Boron Cluster Cations: Transition from Planar to Cylindrical Structures

Abstract

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...

Physically founded phonon dispersions of few-layer materials and the case of borophene

“…[33] In fact, boron displays multiple bulk phases, [33,34] and the formation of clusters, fullerene-type cages and nanotubes made of B is also a subject of ongoing debate. [35][36][37][38][39][40][41][42] The ambientconditions stable phase of B was only recently determined through a series of computational studies, the earliest of which [43] only dates back to 2007. It comes as little surprise, then, that the study of the 2D allotropes of boron has also progressed through iterative improvement upon previous results.…”

SmB6– Cluster Anion: Covalency Involving f Orbitals

“…These boron systems demonstrate the metalloid nature of boron: it will form strong covalent B−B bonds, and also delocalized bonds, of both σ and π types. 4,5 Boron clusters only become more interesting upon the addition of a metal. The metal-like nature of boron allows for an actual metal to weave into an existing aromatic network, leading to high stability.…”

Unveiling the Atomic Structure of Single‐Wall Boron Nanotubes

“…After the prediction of stable, quasi-planar and tubular clusters of elemental boron, 1-4 which could later be confirmed experimentally, [5][6][7] materials scientist have started to search for boron nanostructures similar to graphene and carbon nanotubes. Several models for boron sheets and nanotubes (BNTs) with different underlying lattice structures have been proposed [8][9][10][11][12][13] and first successes in growing pure BNTs were reported.…”