Density Functional Tight Binding Modelling of Lithium Intercalated Graphite with Machine-Learned Repulsive Potential

Abstract

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 the 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 for its longevity–is characterized by multiple phase transitions, ordered and disordered domains, as well as non-equilibrium phenomena, and therefore quite complex. Such complexity emerges particularly at low states of charge (SOC), and complicates both the interpretation of experiments and the computational modelling.From a computational standpoint, targeted system sizes compatible with the SOC range of interest are inaccessible to first-principles calculations, yet require first-principles treatment of key effects such as dispersion and long-range electrostatics. Density Functional Tight Binding (DFTB), a semi-empirical approximation to DFT, offers a high-quality trade-off between accuracy and speed. However, this advantage comes at the cost–or rather initial investment–of pairwise parametrization.As no Li-C DFTB parameters were publicly available yet, we produced a parameter set specifically tailored to this system, employing a parametrization strategy [1] that combines global optimization of electronic parameters via Particle Swarm Optimization (PSO) [2] with our recently developed approach that uses Gaussian Process Regression (GPR) [3] to machine-learn the repulsive potential.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 ab initio methods. We present structural properties and diffusion barriers for some exemplary system states. Additionally, we are able for the first time to resolve the full Potential Energy Surface (PES) of Li motion in stage-I and stage-II LiC108 (SOC 5%). The PES contains information that enables us to implement, and in perspective discuss, both kinetic Monte Carlo (kMC) models of Li-ion mobility in the graphite host, and free-energy sampling which ultimately yields the computed voltage profile of the anode.[1] Panosetti et al., https://arxiv.org/abs/1904.13351 [2] Chou et al., J. Chem. Theory Comput. 2016, 12, 1, 53–64[3] Panosetti et al., J. Chem. Theory Comput. 2020, 16, 4, 2181–2191 Figure 1