Abstract
The vibrational modes, especially the radial breathing modes (RBMs), of single-walled gold nanotubes (SWGTs) have been calculated using the density-functional theory in the generalized gradient approximation, taking into account the gold's relativistic effect. It is found that the maximal frequency of the SWGTs are comparable to that of bulk gold, but its vibrational density of states is quite different. Although the RBM frequencies of the SWGTs are found to depend on both of their diameters and chiral symmetries, a linear variation of them with the inverse tube diameters is still found to hold approximately. It is also found that the scalar relativistic effect increases their bond strength, but shortens greatly their bond lengths, and the tube diameter, increasing so their RBM frequency significantly.
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