Accessing Structural, Electronic, Transport and Mesoscale Properties of Li-GICs via a Complete DFTB Model with Machine-Learned Repulsion Potential

Abstract

Lithium-graphite intercalation compounds (Li-GICs) are the most popular anode material for modern lithium-ion batteries and have been subject to numerous studies—both experimental and theoretical. However, the system is still far from being consistently understood in detail across the full range of state of charge (SOC). The performance of approaches based on density functional theory (DFT) varies greatly depending on the choice of functional, and their computational cost is far too high for the large supercells necessary to study dilute and non-equilibrium configurations which are of paramount importance for understanding a complete charging cycle. On the other hand, cheap machine learning methods have made some progress in predicting, e.g., formation energetics, but fail to provide the full picture, including electrostatics and migration barriers. Following up on our previous work, we deliver on the promise of providing a complete and affordable simulation framework for Li-GICs. It is based on density functional tight binding (DFTB), which is fitted to dispersion-corrected DFT data using Gaussian process regression (GPR). In this work, we added the previously neglected lithium–lithium repulsion potential and extend the training set to include superdense Li-GICs (LiC6−x; x>0) and lithium metal, allowing for the investigation of dendrite formation, next-generation modified GIC anodes, and non-equilibrium states during fast charging processes in the future. For an extended range of structural and energetic properties—layer spacing, bond lengths, formation energies and migration barriers—our method compares favorably with experimental results and with state-of-the-art dispersion-corrected DFT at a fraction of the computational cost. We make use of this by investigating some larger-scale system properties—long range Li–Li interactions, dielectric constants and domain-formation—proving our method’s capability to bring to light new insights into the Li-GIC system and bridge the gap between DFT and meso-scale methods such as cluster expansions and kinetic Monte Carlo simulations.

Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table

“…This is due to the simple one-parameter form of the repulsive potential. Nonetheless, it would be straightforward to refine PTBP with a more flexible and/or many-body repulsive potential. ,,, …”

“…Nonetheless, it would be straightforward to refine PTBP with a more flexible and/or many-body repulsive potential. 42,59,60,61 As one of the most challenging elements for DFTB, phosphorus is considered in the bottom row of Figure 7c (see Figure S7 for additional comparisons). Here, four different prototypes display significant weights in the loss function, namely, graphite, BCC, diamond, and β-Sn (with Boltzmann factors of 0.11, 0.13, 0.22, and 0.40, respectively).…”

Ab initio study of lithium intercalation into a graphite nanoparticle

“…Another source of potential error is non-local DFT's known issue with modelling highly polarizable ions such as Li 102 due to the use of atomic rather than ionic volumes. 103 Anniés et al 104 identify this issue for Pande and Viswanathan's 97 DFT-based Ising model which performs well for low Li abundance stages but not for high Li abundance stages. Further advancements can be made by considering graphite nanoparticles in electrolyte environments at applied voltage as in experimental electrochemistry.…”