Details about ab initio random structure searching (AIRSS) and its application to battery electrode materials can be found in the literature . Briefly, this method searches for low energy structures by generating random but physically sensible initial structures followed by geometry optimisation using firstprinciples calculations. Unlike most other structure prediction methods, there is no iterative improvement process involved, hence the search can be parallelized and distributed over the computing resources easily. The plane wave density functional theory code CASTEP is used for structure searching with a plane wave cut off energy of 340 eV and a k-point spacing of 0.07 2πÅ -1 for sampling the reciprocal space. Core-corrected on-the-fly generated ultrasoft pseudopotentials from CASTEP's built-in QC5 library are used. Further DFT calculations are performed using the VASP code with a plane wave cut off energy of 520 eV and a k-point spacing of 0.04 2πÅ -1 . The PBE exchange-correlation functional is used with the Hubbard correction applied for the d states of Fe. The U value for Fe is set to 4.0 eV based on the fitting of oxide formation energies . A force-based convergence criteria of 0.03 eV Å -1 is used for all geometry optimisations, except when relaxing the input structure for phonon calculations where a tighter tolerance of 0.0001 eV Å -1 is applied. Ferromagnetic spin states have been assumed during the initial search to avoid complicating the energy landscapes. Enumerating spin arrangements for selected low energy phases shows that imposing anti-ferromagnetic orderings typically reduces the energy by 10 to 20 meV per atom, giving minor changes to the computed thermodynamic stabilities. Hence, the FM ordering is used in all further calculations for oxysulphides. Finite-displacement phonon calculations are performed using the Phonopy package with an increased cut off energy of 650 eV. Climbing-image nudged elastic band calculations are performed for determining the Lidiffusion barriers using the VTST code. The supercells are constructed such that periodic images of the Li-vacancy are more than 10 Å away in all directions. To avoid electron localisation upon creating a single Li vacancy, which would otherwise complicate the potential energy surface and the minimum energy pathway, a single electron is removed from the supercell with a neutralising background added. This resembles the case where the polaron formed is far away from the Li-vacancy. The AiiDA framework is used to automate the DFT calculations and preserve their provenance .