DFTB Modeling of Lithium-Intercalated Graphite with Machine-Learned Repulsive Potential

Lithium ion batteries have been a central part of consumer electronics for decades. More recently, they have also become critical components in the quickly arising technological fields of electric mobility and intermittent renewable energy storage. However, many fundamental principles and mechanisms are not yet understood to a sufficient extent to fully realize the potential of the incorporated materials. The vast majority of concurrent lithium ion batteries make use of graphite anodes. Their working principle is based on intercalation, the embedding and ordering of (lithium-) ions in two-dimensional spaces between the graphene sheets. This important process, it yields the upper bound to a battery's charging speed and plays a decisive role in its longevity, is characterized by multiple phase transitions, ordered and disordered domains, as well as nonequilibrium phenomena, and therefore quite complex. In this work, we provide a simulation framework for the purpose of better understanding lithium-intercalated graphite and its behavior during use in a battery. To address large system sizes and long time scales required to investigate said effects, we identify the highly efficient, but semiempirical density functional tight binding (DFTB) as a suitable approach and combine particle swarm optimization (PSO) with the machine learning (ML) procedure Gaussian process regression (GPR) as implemented in the recently developed GPrep package for DFTB repulsion fitting to obtain the necessary parameters. Using the resulting parametrization, we are able to reproduce experimental reference structures at a level of accuracy which is in no way inferior to much more costly methods. We finally present structural properties and diffusion barriers for some exemplary system states.