Advanced Ab Initio Simulations of Layered Oxide Cathodes: Screening Atomistic Arrangements and Accurate Electronic Structures
Authors: Koester Konstantin , Kaghazchi Payam 
Published: December 2024

Layered oxide cathode materials have already been successfully utilized in state-of-the-art commercial lithium-ion batteries and are among the most promising materials for the next generation of non-lithium-based batteries, e.g., sodium-ion batteries. However, there is still a lack of understanding structure-property relations in these materials to such a level that allows for a rational design approach. Ab initio simulations are an important tool to characterize novel materials and to obtain additional insights such as redox mechanisms at the electronic structure level that are not (easily) available by experimental studies. Modelling layered oxide materials faces several challenges such as model selection, geometry calculation, and electronic structure calculations. The main challenge in the model selection is the combinatorial explosion that arises from partial occupations in doped cathode materials which allow for numerous atomistic arrangements. Finding the most reasonable initial atomistic arrangement to perform a full geometry optimization and to obtain a realistic model is of great importance for a reliable prediction of material properties. Once a reasonable geometric model is obtained, the electronic structure calculation by ab initio methods such as density functional theory (DFT) is also challenging due to the delocalized d-orbitals of the transition metals and complex redox processes involving (partial) oxidations of oxygen anions. As accurate electronic structures are crucial to unveil the redox processes in cathode materials, advanced DFT approaches such as (optimized) hybrid functionals or even more accurate GW calculations are required. In this presentation we will show our recent advances for the modelling of layered oxide cathode materials in terms of model selection (atomistic arrangement) and electronic structure calculations.
Finding the lowest energy atomistic arrangement is a combinatorial problem that scales dramatically with supercell size and the concentration of elements. Supercells of novel and practical ternary or quaternary cathode materials can easily have up to 1030 atomistic arrangements. Determining the global energy minimum in these systems becomes a rather complex global optimization problem. Screening for all arrangements by performing DFT calculations is computationally too demanding, and therefore smart heuristic-based optimizers relying on Coulomb- or cluster-expansion-based approaches are required. Here, we will present a novel, self-written software tool to select likely atomistic structures for systems with numerous possible permutations. Our software is able to obtain the global minimum of combinatorial atomistic arrangement problems with 1030 permutations within few minutes on a desktop computer and to obtain low energy structures for problems with 10 to the power of more than 100 on a cluster within a few hours. We will show that, to the best of our knowledge, our software is faster and can tackle larger combinatorial problems than existing solvers (cf. Figure 1) which is particularly useful for modern layered oxide cathode battery materials comprising of a variety of different elements and concentrations. It will be shown how our software can be efficiently used to obtain reasonable atomistic structures for a given composition with a very low computational demand.
Once atomistic arrangements are obtained, the redox process can be predicted by calculating the electronic structure. Hence highly accurate electronic structures are required which can be obtained by hybrid functionals or even more accurate, yet computationally demanding, GW calculations. Therefore, we will continue by discussing methods for accurate electronic structure calculations for layered oxide materials including different hybrid functionals and highly accurate GW calculations. Recent results of our GW studies indicate that smaller Hartree-Fock mixing parameters than the default value are required to describe the electronic structure of layered oxide materials [Phys. Rev. B; 10.1103/PhysRevB.109.155134]. Furthermore, we will show by systematic studies that varying the Hartree-Fock mixing has a significant influence on the electronic structure and thereby on the redox processes assigned from DFT calculations as visualized in Figure 1. Tuning ab initio electronic structure methods becomes especially important for complex materials with oxygen redox that are particularly interesting for practical novel cathodes.
Finally, it will be discussed how our advanced ab initio methods can be utilized together with experimental results to obtain in-depth understanding of layered oxides as cathode materials for sodium-ion batteries (e.g., Adv. Energy Mater.; 10.1002/aenm.202302017) that might enable a more rational design for the next generation of cathode materials.

Figure 1