Experiments on mass-selected boron clusters date back more than 20 years.[1] However, only recently have experimental and theoretical methods advanced enough to allow for structural assignments over a wide range of cluster sizes. To date, most is known about boron cluster anions as a result of the pioneering work of Wang and co-workers, who used a combination of photoelectron spectroscopy and quantum chemistry to determine structures for clusters with up to 20 atoms. [2,3] Throughout this size range, B x À ions appear to have planar, sheet-like structures comprising webs of triangles and occasionally squares. These two-dimensional structures are often bowed and sometimes partly corrugated. This distortion is likely due to strain arising from shorter bond distances at the periphery, where atoms form stronger bonds because they have fewer bond partners. In a recent study it has been suggested that whereas the B 20 À ion forms the planar isomer in experiment, there is an energetically very close-lying regularcylindrical isomer comprising two stacked ten-atom rings. [4] The recent report of the preparation and electron-microscopic characterization of 3-nm-diameter single-walled boron nanotubes [5] has led to speculations that boron clusters may assume cylindrical structures beyond a critical size. We have explored this question further by structurally probing boron cluster cations using a combination of collision cross section measurements and density functional theory (DFT) calculations.The theoretical determination of low-energy boron cluster structures faces various problems, as is apparent from studies like those reviewed in reference [2] (e.g. B 13+ [6][7][8][9] and B 20 [4,10] ). Electronic structures often show multiple-reference character, which makes reliable calculations expensive or virtually impossible for systems larger than B 20 . Even more problematic are the unusual and unexpected features of geometries, which diminish the hope of locating structures of interest by experienced guesses alone. Thus, a computational procedure is needed that is unbiased, efficient, and tolerant of multiplereference cases. As a compromise of these requirements, we have chosen the following strategy. A first set of structures for the neutral clusters was obtained with a genetic algorithm. [11,23] This procedure required on the order of 100 generations resulting in 1000 to 2000 geometry optimizations for each B n cluster. As this approach necessitates a low-cost procedure, we chose the DFT with the BP86 functional, which has been shown to yield reliable structure constants.[12] The relatively small def2-SVP [13] orbital and auxiliary bases were considered sufficient for this purpose.The genetic algorithm converged rapidly for small test cases like B 6 or B 12 , that is, 20 to 40 generations sufficed for convergence. Trial runs for larger clusters (B 16 , B 20 , B 24 ) failed to find some of the low-energy structures even after 80 generations. To speed up convergence, we seeded the initial population with optimized structures...

The structures and energetics of small tin cluster Sn(n)(-) anions up to n=15 were determined by a combination of density-functional theory and three different experimental methods: Ion mobility spectrometry, trapped ion electron diffraction, and collision induced dissociation. We find compact, quasispherical structures up to n=12. Sn(12)(-) is a slightly distorted hollow icosahedron while Sn(13)(-) to Sn(15)(-) have prolate structures, consisting of merged, hollow, in part incomplete, deltahedral subunits: Sn(13)(-) consists of a face-sharing pentagonal bipyramid and tricapped trigonal bipyramid, Sn(14)(-) comprises a face-sharing dicapped trigonal prism and capped square-antiprism, and Sn(15)(-) consists of two face-sharing tricapped trigonal prisms.

By a combination of gas phase ion mobility measurements and relativistic density functional theory calculations with inclusion of spin-orbit coupling, we assign structures of lead cluster cations and anions in the range between 4 and 15 atoms. We find a planar rhombus for the tetramer, a trigonal bipyramid for the pentamer, and a pentagonal bipyramid for the heptamer, independent of charge state. For the hexamer, the cation and anion structures differ: we find an octahedron for the anion while the cation consists of fused tetrahedra. For the octamer, we find in both cases structures based on the pentagonal bipyramid motif plus adatom. For the larger clusters investigated we always find different structures for cations and anions. For example, Pb(12)(-) is confirmed to be a hollow icosahedron while Pb(12)(+) is a truncated filled icosahedron. Pb(13)(+) is a filled icosahedron but Pb(13)(-) is a hollow icosahedron with the additional atom capping a face. In order to get experimental information on the relative stabilities, we investigated the collision induced dissociation mass spectra for the different cluster sizes and charge states, and observe a strong correlation with the calculated fragmentation energies. Up to n = 13 the main fragmentation channel is atom loss; for the larger cluster sizes we observe fission into two large fragments. This channel is dominant for larger anions, less pronounced but clearly present for the cations.

The structures of medium sized tin cluster anions Sn(n)(-) (n = 16-29) were determined by a combination of density functional theory, trapped ion electron diffraction and collision induced dissociation (CID). Mostly prolate structures were found with a structural motif based on only three repeatedly appearing subunit clusters, the Sn(7) pentagonal bipyramid, the Sn(9) tricapped trigonal prism and the Sn(10) bicapped tetragonal antiprism. Sn(16)(-) and Sn(17)(-) are composed of two face connected subunits. In Sn(18)(-)-Sn(20)(-) the subunits form cluster dimers. For Sn(21)(-)-Sn(23)(-) additional tin atoms are inserted between the building blocks. Sn(24)(-) and Sn(25)(-) are composed of a Sn(9) or Sn(10) connected to a Sn(15) subunit, which closely resembles the ground state of Sn(15)(-). Finally, in the larger clusters Sn(26)(-)-Sn(29)(-) additional bridging atoms again connect the building blocks. The CID experiments reveal fission as the main fragmentation channel for all investigated cluster sizes. This rather unexpected "pearl-chain" cluster growth mode is rationalized by the extraordinary stability of the building blocks.

The structures of bismuth cluster cations in the range between 4 and 14 atoms have been assigned by a combination of gas phase ion mobility and trapped ion electron diffraction measurements together with density functional theory calculations. We find that above 8 atoms the clusters adopt prolate structures with coordination numbers between 3 and 4 and highly directional bonds. These open structures are more like those seen for clusters of semiconducting-in-bulk elements (such as silicon) rather than resembling the compact structures typical for clusters of metallic-in-bulk elements. An accurate description of bismuth clusters at the level of density functional theory, in particular of fragmentation pathways and dissociation energetics, requires taking spin-orbit coupling into account. For n = 11 we infer that low energy isomers can have fragmentation thresholds comparable to their structural interconversion barriers. This gives rise to experimental isomer distributions which are dependent on formation and annealing histories.

We employ a combination of ion mobility measurements and an unbiased systematic structure search with density functional theory methods to study structure and energetics of gas phase tin cluster cations, Sn(n)(+), in the range of n = 3-15. For Sn(13)(+) we also carry out trapped ion electron diffraction measurements to ascertain the results obtained by the other procedures. The structures for the smaller systems are most easily described by idealized point group symmetries, although they are all Jahn-Teller distorted: D(3h) (trigonal bipyramid), D(4h) (octahedron), D(5h) (pentagonal bipyramid) for n = 5, 6, and 7. For the larger systems we find capped D(5h) for Sn(8)(+) and Sn(9)(+), D(3h) (tricapped trigonal prism) and D(4d) (bicapped squared antiprism) plus adatoms for n = 10, 11, 14, and 15. A centered icosahedron with a peripheral atom removed is the dominant motif in Sn(12)(+). For Sn(13)(+) the calculations predict a family of virtually isoenergetic isomers, an icosahedron and slightly distorted icosahedra, which are about 0.25 eV below two C(1) structures. The experiments indicate the presence of two structures, one from the I(h) family and a prolate C(1) isomer based on fused deltahedral moieties.

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