Optimization of the Calculations of the Electronic Structure of Carbon Nanotubes

Abstract

A method is proposed for calculating the electronic structure and physical properties (in particular, Young’s modulus) of nanotubes, including single-walled carbon nanotubes. This method explicitly accounts for the periodic boundary conditions for the geometric structure of nanotubes and makes it possible to decrease considerably (by a factor of 10–103) the time needed to calculate the electronic structure with minimum error. In essence, the proposed method consists in changing the geometry of the structure by partitioning nanotubes into sectors with the introduction of the appropriate boundary conditions. As a result, it becomes possible to reduce substantially the size of the unit cell of the nanotube in two dimensions, so that the number of atoms in a new unit cell of the modified nanotube is smaller than the number of atoms in the initial unit cell by a factor equal to an integral number. A decrease in the unit cell size and the corresponding decrease in the number of atoms provide a means for drastically reducing the computational time, which, in turn, substantially decreases with an increase in the degree of partition, especially for nanotubes with large diameters. The results of the calculations performed for carbon and non-carbon (boron nitride) nanotubes demonstrate that the electronic structures, densities of states, and Young’s moduli determined within the proposed approach differ insignificantly from those obtained by conventional computational methods.