Validation of density functional methods for the calculation of small gold clusters.

The performance of various density functional theory methods on the geometries and energetics of Au(2), Au(3), Au(4), and Au(5) has been systematically evaluated. The results were compared with those from experiments or high-level wave function theory methods. In the present study, spin-orbit (SO) coupling was considered. It was found that SO coupling plays a very important role in the calculation of both the atomization energies and relative stability of the isomers of gold clusters. Functionals including SO coupling effect will overestimate the atomization energies of gold clusters compared with those just including the scalar relativistic (SC) effect. On the other hand, hybrid functionals will underestimate the atomization energies compared with those of the corresponding pure functionals. For the calculation of the relative stability of the different isomers, many functionals not including SO coupling will predict the wrong stability order. In addition, SO correction to the atomization energy of the cluster (ΔE(SO)) has a weak dependence on the choice of functional. A linear relationship was established between ΔE(SO) and the number of Au atoms and Au-Au bonds in the cluster. The relationship indicates that inclusion of SO coupling will favor the isomer with more Au-Au bonds. Among all of the functionals evaluated, the SO TPSSh method has the best overall performance, and SC M06-L also performs well, although it predicts that the two isomers of Au(3) are almost degenerate in energy.