Aurophilic Interactions from Wave Function, Symmetry-Adapted Perturbation Theory, and Rangehybrid Approaches

The aurophilic interaction is examined in three model systems Au2((3)Σg(+)), (AuH)2, and (HAuPH3)2 which contain interactions of pairs of the Au centers in the oxidation state (I). Several methods are employed ranging from wave function theory-based (WFT) approaches to symmetry-adapted perturbation theory (SAPT) and range-separated hybrid (RSH) density functional theory (DFT) methods. The most promising and accurate approach consists of a combination of the DFT and WFT approaches in the RSH framework. In this combination the short-range DFT handles the slow convergence of the correlation cusp, whereas the long-range WFT is best suited for the long-range correlation. Of the three tested RSH DFT methods, the one which uses a short-range exchange functional based on the Ernzerhof-Perdew exchange hole model with a range-separation parameter of 0.4 bohr(-1) seems to be the best candidate for treatment of gold. In combination with the long-range coupled cluster singles, doubles, and noniterative triples [CCSD(T)] treatment it places the strength of aurophilic bonding in (HAuPH3)2 at 5.7 kcal/mol at R = 3.09 Å. This value is somewhat larger than our best purely WFT result based on CCSD(T), 4.95 kcal/mol (R = 3.1 Å), and considerably smaller than the Hartree-Fock+dispersion value of 7.4 kcal/mol (R = 2.9 Å). The 5.7 kcal/mol estimate fits reasonably well within the prediction of the empirical relationship proposed by Schwerdtfeger et al. (J. Am. Chem. Soc.1998, 120, 6587). A direct computation of dispersion energy, including exchange corrections, results in values of ca. -9 kcal/mol for Au2((3)Σg(+)) and (AuH)2 and -13 kcal/mol for (HAuPH3)2 at the distance of a typical aurophilic bond, R = 3.0 Å.