Figure 3. Optimized geometries from [35] showing 16 hydrogen atoms bonded in the tube in the two different ways: (A) following two zigzag lines parallel to the tube axis and (B) following an "armchair" ring vertical to the tube axis. In the lower part of the figure we see the tube toward its axis and we report the changing of its diameter in angstroms. Modified from [35], G. E. Froudakis, Nano Lett. 1, 179 (2001). © 2001, American Chemical Society.

a small 4.1 A and large 7.2 A diameter of an ellipsis. In the case of the ring orientation we see an enlargement of the tube diameter from 5.4 to 6.2 A but keeping the cyclic shape (Fig. 3b). The second orientation is more favorable because the strain can be relaxed with the enlargement of one ring that does not affect the whole tube, while in the first case, an axial enlargement of the tube cannot take place only in one zigzag C line. This effect results in an energy difference of 2.6 eV between these two orientations. It is worth mentioning that in the line format we have no change in the volume of the tube while in the ring one, we have a 30% enlargement of the volume.

Since the hydrogens "prefer" to form rings around the tube the next question that arise is how close can those rings be? For answering this question in [35] we performed calculations with two different zigzag ring orientations (48 carbons and 32 hydrogens in the QM region). In the first, the rings were separated and in the second they were close together as can be seen in Figure 4a (middle and right upper part, respectively). After optimizing the geometries the separated configuration showed a repeated increasing and decreasing of the tube diameter of almost 1 A. On the other hand, when the rings were closed together, the tube diameter was increased in the first ring by 1 A and decreased to the normal value at the last ring. The total energy of the "ring by ring" configuration was favored energetically from the "all rings together" configuration by 17 eV

This energy difference can be explained from the nature of the hybridization of the carbon atoms. During hydrogen addition the carbon atoms pass from sp2 to sp3 hybridization and a three-dimensional (3D) bond orientation is preferable. This 3D orientation can be obtained by the continued changing of the tube diameter in the "ring by ring"

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