End-cap effects on vibrational structures of finite-length carbon nanotubes.

Vibrational structures of C60-related finite-length nanotubes, C(40+20n) and C(42+18n) (1 < or = n < or = 4), in which n is, respectively, the number of cyclic cis- and trans-polyene chains inserted between fullerene hemispheres, are analyzed from density functional theory (DFT) calculations. To illuminate the end-cap effects on their vibrational structures, the corresponding tubes terminated by H atoms C(20n)H20 and C(18n)H18 (1 < or = n < or = 5) are also investigated. DFT calculations show a broad range of vibrational frequencies for the finite-size nanotubes: high-frequency modes (1100-1600 cm(-1)) containing oscillations along tangential directions (tangential modes), medium-frequency modes (700-850 cm(-1)) whose oscillations are located on the edges or end caps, and low-frequency modes (300-600 cm(-1)) involving oscillations along the radial directions (radial modes).