We have calculated the adsorption energies for different hydrogen dimers adsorbed at the surface of zigzag single-walled carbon nanotubes (SWCNs) (n,0) (for n = 6-28) to identify the range of nanotube structural parameters that provide optimal adsorption energetics. We determined that, for H(2) gas in equilibrium with adsorbed hydrogen dimers, under normal conditions, carbon nanotubes with diameters in the range of 0.77 +/- 0.19 nm have a minimum energy overhead for hydrogen release and uptake in the hydrogen storage process. Most interestingly, we also found that the adsorption energies of hydrogen are correlated to the modulations of the nanotube density of states, because of the quantum confinement of electrons along the circumference of the SWCN. This effect is discussed from the perspective of chemical bond formation and is related to the valence to conduction band excitation energy.