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Register a new userAtomic cluster expansion of scalar, vectorial and tensorial properties and including magnetism and charge transfer
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Authors
Ralf Drautz
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The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the atoms. In particular, atomic species, magnetic moments and charges are attached to the atomic positions and an atomic cluster expansion that includes the different degrees of freedom on equal footing is derived. Expressions for the efficient evaluation of forces and torques are given. Relations to other methods are discussed.
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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.
Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables -- such as the cohesive energy, the electron density, or a variety of response properties -- as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects, ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics, to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.
The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems. Our presentation extends the derivation by proposing a precomputation algorithm that yields immediate guarantees that a complete basis is obtained. We provide a fast recursive algorithm for efficient evaluation and illustrate its performance in numerical tests. Finally, we discuss generalisations and open challenges, particularly from a numerical stability perspective, around basis optimisation and parameter estimation, paving the way towards a comprehensive analysis of the convergence to a high-fidelity reference model.
Machine learning of atomic-scale properties is revolutionizing molecular modelling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed and reliability of machine-learning potentials, however, depends strongly on the way atomic configurations are represented, i.e. the choice of descriptors used as input for the machine learning method. The raw Cartesian coordinates are typically transformed in fingerprints, or symmetry functions, that are designed to encode, in addition to the structure, important properties of the potential-energy surface like its invariances with respect to rotation, translation and permutation of like atoms. Here we discuss automatic protocols to select a number of fingerprints out of a large pool of candidates, based on the correlations that are intrinsic to the training data. This procedure can greatly simplify the construction of neural network potentials that strike the best balance between accuracy and computational efficiency, and has the potential to accelerate by orders of magnitude the evaluation of Gaussian Approximation Potentials based on the Smooth Overlap of Atomic Positions kernel. We present applications to the construction of neural network potentials for water and for an Al-Mg-Si alloy, and to the prediction of the formation energies of small organic molecules using Gaussian process regression.
Two-dimensional CrI3 has attracted much attention as it is reported to be a ferromagnetic semiconductor with the Curie temperature around 45K. By performing first-principles calculations, we find that the magnetic ground state of CrI3 is variable under biaxial strain. Our theoretical investigations show that the ground state of monolayer CrI3 is ferromagnetic under compression, but becomes antiferromagnetic under tension. Particularly, the transition occurs under a feasible in-plane strain around 1.8%. Accompanied by the transition of the magnetic ground state, it undergoes a transition from magnetic-metal to half-metal to half-semiconductor to spin-relevant semiconductor when strain varies from -15% to 10%. We attribute these transitions to the variation of the d-orbitals of Cr atoms and the p-orbitals of I atoms. Generally, we report a series of magnetic and electronic phase transition in strained CrI3, which will help both theoretical and experimental researchers for further understanding of the tunable electronic and magnetic properties of CrI3 and their analogous.
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