Experimental and computational simulations revealed that boron clusters, which favor planar (2D) structures up to 18 atoms, prefer 3D structures beginning at 20 atoms. Using global optimization methods, we found that the B20 neutral cluster has a double-ring tubular structure with a diameter of 5.2 Å. For the B 20 ؊ anion, the tubular structure is shown to be isoenergetic to 2D structures, which were observed and confirmed by photoelectron spectroscopy. The 2D-to-3D structural transition observed at B20, reminiscent of the ring-to-fullerene transition at C20 in carbon clusters, suggests it may be considered as the embryo of the thinnest single-walled boron nanotubes.photoelectron spectroscopy ͉ density functional calculation ͉ global minimum search S mall atomic clusters often exhibit structures and properties remarkably different from those of their bulk counterparts. For example, the most stable form of carbon is graphite, consisting of layers of two-dimensional (2D) graphene sheets. Yet small carbon clusters form chains, rings, and fullerenes (1-5). Boron, carbon's lighter neighbor, is also a strongly covalent material consisting of B 12 icosahedral cages (6-8). But small boron clusters were predicted to be planar (9-11), in stark contrast to the bulk three-dimensional (3D) cages. Planar boron clusters have been recently produced in the gas phase and experimentally confirmed up to B 15 (12)(13)(14). However, it is still unclear at what critical size the 2D-to-3D structural transition occurs. We show from concerted photoelectron spectroscopy (PES) and global geometry optimization theoretical studies (15-17) that the transition occurs at the size of 20 atoms. The B 20 neutral cluster is found to overwhelmingly favor a double-ring tubular-type structure over any 2D isomers, whereas in the anion the tubular and several 2D structures are close in energy. The 2D-to-3D transition at B 20 is reminiscent of the ring-to-cage transition at C 20 , which forms the smallest fullerene (5). The tubular B 20 is the smallest stable 3D boron cluster and can be viewed as the embryo of the thinnest boron nanotube, with a diameter of 5.2 Å.
Methods
PES.The experiments were carried out by using a magnetic-bottle time-of-flight PES apparatus equipped with a laser vaporization supersonic cluster source (15, 17). B n Ϫ cluster anions were produced by laser vaporization of a disk target made of enriched 10 B isotope (99.75%) in the presence of a helium carrier gas and were analyzed with a time-of-flight mass spectrometer. The B 20 Ϫ clusters were mass-selected and decelerated before irradiation by a photodetachment laser beam. Photoelectrons were collected at nearly 100% efficiency by the magnetic bottle and analyzed in a 3.5-m-long electron flight tube. The photoelectron spectra were calibrated by the known spectrum of Rh Ϫ , and the energy resolution of the apparatus was ⌬E k ͞E k ϳ 2.5%, i.e., 25 meV for 1-eV electrons. Effort was devoted to control the cluster temperatures (Fig. 4, which is published as supporting information on th...