Accurate Spin-State Energetics for Aryl Carbenes.

A test set of 12 aryl carbenes (AC12) is compiled with the purpose of establishing their adiabatic singlet-triplet energy splittings using correlated wave function based methods. The set covers both singlet and triplet ground state aryl carbenes, as well as a range of magnitudes for the ground state to excited state gap. The performance of coupled cluster methods is examined with respect to the reference wave function, the basis set, and a number of additional methodological parameters that enter the calculation. Inclusion of perturbative triples and basis set extrapolation with a combination of triple and quadruple-ζ basis sets are both required to ensure high accuracy. When canonical coupled cluster calculations become too expensive, the domain-based local pair natural orbital approach DLPNO-CCSD(T) can be used as a reliable method for larger systems, as it achieves a mean absolute error of only 0.2 kcal/mol for the singlet-triplet gaps in the present test set. Other first-principles wave function methods and selected density functional methods are also evaluated. Second-order Møller-Plesset perturbation theory approaches are only applicable in conjunction with orbital optimization (OO-MP2). Among the representative density functional methods tested, only double hybrid functionals perform sufficiently accurately to be considered useful for systems with small singlet-triplet gaps. On the basis of the reference coupled cluster results, projected gas-phase free energies are reported for all aryl carbenes. Finally, the treatment of singlet-triplet gaps in solution is discussed in terms of both implicit and explicit solvation.