The full Li-Fe-O-S chemical space can be represented as a tetrahedron with vertices being the elemental species, as shown in Fig. . In oxysulphides, both oxygen and sulphur typically have the -2 oxidation states. For metal cations, Li is expected to be in the + 1 state and we limit Fe to be in the + 2 and + 3 states. To maintain charge neutrality, the sum of the oxidation states for a given composition should be zero. This means that the compositions to be searched are located on two cross-sectional planes of the full Li-Fe-S-O tetrahedron: one for those with Fe in + 3 and the other for + 2, as shown in Fig. . Plane wave density functional theory calculations are known to have cubic scaling, to keep the problem tractable, we limit the search to compositions with the number atoms of atoms in the empirical formula ≤ 12, and the total number of atoms in the full formula ≤ 24. Even with these constrains applied, there are still 33 candidate compositions to be searched. As a result, we have to perform coarse samplings of the phase space initially, where about 600 random structures generated and relaxed for each composition. Afterwards, compositions that have the lowest energy structure close to the convex are selected for further searching.