Symmetry properties of single-walled boron nitride nanotubes

The symmetry operations for armchair, zigzag, and chiral boron nitride nanotubes (BN-NT’s) are identified. It is found that each type belongs to a different family of nonsymmorphic rod groups. Armchair BN-NT’s with even index n are found to be centrosymmetric. We determine the numbers of Raman- and infrared-active vibrations in single-walled BN-NT’s. We find that, in contrast to achiral carbon nanotubes, zigzag BN-NT’s possess almost twice the Raman- and infrared-active vibrations as armchair BN-NT’s.