Optical properties of sub 2 nm long (6,5) single-walled carbon nanotubes: first principles investigation

Optical properties of (6,5) single-walled carbon nanotubes (SWCNTs) of 1 and 2?nm lengths were studied with the help of time-dependent density functional theory and transition density matrix based analysis. Electronic band gap of all SWCNTs is found to be in the range 0.82–1.67?eV. The peak absorptions occur around 600?nm for 1?nm nanotubes and get broader as the length increases to 2?nm. The natural transition orbital analysis was applied to understand the electron delocalisation upon absorption. Finally, the exciton sizes were determined and found to be in the range 6.80–7.25?Å for 1?nm SWCNTs, and 6.82–11.56?Å for 2?nm SWCNTs, which were further used in the electron delocalisation analysis. All the excitons were found to be Frenkel in nature. This study illustrates how the excited state properties in SWCNTs can vary upon length change and improves the understanding of electronic excitations in SWCNTs, which would be beneficial in photovoltaic applications.