Assignment of the G(+) and G(-) Raman bands of metallic and semiconducting carbon nanotubes based on a common valence force field

We propose a model for calculating the phonon frequencies of any (n,m) nanotube by considering explicitly the curvature of the system and the effects of long-range interactions determined by pi electrons. We show that the electron-phonon coupling strength is directly related to the electronic structure of the nanotube and it is the main interaction responsible for the different behavior shown in the Raman spectra by metallic and semiconducting nanotubes. On the basis of the vibrational valence force field derived in this work we propose an assignment of the G band. Moreover, based on symmetry-selection rules, we can state that the LO modes of armchair nanotubes and the TO modes of zigzag nanotubes at GAMMA= 0 are silent in the Raman spectra.