Small gold cluster anions ${{\mathrm{Au}}_n}^{-}$ are known for their unusual two-dimensional (2D) structures, giving rise to properties very different from those of bulk gold. Previous experiments and calculations disagree about the number of gold atoms $n_c$ where the transition to 3D structures occurs. We combine trapped ion electron diffraction and state of the art electronic structure calculations to resolve this puzzle and establish $n_c=12$. It is shown that theoretical studies using traditional generalized gradient functionals are heavily biased towards 2D structures. For a correct prediction of the 2D-3D crossover point it is crucial to use density functionals yielding accurate jellium surface energies, such as the Tao-Perdew-Staroverov-Scuseria (TPSS) functional or the Perdew-Burke-Ernzerhof functional modified for solids (PBEsol). Further, spin-orbit effects have to be included, and large, flexible basis sets employed. This combined theoretical-experimental approach is promising for larger gold and other metal clusters.

• Received 27 November 2007

DOI:https://doi.org/10.1103/PhysRevA.77.053202