On the other hand, two anti-Ruddlesden-Popper phases, Li 2 Fe 2 S 2 O and Li 4 Fe 3 S 3 O 2 , have been found to be close to the convex hull and more promising for cathode applications with specific capacity higher than that of the Li 2 FeSO. The former has a layered structure as shown in Fig. , which resembles the Ruddlesden-Popper (RP) phases with a general formula A n+1 B n X 3n+1 . The RP series can be regarded as alternating perovskite-like (ABX 3 ) and rock salt like (AX) environments along the z the direction. The number n indicates the number of complete ABX 3 perovskite layers between the rock salt BX layer. In contrast to normal RP phases, such as Sr 3 Ru 2 O 7 , where cations take the A and B sites, here they take the anion X sites instead, and S and O occupy the A and B sites respectively. This gives the anti-Ruddleseden Popper structured oxysulphides a general formula S n+1 O n (Fe/Li) 3n+1 . The Li 2 Fe 2 S 2 O phase (space group Pc) has n = 1 with one perovskite layer followed by the rock salt layer as shown in Fig. , and it is only about 3 meV from the convex hull. Likewise, the Li 4 Fe 3 S 3 O 2 phase (space group Cm) has two perovskite layers (e.g. n = 2) in the unit cell, as shown in Fig. . This phase is slightly less stable with a distance to hull of 18 meV per atom. Different Li/Fe orderings in the primitive cell and supercells of both phases have been enumerated, and twenty structures with the lowest electrostatic energies are further relaxed by DFT for each case. Unlike the cubic perovskite, the base structure of the RP phase is not unique, which can affect the initial rankings based on the electrostatic energies. We used the experimental structure of Sr 2 RuO 4 , Sr 3 Ru 2 O 7 and the structures obtained from the search as the initial templates. For Li 2 Fe 2 S 2 O, performing the enumeration did not generate any structure with lower energy. In fact, using the ideal Sr 2 RuO 4 structure as the template would miss the lowest energy structure that is found in the search. On the other hand, repeating the same procedure for Li 4 FeS 3 O 2 has generated many structures with lower energies by up to 14 meV per atom (distance to hull is reduced to 4 meV), and starting from the ideal structure appears to give better results. The lowest energy structure (space group C2/m) contains OLi 4 Fe 2 tilted octahedra in a a + b 0 c 0 tilt system, as shown in Fig. .