Nonlocal effects on the structural transition of gold clusters from planar to three-dimensional geometries.

Conventional density functional theory calculations heavily bias planar structures in gold clusters, failing to predict the structural transition from planar to three-dimensional geometries in experimentally detected gold species. Inspired by recent progress in calculating the defect energies of coinage metals with nonlocal effect-enhanced hybrid functionals, we have studied nonlocal effects in gold clusters. Although the hybrid functional was accurate for bulk gold, it heavily biased the planar structure for gold clusters. By including dispersive interactions into semilocal density functional calculations, we obtained an accurate vacancy formation energy of 0.72 eV for bulk gold along with the correct structural transition for gold clusters. The transition was found to occur at Au 12 - for gold anions and at Au 8 + for gold cations, agreeing very well with the experimental results. For neutral gold clusters, we found the transition to occur at Au 10 , indicating the need for experimental verification. The results show the importance of nonlocal effects in the study of gold clusters, calling for further comprehensive theoretical and experimental studies to evaluate nonlocal effects in Au and other precious metals.