Modeling intercalation chemistry with multi-redox reactions by sparse lattice models in disordered rocksalt cathodes

Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate the performance of energy storage. The application of commonly used cluster expansion techniques to model the intercalation thermodynamics of such systems from \textit{ab-initio} is challenged by the combinatorial increase in configurational degrees of freedom as the number of species grows. Such challenges necessitate efficient generation of lattice models without over-fitting and proper sampling of the configurational space under charge balance in ionic systems. In this work, we introduce a combined approach that addresses these challenges by (1) constructing a robust cluster-expansion Hamiltonian using the sparse regression technique, including $\ell_0\ell_2$-norm regularization and structural hierarchy; and (2) implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic configurations using the table-exchange method and an ensemble-average approach. These techniques are applied to a disordered rocksalt oxyfluoride Li$_{1.3-x}$Mn$_{0.4}$Nb$_{0.3}$O$_{1.6}$F$_{0.4}$ (LMNOF) which is part of a family of promising earth-abundant cathode materials. The simulated voltage profile is found to be in good agreement with experimental data and particularly provides a clear demonstration of the Mn and oxygen contribution to the redox potential as a function of Li content.