Bulk fragment and tubelike structures ofAuN(N=2−26)

Using the relativistic all-electron density-functional calculations on the ${\mathrm{Au}}_{N}$ $(N=2\text{\ensuremath{-}}26)$ in the generalized gradient approximation, combined with the guided simulated annealing, we have found that the two- to three-dimensional structural transition for ${\mathrm{Au}}_{N}$ occurs between $N=13$ and 15, and the ${\mathrm{Au}}_{N}$ $(16\ensuremath{\le}N\ensuremath{\le}25)$ prefer also the pyramid-based bulk fragment structures in addition to the ${\mathrm{Au}}_{20}$. More importantly, the tubelike structures are found to be the most stable for ${\mathrm{Au}}_{24}$ and ${\mathrm{Au}}_{26}$, offering another powerful structure competitor with other isomers, e.g., amorphous, bulk fragment, and gold fullerene. The mechanism to cause these unusual ${\mathrm{Au}}_{N}$ may be attributed to the stronger $s$-$d$ hybridization and the $d$-$d$ interaction enhanced by the relativistic effects.