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In this work the electronic structure and optical properties such as dielectric function and optical constants of 3, 3, 5, 0 and 4, 2 small diameter carbon and boron nitride nanotubes with comparable 4Å diameter, have been investigated within the framework of density functional theory DFT using the full potential linear augmented plane wave FP-LAPW method. The calculated electronic structures show depending the chirality, small diameter carbon nanotubes can have metallic or semiconducting behavior while boron nitride nanotubes are wide semiconducting gap independent the tube’s chirality. It is also revealed that unlike the boron nitride nanotubes, the absorption spectra of 4Å single-walled carbon nanotubes depend strongly on their chiralities. Our results are in good agreement with the previous reported data.