Geometry, and Normal Modes of Vibration (3N-6) for Di and Tetra- Rings Layer (6, 0) Linear (Zigzag) SWCNTs; A DFT Treatment

Abstract

Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single  wall  carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequencies (symmetric and asymmetric modes) based on the image modes applied by the Gaussian 09 display. The whole relations for the vibration modes were also done including \(\nu\)CH stretching, \(\nu\)C--C stretching, \(\delta\)CH, \(\delta\)ring (\(\delta\)C--C--C) deformation in plane of the molecule) and \(\gamma\)CH, \(\gamma\)ring (\(\gamma\)C--C--C) deformation out of plane of the molecule. The assignment also included modes of puckering, breathing and clock-anticlockwise bending vibrations.