Density　functional　theory　(DFT)　calculations　are　employed　to　investigate　the　full　catalytic　cycle　of　CO　oxidation　by　N2O　on　yttrium　oxide　clusters　Y2MO5　(M　=　Y,　Al)　in　the　gas-phase.　Extensive　structural　searches　show　that　both　the　ground-state　structures　of　Y3O5　and　Y2AlO5　contain　an　oxygen　radical　(Ot)　which　plays　an　important　role　in　CO　oxidation.　Energy　profiles　are　calculated　to　determine　the　reaction　mechanisms.　Molecular　electrostatic　potential　maps　(MEPs)　and　natural　bond　orbital　(NBO)　analyses　are　employed　to　rationalize　the　reaction　mechanisms.　The　results　indicate　that　the　whole　catalytic　cycle　for　the　reaction　CO　+　N2O　→　CO2　+　N2,　conducted　by　yttrium　oxide　clusters　Y2MO5　(M　=　Y,　Al),　is　favored　both　thermodynamically　and　kinetically.　Moreover,　compared　with　the　previous　report　on　di-nuclear　YAlO3+　and　Y2O3+,　it＇s　obvious　we　can　conclude　that　tri-nuclear　Y3O5　and　Y2AlO5　exhibit　greatly　enhanced　catalytic　activity　toward　CO/N2O　couples.　©　The　Royal　Society　of　Chemistry　2015.