Universal empirical formula for optical transition energies of semiconducting single-walled carbon nanotubes

A general empirical relation for calculating first seven optical transition energies of semiconducting single wall carbon nanotubes (SWCNTs) is proposed here for the first time. The proposed formula effectively relates first seven optical transition energies of semiconducting SWCNTs with their chiral indices (n, m) through exponential form containing two specific terms (n+2m) and (2n-m). Both mod 1 and mod 2 types of semiconducting tubes are considered here over a wide diameter range from 0.4 nm to 4.75 nm. It was observed that the proposed empirical relations can predict the recent experimental data of those optical transitions with high accuracy.