  The vibrational modes of some single wall carbon nanotube (SWNT)
intramolecular junctions (IMJs) have been calculated using the newest Brenner
reactive empirical bond order (REBO) potential, based upon which their
nonresonant Raman spectra have been further calculated using the empirical bond
polarizability model. It is found that the Raman peaks induced by pentagon
defects lie out of the $G$-band of the SWNTs, so the high-frequency part of the
Raman spectra of the SWNT IMJs can be used to determine experimentally their
detailed geometrical structures. Also, the intensity of the Raman spectra has a
close relation with the number of pentagon defects in the SWNT IMJs. Following
the Descartes-Euler Polyhedral Formula (DEPF), the number of heptagon defects
in the SWNT IMJs can also be determined. The first-principle calculations are
also performed, verifying the results obtained by the REBO potential. The $G$
band width of the SWNT IMJ can reflect the length of its transition region
between the pentagon and heptagon rings.
