The adsorption of atomic and molecular hydrogen on armchair and zigzag boron carbonitride nanotubes is investigated within the ab initio density functional theory. The adsorption of atomic H on the $\mathrm{B}{\mathrm{C}}_{2}\mathrm{N}$ nanotubes presents properties which are promising for nanoelectronic applications. Depending on the adsorption site for the H, the Fermi energy moves toward the bottom of the conduction band or toward the top of the valence band, leading the system to exhibit donor or acceptor characteristics, respectively. The ${\mathrm{H}}_{2}$ molecules are physisorbed on the $\mathrm{B}{\mathrm{C}}_{2}\mathrm{N}$ surface for both chiralities. The binding energies for the ${\mathrm{H}}_{2}$ molecules are slightly dependent on the adsorption site, and they are near to the range to work as a hydrogen storage medium.
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