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

Abstract

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.

Cationic gold clusters ligated with differently substituted phosphines: effect of substitution on ligand reactivity and binding

“…37 Similarly, Mollenhauer and Gaston 39 demonstrated a sharp increase in the Au-P binding energy from 18 kcal mol À1 to 29 kcal mol À1 when PH 3 is replaced with PMe 3 , whereas the Au-PPh 3 system is only slightly more strongly bound than the Au-PMe 3 complex (B31 kcal mol À1 ). Substantially higher binding energies of 72 and 75 kcal mol À1 for PMe 3 and PPh 3 , were reported in that study for cationic Au 6 L 6 2+ clusters 39 indicating that ligand binding energy may be affected by the cluster size and charge. Nevertheless, similar to the MeAuPR 3 complex discussed earlier, PPh 3 is slightly more strongly bound to the cluster core than PMe 3 .…”

Effect of Charge and Phosphine Ligands on the Electronic Structure of the Au8 Cluster

“…As a consequence, the binding energy changes up to 5 and 11 kcal/mol when the dispersion correction is included for neutral and plus one-charged Au–PPh 3 and Au 2 PPh 3 complexes. 48 However, we did not consider an additional dispersion correction for our DFT method because we were looking for structural changes and electronic behavior and qualitative energy trends.…”

Ligand-protected gold clusters: the structure, synthesis and applications

“…176 The differences between the Au7P interatomic distances in AuPH 3 , Au 2 PH 3 , AuPH 3 and Au 2 PH 3 calculated at the DFT and CCSD(T) levels of theory are even smaller, namely, 0.01 # A. 177 The persion-corrected PBE-D3, TPSS-D3 functionals are recommended for calculations of bond energies in the Au n clusters (n 4 20) with an accuracy of 4 kJ mol 71 . 176 The contribution of spin ± orbit coupling to the Au7Au bond energy can be correctly included using the PBE-PBE-2c functional.…”