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