Geometric　structures,　electronic　properties,　and　stabilities　of　small　Zrn　and　Zrn+　(n　=　2-10)　clusters　have　been　investigated　using　density　functional　theory　with　effective　core　potential　LanL2DZ　basis　set.　For　both　neutral　and　charged　systems,　several　isomers　and　different　multiplicities　were　studied　to　determine　the　lowest　energy　structures.　Many　most　stable　states　with　high　symmetry　were　found　for　small　Zrn　clusters.　The　most　stable　structures　and　symmetries　of　Zrn+　clusters　are　the　same　as　the　neutral　ones　except　n　=　4　and　7.　We　found　that　the　clusters　with　n　>　3　possess　highly　compact　structures.　The　clusters　are　inclined　to　form　the　caged-liked　geometry　containing　pentagonal　structures　for　n　>　8,　which　is　in　favor　of　energy.　From　the　formation　energy　and　second-order　energy　difference,　we　obtained　that　2-,　5-,　7-atoms　of　neutral　and　4-,　7-atoms　cationic　clusters　are　the　magic　numbers.　Furthermore,　the　highest　occupied　molecular　orbital-lowest　unoccupied　molecular　orbital　gaps　display　that　the　Zr3,　Zr6,　Zr4+,　and　Zr9+　are　more　stable　in　chemical　stability.　©　2009　Wiley　Periodicals,　Inc.