Small Gold-Thiolate Clusters Au3(SMe)3: Benchmarking of Density Functionals and Bonding Analysis

We present a benchmark study on popular density functionals for their efficiency and accuracy in the geometry and relative stability of gold-thiolate nanoclusters taking Au3(SMe)3 isomers. We have used normalized mean absolute error (NMAE) analysis as a parameter to compare the results with the reference methods - DLPNO-CCSD(T) and RI-SCS-MP2. We have also compared the performance on the thiolate interaction energy of the stable geometries using the results from our benchmark study. One of the promising functional is PBE that shows robust performance for geometry optimization. On the other hand, M06-2X stands out as the proper choice for the relative energies of the clusters. With the selected methods, we have analyzed the gold-sulfur interaction in Au3(SMe)3 and a comparison is made with AuSMe. The bonding analysis has revealed a partial covalency between gold and sulfur atoms in general. On going from AuSMe to Au3(SMe)3, a substantial flow of charge from gold atoms to thiolate ligands as a result of the increase in gold s-d hybridization. As the s-d mixing in Au increases, the main character of Au-S interaction shifts from covalent to ionic. Hence, a covalent-charge-transfer interaction dominates in gold-sulfur bonding and gives rise to a charge-shift bonding.