Performance of Density Functionals and Semiempirical 3c Methods for Small Gold-Thiolate Clusters

In light of the recent surge in computational studies of gold thiolate clusters, we present a comparison of popular density functionals (DFAs) and three-part corrected methods (3c-methods) on their performance by taking a data set named as AuSR18 consisting of 18 isomers of Au(SCH₃) (m ≤ n = 1-3). We have compared the efficiency and accuracy of the DFAs and 3c-methods in geometry optimization with RI-SCS-MP2 as the reference method. Similarly, the performance for accurate and efficient energy evaluation was compared with DLPNO-CCSD(T) as the reference method. The lowest energy structure among the isomers of the largest stoichiometry from our data set, AuSR18, i.e., Au₃(SCH₃)₃, is considered to evaluate the computational time for SCF and gradient evaluations. Alongside this, the numbers of optimization steps to locate the most stable minima of Au₃(SCH₃)₃ are compared to assess the efficiency of the methods. A comparison of relevant bond lengths with the reference geometries was made to estimate the accuracy in geometry optimization. Some methods, such as LC-BLYP, ωB97M-D3BJ, M06-2X, and PBEh-3c, could not locate many of the minima found by most of the other methods; thus, the versatility in locating various minima is also an important criterion in choosing a method for the given project. To determine the accuracy of the methods, we compared the relative energies of the isomers in each stoichiometry and the interaction energy of the gold core with the ligands. The dependence of basis set size and relativistic effects on energies are also compared. The following are some of the highlights. TPSS has shown accuracy, while mPWPW shows comparable speed and accuracy. For the relative energies of the clusters, the hybrid range-separated DFAs are the best option. CAM-B3LYP excels, whereas B3LYP performs poorly. Overall, LC-BLYP is a balanced performer considering both the geometry and relative stability of the structures, but it lacks diversity. The 3c-methods, although fast, are less impressive in relative stability.