Band structure of semiconducting (0,n) carbon nanotubes (coefficients 0, n are the indices of the two-dimensional primitive lattice vectors of the graphene lattice) is calculated in terms of the linear augmented cylindrical wave method. The results are used to correlate the first and second minimum direct energy differences E11 and E22 between the singularities of the conduction and valence bands with the nanotube diameter d. Significant deviations from the equation Eii∼d−1,i=1,2, are observed. The gap energies E11(d−1) and E22(d−1) are oscillating functions that gradually decay to zero as d−1 goes to zero, reach their maximum at d−1 between 0.08 and 0.1 Å−1, and decrease abruptly at d−1>0.1 Å−1. There are two branches of the dependence of Eii on d even for nanotubes with the same chirality. This ambiguity complicates the determination of the structure of nanotubes on the basis of optical gaps, but, on the other hand, it opens the opportunity to classify experimental data more specifically.

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