahigh vacuum (UHV) surface science techniques have provided useful insights, we still know relatively little about the structure of electrodes in contact with electrolytes under operating conditions. Here, we report the surface structure evolution of a SrTiO3 electrode during water splitting, before and after training with a positive bias. Operando high-energy X-ray reflectivity measurements demonstrate that training the electrode irreversibly reorders the surface. Scanning electrochemical microscopy (SECM) at open circuit correlates this training with a tripling of the activity toward photo-induced water splitting. A novel first-principles joint density-functional theory (JDFT) simulation constrained to the X-ray data via a generalized penalty function identifies an anatase-like structure for the more active, trained surface.
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule.
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