The Structure, Stability, and Properties of a One-Dimensional $\alpha $-Boron Structure*

Boron is an electron deficient element exhibiting a complex and versatile chemistry. In this work we have performed a preliminary study on the structural stability and electronic properties of one-dimensional $\alpha $-boron structures based on the SCED-LCAO molecular dynamics scheme (MD) [PRB 74, 15540 (2006)]. The one-dimensional $\alpha $-boron structures were generated by constructing icosahedra B$_{12}$ clusters, referred as $\alpha $-boron balls, and arranging them in one-dimension. Such structures were stabilized through the simulated annealing based on the SCED-LCAO MD. We found that: (1) the $\alpha $-boron ball is compressed in comparison to its bulk counterpart ($\alpha $-phase); (2) the distance between ``$\alpha $-boron balls'' is shorter in the center of the chain than that at the two ends and decreases as the length of the chain increases; (3) the HOMO-LUMO gap is very small ($\sim$1 meV) in the finite chains, but it opens up when the chain length becomes infinite. The optimized lattice constant of the infinite $\alpha $-boron chain was found to be 2.998 {\AA} and its energy gap is found to be 0.74 e. The stability and properties of ring-shaped one-dimensional $\alpha $-boron structures will also be discussed.