In　Li-excess　transition　metal-oxide　cathode　materials,　anionic　oxygen　redox　can　offer　high　capacity　and　high　voltages,　although　peroxo　and　superoxo　species　may　cause　oxygen　loss,　poor　cycling　performance,　and　capacity　fading.　Previous　work　showed　that　undesirable　formation　of　peroxide　and　superoxide　bonds　was　controlled　to　some　extent　by　Mn　substitution,　and　the　present　work　uses　density　functional　calculations　to　examine　the　reasons　for　this　by　studying　the　anionic　redox　mechanism　in　Li8MnO6.　This　material　is　obtained　by　substituting　Mn　for　Sn　in　Li8SnO6　or　for　Zr　in　Li8ZrO6　,　and　we　also　compare　this　to　previous　work　on　those　materials.　The　calculations　predict　that　Li8(M)nO(6)　is　stable　at　room　temperature　(with　a　band　gap　of　3.19　eV　as　calculated　by　HSE06　and　1.82　eV　as　calculated　with　the　less　reliable　PBE+U),　and　they　elucidate　the　chemical　and　structural　effects　involved　in　the　inhibition　of　oxygen　release　in　this　cathode.　Throughout　the　whole　delithiation　process,　only　O2-　ions　are　oxidized.　The　directional　Mn-O　bonds　formed　from　unfilled　3d　orbitals　effectively　inhibit　the　formation　of　O-O　bonds,　and　the　layered　structure　is　maintained　even　after　removing　3　Li　per　Li8MnO6　formula　unit.　The　calculated　average　voltage　for　removal　of　3　Li　is　3.69　V　by　HSE06,　and　the　corresponding　capacity　is　389　mAh/g.　The　high　voltage　of　oxygen　anionic　redox　and　the　high　capacity　result　in　a　high　energy　density　of　1436　Wh/kg.　The　Li-ion　diffusion　barrier　for　the　dominant　interlayer　diffusion　path　along　the　c　axis　is　0.57　eV　by　PBE+U.　These　results　help　us　to　understand　the　oxygen　redox　mechanism　in　a　new　lithium-rich　Li8MnO6　cathode　material　and　contribute　to　the　design　of　high-energy　density　lithium-ion　battery　cathode　materials　with　favorable　electrochemical　properties　based　on　anionic　oxygen　redox.