The vibration properties of the (n,0) boron nitride nanotubes from ab initio quantum chemical simulations

The vibration spectrum of single-walled zigzag boron nitride (BN) nanotubes is simulated with an ab initio periodic quantum chemical method. The trend towards the hexagonal monolayer (h-BN) in the limit of large tube radius R is explored for a variety of properties related to the vibrational spectrum: vibration frequencies, infrared intensities, oscillator strengths, and vibration contributions to the polarizability tensor. The (n,0) family is investigated in the range from n = 6 (24 atoms in the unit cell and tube radius R = 2.5 Å) to n = 60 (240 atoms in the cell and R = 24.0 Å). Simulations are performed using the CRYSTAL program which fully exploits the rich symmetry of this class of one-dimensional periodic systems: 4n symmetry operators for the general (n,0) tube. Three sets of infrared active phonon bands are found in the spectrum. The first one lies in the 0–600 cm−1 range and goes regularly to zero when R increases; the connection between these normal modes and the elastic and piezoelectric constants of h-BN is discussed. The second (600–800 cm−1) and third (1300–1600 cm−1) sets tend regularly, but with quite different speed, to the optical modes of the h-BN layer. The vibrational contribution of these modes to the two components (parallel and perpendicular) of the polarizability tensor is also discussed.