Periodic trends in the geometric structures of 13-atom metal clusters

We report structures of X₁₃ clusters for 26 metal elements found by global optimization of the energy calculated by density functional theory. The icosahedron is unstable in 19 of those cases. There are at least 11 truly distinct structures among the 26 global minima. Differences in geometries between elements are understood as resulting from competing structural principles. Periodic trends in structure relate to atomic properties. Cagelike features correlate with hardness, (IE-EA)∕2, and the number of 90^∘{} bond angles correlates with p- and d-type orbital participations in localized bonds.