Polarization of metallic carbon nanotubes from a model that includes both net charges and dipoles

A technique commonly used to determine the polarization of carbon nanotubes is to associate with each atom a dipole, whose value is computed self-consistently considering the external field and the interactions with the other dipoles. We extend here this semi-empiric description by associating with each atom both a net electric charge and a dipole. Considering net charges in addition to the dipoles enables one to address the fact that electrons move from one part of the molecule to the other in response to an external field. It also enables one to account for the accumulation of extra charges. Those effects, which actually occur in any metallic structure, are poorly accounted for by models that rely on dipoles only. We propose here a computational scheme to determine those charges and dipoles based on the requirement that the total electrostatic energy of this system is minimized. As an application, we study the polarization of a (5,5) nanotube, which is either isolated, close to a metallic surface, or in direct contact with it, as required for simulations of field emission. Compared to the model wherein only dipoles are considered, this technique gives a better account of the metallicity of this kind of nanotube. It also enables one to account for the equilibration of the chemical potentials at the back contact with the metallic support.