  Using the relativistic all-electron density-functional calculations on the
AuN (N=2-26) in the generalized gradient approximation, combined with the
guided simulated annealing, we have found that the two- to three-dimensional
structural transition for AuN occurs between N=13 and 15, and the AuN (16<= N
<=25) prefer also the pyramid-based bulk fragment structures in addition to the
Au20. More importantly, the tubelike structures are found to be the most stable
for Au24 and Au26, offering another powerful structure competitor with other
isomers, e.g., amorphous, bulk fragment, and gold fullerene. The mechanism to
cause these unusual AuN may be attributed to the stronger s-d hybridization and
the d-d interaction enhanced by the relativistic effects.
