An accurate machine learning calculator for the lithium-graphite system

Machine-learning potentials are accelerating the development of energy materials, especially in identifying phase diagrams and other thermodynamic properties. In this work, we present a neural network potential based on atom-centered symmetry function descriptors to model the energetics of lithium intercalation into graphite. The potential was trained on a dataset of over 9000 diverse lithium-graphite configurations that varied in applied stress and strain, lithium concentration, lithium-carbon and lithium-lithium bond distances, and stacking order to ensure wide sampling of the potential atomic configurations during intercalation. We calculated the energies of these structures using density functional theory (DFT) through the Bayesian error estimation functional with van der Waals correlation exchange-correlation functional, which can accurately describe the van der Waals interactions that are crucial to determining the thermodynamics of this phase space. Bayesian optimization, as implemented in Dragonfly, was used to select optimal set of symmetry function parameters, ultimately resulting in a potential with a prediction error of 8.24 meV atom(-1) on unseen test data. The potential can predict energies, structural properties, and elastic constants at an accuracy comparable to other DFT exchange-correlation functionals at a fraction of the computational cost. The accuracy of the potential is also comparable to similar machine-learned potentials describing other systems. We calculate the open circuit voltage with the calculator and find good agreement with experiment, especially in the regime x >= 0.3, for x in LixC6. This study further illustrates the power of machine learning potentials, which promises to revolutionize design and optimization of battery materials.