4. Conclusions

In analogy to the existing transition metal chalcogenide nanotubes, we have investigated hypothetical noble-metal chalcogenide nanotubes (PdS2, PdSe2, PtS<sup>2</sup> and PtSe<sup>2</sup> NTs) through density functional theory calculations. We have shown that formation of these nanotubes is possible, since they have smaller strain energies than MoS<sup>2</sup> or WS<sup>2</sup> nanotubes. Furthermore, we have found that the strain energy of the studied nanotubes is chirality independent and decreases inverse quadratically with the tube diameter. Moreover, PdX<sup>2</sup> nanotubes are more stable than PtX<sup>2</sup> for nanotubes with small diameters. We have also examined the electronic structure of noble-metal chalcogenide monolayers and nanotubes, which are found to be all indirect band gap semiconductors in the ranges of 0.6–1.1 eV (0.9–1.7 eV) and 0.3–0.8 eV (0.6–1.3 eV) for PdS<sup>2</sup> (PtS2) and PdSe<sup>2</sup> (PtSe2) NTs, respectively. These NTs band gaps increase with the diameter rapidly approaching that of the respective pristine 2D monolayer.

#### Acknowldgements

This work was supported by the German Research Council (Deutsche Forschungsgemeinschaft, HE 3543/18-1), the European Commission (FP7-PEOPLE-2009-IAPP QUASINANO, GA 251149 and FP7-PEOPLE-2012-ITN MoWSeS, GA 317451).

### Author Contributions

Nourdine Zibouche, Agnieszka Kuc, Pere Miró and Thomas Heine generated, analyzed and discussed the results. Thomas Heine conceived this project. All authors contributed in writing this paper.
