Chirality-Dependent Properties of Carbon Nanotubes. Electronic Structure: Optical Dispersion Properties, Hamaker Coefficients and van der Waals - London dispersion interactions
Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based calculations to obtain the band structures and the frequency dependent dielectric response function from 0-30 eV for 64 SWCNTs differing in radius, electronic structure classification, and geometry. The resulting optical dispersion properties can be categorized over three distinct energy intervals (M, pi, and sigma, respectively representing 0-0.1, 0.1-5, and 5-30 eV regions) and over radii above or below the zone-folding limit of 0.7 nm. While pi peaks vary systematically with radius for a given electronic structure type, peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. Based on these calculated one-electron dielectric response functions we compute and review Van derWaals - London dispersion spectra, full spectral Hamaker coefficients, and van derWaals - London dispersion interaction energies for all calculated frequency dependent dielectric response functions. Our results are categorized using a new optical dielectric function classification scheme that groups the nanotubes according to observable trends and notable features (e.g. the metal paradox) in the 0-30 eV part of the optical dispersion spectra. While the trends in these spectra begin to break down at the zone folding diameter limit, the trends in the related van derWaals - London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class.