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, sigma peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. We also observe the so-called metal paradox, where a SWCNT has a metallic band structure and continuous density of states through the Fermi level but still behaves optically like a material with a large optical band gap between M and pi regions. This paradox appears to be unique to armchair and large diameter zigzag nanotubes. Based on these calculated one-electron dielectric response functions we compute and review van der Waals-London dispersion spectra, full spectral Hamaker coefficients, and van der Waals-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 der Waals-London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class.