Assessment of theoretical methods for complexes of gold(I) and gold(III) with unsaturated aliphatic hydrocarbon: Which density functional should we choose?

Gold-substrate interaction is essential in gold-catalyzed organic transformations. This study uses high-level coupled cluster calculations with core-valence correlation and complete basis set (CBS) limit extrapolation as a reference, for assessing the performance of popular density functional theory (DFT) approximations for a variety of Au(I)/Au(III) complexes with unsaturated aliphatic hydrocarbon C_nH_m substrates (ethene, ethyne, and allene). The tested functionals cover from LDA to GGA and meta-GGA, and to hybrids and double hybrids (LSDA, PBE, M06-L, TPSS, B3LYP, PBE0, M06, M06-2X, TPSSh, B2-PLYP, B2GP-PLYP). Both the geometry and bond dissociation energy (D_e) of the Au-C_nH_m complexes are studied. Our findings show that B2GP-PLYP, PBE0, and B2-PLYP are the best performing functionals for this set of Au-C_nH_m complexes. DFT dispersion correction (DFT-D3), though very helpful for some functionals (e.g., B3LYP and B2-PLYP), does not uniformly improve the results of all functionals. Ab initio methods like MP2 and SCSMP2 are also tested. MP2 is found to be the worst performing method, and while SCSMP2 greatly improves the results, still its accuracy is lower than that of the best functionals, B2GP-PLYP, PBE0, and B2-PLYP.