  The electrical and chemical properties of carbon nanotubes vary significantly
with different chirality and diameter, making the experimental determination of
these structural properties important. Here, we show that the vibrational
density of states (VDOS) contains information on the structure of carbon
nanotubes, particularly at low frequencies. We show that the diameter and
chirality of the nanotubes can be determined from the characteristic low
frequency $L$ and $L'$ modes in the VDOS. For zigzag nanotubes, the $L$ peak
splits into two peaks giving rise to another low energy $L"$ peak. The
significant changes in the frequencies and relative intensities of these peaks
open up a route to distinguish among structurally different nanotubes. A close
study of different orientations of Stone-Wales defects with varying defect
density reveals that different structural defects also leave distinct
fingerprints in the VDOS, particularly in the $L$ and $L'$ modes. With our
results, more structural information can be obtained from experiments which can
directly measure the VDOS, such as inelastic electron and inelastic neutron
spectroscopy.
