From spatial symmetry to vibrational spectroscopy of single-walled nanotubes

The classification of a molecule’s spatial symmetry is an essential initial step in predicting its vibrational spectra. When a (chemical) substitution is made, the relationship between the spatial symmetries of the molecule and its derivatives governs the differences between their corresponding vibrational spectra. These text-book statements of molecular spectroscopy have also found recent and successful applications with much larger molecules, namely single-walled nanotubes. The purpose of this work is to review the profound interplay between the spatial symmetry and the numbers of Raman-and infrared-active vibrations in single-walled carbon and boron nitride nanotubes.