In addition to good electronic conductivity, the existence of fast lithium ion conduction pathways is also crucial for cathode materials. For Li 2 Fe 2 S 2 O, the Li atoms only occupy the sites within the Li 2 O layer of the perovskite environment as shown in Fig. . Each Li is under octahedral coordination by four S atoms and two O atoms, and it has four nearest neighbour Li atoms and four next nearest neighbours. The coordination octahedron is facesharing with the nearest neighbours and edge-sharing between the next-nearest neighbours, giving two possible kinds of migration pathways as labelled by A and B in Fig. . The climbingimage nudged elastic band (NEB) method has been use to study the minimum energy pathway for a single Li vacancy to migrate. The barrier between the nearest neighbour (NN) sites is found to be 0.38 eV, and for the next-nearest neighbour (NNN) it is increased to 0.96 eV, as shown in Fig. . The large difference in the barrier heights between the two cases can be understood as the former requires the Li atom to go through the face of the coordination octahedron around it, whereas the latter needs to go squeeze through the edge made of two S atoms with additional repulsion from the nearby Li atoms. In layered cathode materials, the Li atoms are known to take an indirect route though the tetragonal sites going though the faces of LiO 6 octahedra, rather than the direct path though the edges . The Li 4 Fe 3 S 3 O structure has many in-equivalent pathways, and we select representative paths connecting the nearest and next-nearest migrations in both the perovskite layer and the rock salt layer, as shown in Fig. . The A and B paths corresponds to the NN and NNN pathways inside the perovskite environment, and they have transitions state barriers 0.30 eV and 1.74 eV respectively. The higher barrier of the NNN pathway can be attributed to the increased repulsion from the Fe 2+ ions when compared to that in Li 2 Fe 2 S 2 O. Path C and Path D are pathways for Li to diffuse within the rock salt layer. The former is found to have a barrier height of 0.45 eV and the latter is 0.92 eV. Unlike the diffusion in the perovskite layer, here the NN path (Path C) goes though an edge of the octahedron formed by two S atoms. We have also considered the potential pathway though the tetrahedral site coordinated by four S 2-in analogy to the diffusion in layered Li metal oxides. However, the Li atom is found to be not stable at that intermediate site, since after relaxations the Li atom returns to its starting position. This can be understood as the occupation of the tetrahedral site would in fact result in very short Li-Fe separation with the Fe atom in the perovskite ordered layer above/below, giving rise to increased electrostatic energies. Here, the direct oxygen-dumbbell hop of Path C is already much lower than the counterpart in LiCoO 2 , which can be attributed to larger and more polarizable S 2-compared with O -2 .