Density functional calculations have been carried out to obtain the geometric and electronic structure of boron sheets and nanotubes. The buckled boron sheet formed by alternating up and down rows of B atoms, with a buckling height of 0.85 Å, is about 0.20 eV/B atom more stable than the corresponding atomically flat sheet. Two different B–B bond-lengths characterize the buckled geometry: (i) 1.63 Å between the B atoms in a row and (ii) 1.81 Å between the B atoms in adjacent rows. Boron nanotubes (BNTs) formed by rolling up a B sheet exhibit also a buckled surface when their helicity allows for the formation of alternating up and down B rows in the surface. In all other cases, BNTs exhibit only flat surfaces. Hence, all the (n , 0) BNTs have a buckled geometry, while not all the (n , n ) BNTs have the same geometry. The buckled and flat nanostructures have different geometric and bonding characteristics, but both are metallic.
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