Planar-to-tubular structural transition in boron clusters: B 20 as the embryo of single-walled boron nanotubes

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 B 20 neutral cluster has a double-ring tubular structure with a diameter of 5.2 Å. For the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{B}}_{20}^{-}\end{equation*}\end{document} 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 B 20 , reminiscent of the ring-to-fullerene transition at C 20 in carbon clusters, suggests it may be considered as the embryo of the thinnest single-walled boron nanotubes.