In this chapter we review the existing theoretical literature of hydrogen and oxygen interaction to single walled carbon nanotubes. The importance of theoretical simulations for understanding the adsorption procedure and for improving the storage capacity of these nanomaterials is underlined. We report three different approaches to treating large systems with ab initio methods the periodic DFT, the mixed QM/MM model, and the cluster model. For all advantages and disadvantages are presented.

Specifically for the hydrogen adsorption, it is showed that both periodic DFT and mixed QM/MM models can successfully be employed in the SWNT and provide a solution to the problem of making accurate calculations in large systems like nanotubes. The results of Bauschlicher [34] and Froudakis [35] demonstrate that atomic hydrogen will bind to the tube walls and not enter in the tube interior. This binding can take place either in pairs of lines toward the tube axis, as the first suggests, or in zigzag rings around the tube walls, supported by the second. This will result in a change of the tube shape during the hydrogen adsorption and an enlargement of the tube volume [35]. Both found 50% to be the maximum coverage of the tube walls. After the tube walls are half filled with hydrogen, the energetically more favorable procedure of hydrogen insertion in the tube is obtained [35].

Since the storage capacity is mostly obtained by molecular hydrogen, Froudakis [41] tried to answer why alkali-doped carbon nanotubes possess high hydrogen uptake as put forward by Chen et al. in 1999 [9]. His results demonstrate a charge transfer from the alkali metal to the tube that polarizes the H2 molecule. This charge induced dipole interaction characterizes the H2 physisorption on alkali metal doped tubes and is responsible for the higher hydrogen uptake of the doped tubes.

As a general remark for hydrogen we can report that in the last couple of years the theoretical modeling of the hydrogen storage in carbon nanotubes has obtained only its first goal (i.e., to give an understanding of what it is going on in the laboratory experiments by explaining the elementary parts of the adsorption procedure). The second and most important goal, which is still to come, is to predict how the storage capacity of carbon nanotubes can be improved and reach a sufficient level for commercial use in fuel-cell electric vehicles.

As far the oxygen adsorption in carbon nanotubes is concerned we showed that atomic oxygen exothermically reacts with the tube walls performing epoxides. For molecular oxygen the picture is not so clear. Both singlet and triplet states have to be taken into account. These configuration states have to be combined with the two different isomers found, resulting a complicated potential energy hypersurface (PES). This complicated PES characterizes the oxygen adsorption to carbon nanotubes and is also responsible for the controversy existing in the literature.

According to our results there are two different possibilities for the atmospheric oxygen adsorption to carbon nano-tubes: In the first the O2 is excited to its singlet electronic configuration and then it automatically reacts exothermically with the tube. In the second case we start with O2 in its triplet ground state and an energy of ~15 kcal/mol has to be offered to the system in order to overpass the energy barrier and react with the tube. The latter pathway can be supported by the existence of defects in the tube and temperature in the environment.

Considering this theoretical result together with the experimental observation that the electronic and transport properties of carbon nanotubes are extremely sensitive to

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