Empirical Relation of Second Optical Transition Energies of Metallic Single Wall Carbon Nanotubes with their Chirality

In this work we have examined the empirical relationship between the second optical transition energies (E22) and the chirality of metallic single-wall carbon nanotubes (SWCNTs). By deriving a quick and effective method, an empirical formula that predicts optical energy based on chiral indices (n, m) of the SWCNTs. Here, we compiled a range of SWCNTs with chiral indices from (4, 0) to (20, 20) and calculated their diameters and M22 values, which were then compared to empirical data from previous studies. With this suggested approach, the chiral index of metallic SWCNT can be used to directly assume its second optical transition energy. The experimental data is compared with the expected results. The average error between the computed and experimental values was determined, to visually present the findings, named the Katuara plot.