Energies of optical transitions in metal and semiconductor nanotubes

The energies of low-energy optical transitions were calculated, using the linearized attached cylindrical waves (LACW) method, as a function of inverse diameter d−1 for (n, n) metal nanotubes with n ranging from 3 to 12 and for (n, 0) semiconductor nanotubes with n ranging from 10 to 25. The calculations show that E11 in the metal nanotubes is higher than in the semiconductor nanotubes. Significant violations of the E11 ∼ d−1 relationship are observed. For metal nanotubes, the situation is more complex because of the close energies of the π-π*-and σ-π* vertical transitions and because of the intersection of these characteristics in the range of 0.7 nm−1 < d−1 < 1.0 nm−1 (n = 8, 9, 10). For the semiconductor nanotubes, the E11 versus d−1 relationship is not linear, rather, it is oscillating; the E11(d−1) function alternates between two curves that refer to the (n, 0) nanotubes for which division of n by 3 gives 1 or 2 in the residue. On one hand, these features hamper the use of optical measurements in structure determination for the nanotubes; on the other, new criteria for nanotube classification appear.