Accurate Diels-Alder reaction energies from efficient density functional calculations.

We assess the performance of the semilocal PBE functional; its global hybrid variants; the highly parametrized empirical M06-2X and M08-SO; the range separated rCAM-B3LYP and MCY3; the atom-pairwise or nonlocal dispersion corrected semilocal PBE and TPSS; the dispersion corrected range-separated ωB97X-D; the dispersion corrected double hybrids such as PWPB95-D3; the direct random phase approximation, dRPA, with Hartree-Fock, Perdew-Burke-Ernzerhof, and Perdew-Burke-Ernzerhof hybrid reference orbitals and the RPAX2 method based on a Perdew-Burke-Ernzerhof exchange reference orbitals for the Diels-Alder, DARC; and self-interaction error sensitive, SIE11, reaction energy test sets with large, augmented correlation consistent valence basis sets. The dRPA energies for the DARC test set are extrapolated to the complete basis set limit. CCSD(T)/CBS energies were used as a reference. The standard global hybrid functionals show general improvements over the typical endothermic energy error of semilocal functionals, but despite the increased accuracy the precision of the methods increases only slightly, and thus all reaction energies are simply shifted into the exothermic direction. Dispersion corrections give mixed results for the DARC test set. Vydrov-Van Voorhis 10 correction to the reaction energies gives superior quality results compared to the too-small D3 correction. Functionals parametrized for energies of noncovalent interactions like M08-SO give reasonable results without any dispersion correction. The dRPA method that seamlessly and theoretically correctly includes noncovalent interaction energies gives excellent results with properly chosen reference orbitals. As the results for the SIE11 test set and H2(+) dissociation show that the dRPA methods suffer from delocalization error, good reaction energies for the DARC test set from a given method do not prove that the method is free from delocalization error. The RPAX2 method shows good performance for the DARC, the SIE11 test sets, and for the H2(+) and H2 potential energy curves showing no one-electron self-interaction error and reduced static correlation errors at the same time. We also suggest simplified DARC6 and SIE9 test sets for future benchmarking.