Benchmark studies on the large errors of calculated binding energies in metallophilic interactions

Aurophilicity is a d¹⁰-d¹⁰ closed-shell interaction, which is repulsively calculated by the Hartree-Fork (HF) method, whereas binding energies (E_b) are largely overestimated under the second-order Møller-Plesset (MP2) method, compared to the coupled cluster singles and doubles with perturbative triples [CCSD(T)] method. The unusual energy errors between different wave functional methods were also verified in other closed-shell metallophilic systems and even were taken as a label of metallophilic interaction. Here, we performed a benchmark study on a collection of structures with weak interactions, sp-sp bonds, sp-d bonds, and d-d bonds, to investigate the influence factor of the errors of HF and MP2 methods. It was found that the large energy errors of HF and MP2 methods were not specified for closed-shell interactions, and the errors could also be very large for many covalent bonds, which was strongly related to the azimuthal quantum number of interaction orbitals. Compared to the CCSD(T) method, the MP2 method weakens the s-s covalent interactions slightly, strengthens the p-p covalent interactions slightly, and overestimates the d-d covalent interactions largely (can be -170 kcal/mol for the Re-Re quadruple bond). This benchmark study suggests that the special energy errors in metallophilicity may result from the participation of d orbitals. Benchmark studies on various density functional methods were also given for calculating binding energies of d-d bonds.