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Figure 2. The calculations of Lee and Lee [31] for the chemical adsorption of H in SWNTs: (a) (5,5) SWNT before storage; (b) hydrogens adsorbed at the exterior of the tube wall; (c) adsorption of a single hydrogen atom at the interior of the wall; (d) initial and (e) fully relaxed geometry of (d); (f) molecular hydrogen inside the (5,5) SWNT; (g) H2 inside (10,0) SWNT with an analogy of two H per one C atom and with 2.4 H/C (f). Bond lengths are in A.

place, with the relaxation accuracy that the large size of the tube guarantees.

Bauschlicher used an (10,0) carbon nanotube for studying the hydrogen and fluorine binding to its wall [33] and for examining the maximum coverage of the tube wall [34]. The entire model used 200 carbon atoms while the ab initio section includes 24 carbon atoms. The ONIOM two level method of Dapprich and co-workers [21] was used for this purpose as it is implemented in the Gaussian 98 program package [36]. The higher level was treated with DFT and the lower level with MM. More specifically the B3LYP hybridic functional together with the 4-31G basis set was employed for the QM part and the universal force field (UFF) for the MM part. The preferable sites for the chemisorption of one, two, and four hydrogen atoms in the tube walls are reported together with the binding energies [33].

In [35] we applied the QM/MM approach in a 200-atom (4,4) SWNT, treating up to 64 carbons and 32 hydrogens with the higher level of theory (Fig. 1b). The small diameter of the tube together with the large number of atoms considered allow the higher level model to include a cylindrical part of the tube. This is very critical for investigating changes of the shape of the tube during the adsorption procedure.

In Figure 1b, we can see the two-level ONIOM [21] model that was used in [35]. The B3LYP functional was employed for inner part of the tube, as in [33, 34]. Nevertheless a larger set of double-^ basis was employed (6-31G*) that includes polarization functions. The two outer cylindrical parts were treated with the UFF while the dangling bonds at the ends of the tube were saturated with hydrogen atoms.

All the computations were performed with the Gaussian 98 program package [36].

These studies [33-35] mainly try to answer two questions: The first concerns the coverage of SWNTs by hydrogen atoms and the second deals with the difficulty of putting hydrogen atoms inside the tube. From the work of Bauschlicher [33] and Froudakis [35] it is clear that the hydrogen atoms that approach the SWNT will be bound to the tube walls in neighboring C atoms for minimizing the loss of C-C n bonds. But there are many different ways of doing this: One is to follow a zigzag line parallel to the tube axis while another is to follow an armed chair ring vertical to the tube axis. First principle calculations [35] showed that the second procedure is energetically more favorable as has also been found experimentally for similar systems [13].

Furthermore it is interesting to see the effect of the two different hydrogen chemisorption patterns mentioned before on the shape of the tube walls. In Figure 3 we can see the optimized structures with 64 C and 16 H atoms in the QM region from [35]. The C atoms that hydrogens are bonded to pass from the sp2 to sp3 hybridization. This affects drastically the bond lengths and the size of the tube hexagons. The C-C bond length increases from 1.43 to 1.59 A while the diameter of the hexagons goes from 2.84 to 3.15 A if four hydrogen atoms are attached to this hexagon (Fig. 3b). These cause a strain that leads to tube deformation.

In the case of the line orientation of the hydrogens the shape of the tube changes from cyclic to elliptic (Fig. 3a). The 5.4 A diameter of the tube without hydrogen split to

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