Beryllium Oxide Nanotubes and their Connection to the Flat Monolayer

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Single-walled zigzag beryllium oxide (BeO) nanotubes are simulated with an ab initio quantum chemical method. The (n,0) family is investigated in the range from n = 8 (32 atoms in the unit cell and tube radius R = 3.4 Å) to 64 (256 atoms in the cell and R = 27.1 Å). The trend toward the hexagonal monolayer (h-BeO) in the limit of large tube radius R is explored for a variety of properties: rolling energy, elastic modulus, piezoelectric constant, vibration frequencies, infrared (IR) intensities, oscillator strengths, and electronic and nuclear contributions to the polarizability tensor. Three sets of IR-active phonon bands are found in the spectrum. The first one lies in the 0–300 cm–1 frequency range and exhibits a very peculiar behavior: the vibration frequencies do tend regularly toward zero when R increases while their IR intensities do not; the nature of these normal modes is unveiled by establishing a connection between them and the elastic and piezoelectric constants of h-BeO. The second (680–730 cm–1) and third (1000–1200 cm–1) sets tend regularly, but with quite different slope, to the optical modes of the h-BeO layer. The vibrational contribution of these modes to the two components (parallel and perpendicular) of the polarizability tensor is also discussed. 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.