At What Size Do Neutral Gold Clusters Turn Three-Dimensional?

Recent experiments and calculations have established the transition from two-dimensional (2D) to three-dimensional (3D) structures at a cluster size of 8 and 12 atoms for gold cluster cations and anions. For neutral gold clusters, however, experimental data are scarce, and existing theoretical studies disagree on the 2D–3D crossover point. We present the results of global structure optimizations of neutral gold clusters Aun for n = 9–13 using a genetic algorithm and meta-generalized density functional theory. The relative energies of the lowest-lying isomers are computed using the revTPSS functional and the random phase approximation (RPA). Thermal, scalar relativistic, and spin–orbit effects are included, and basis set extrapolations are performed for the RPA calculations. For the 2D–3D transition of gold cluster cations and anions, this methodology yields near-quantitative agreement with cross section and electron diffraction measurements. For neutral gold clusters, the 2D and 3D structures are predicted to be almost isoenergetic at n = 11 gold atoms, while clusters with n > 11 are manifestly 3D. Thus, neutral gold clusters turn 3D at an unusually large size of 11 gold atoms.