A balanced procedure for the treatment of cluster-ligand interactions on gold phosphine systems in catalysis

Ligand-protected metal clusters are difficult to describe within density functional theory due to the need to treat the electronic structure of the cluster, possible charge transfer between the ligands and the cluster, and weak ligand-ligand interactions in a balanced manner. We demonstrate the use of an appropriate, stepwise benchmarking process that accounts for the nonadditivity of these different contributions to stability and catalytic activity. We consider both open- and closed-shell clusters, differently charged systems, and ligands of increasing complexity for gold phosphine systems. The use of a dispersion correction to density functional calculations was found to be crucial for both structure optimization and the calculation of binding energies. We find that PBE-D3 performs well with a variation in energetics of 0.7-10.9 kcal/mol, PBE0-D3 better with 0.0-3.3 kcal/mol, and B2PLYP-D3 the best with 0.2-2.4 kcal/mol, when compared to the best available benchmark [CCSD(T) or SCS-MP2]. Our systematic procedure clarifies that these functionals all give accurate results for certain cases, but for the total performance over a range of interactions, they perform in accordance with Jacob's ladder.