Vibrational spectra and phonon dispersion analysis of a single-walled zigzag carbon nanotube: A first principles study

Abstract

This paper reports a vibrational spectroscopic study on a zigzag single-walled carbon nanotube (SWCNT) using the first-principles method based on density functional theory (DFT). The most suitable exchange correlation functional for DFT analysis was determined by comparing the predicted value of band gap of the SWCNT under study with the experimental value reported in the literature. General gradient approximation functional in combination with revised Perdew–Burke–Ernzerh sub-functional was found to give the best results. Using this optimum combination, phonon density of states and phonon dispersion curves have been determined. The analysis of results obtained focuses on symmetry considerations, group theory analysis, segregation of Raman active and infrared (IR) active vibrational modes and interpretation of the Raman and IR spectra obtained. The earlier approaches to the problem rely upon the zone folding technique and force constant models in which structural relaxation factor is not taken care of. An ab initio approach has been adopted by the authors in this work, which is advantageous as it neither depends on some predefined parameter nor does it ignore the structural relaxation factor. Analysis of the Raman spectrum reveals some additional peaks other than the commonly known radial breathing mode, D, G, and G′ bands in the SWCNT spectra, which have been recently reported to be observed experimentally also. Similarly, the theoretically developed IR spectrum for the simulated SWCNT is also in agreement with experimental observations. The methodology presented thus provides a very useful and novel simulation route to predict the vibrational modes, Raman spectra, and IR spectra of SWCNTs theoretically.