Singlet–Triplet Gap in Covalently and Weakly Bound Carbenes: Studying the Dependence on the Exchange–Correlation Functional

We systematically analyze here the performance of density functional approximations for the calculation of the singlet-triplet gap of covalently bound carbenes (i.e., substituted arylcarbenes of increasing size and with different electroactive substituents) and weakly bound carbenes (diphenylcarbene noncovalently interacting with H₂O, CH₃OH, ClCF₃, BrCF₃, and ICF₃ molecules). The calculations revealed an unexpected functional dependence, in the sense that low levels of the functional hierarchy (e.g., BLYP or PBE) provide lower errors than more sophisticated functionals (e.g., hybrid and double-hybrid expressions), thus evidencing a subtle yet marked interplay between the ingredients of any modern exchange-correlation functional. The decomposition of the results as a function of those ingredients allowed us to isolate those functionals overestimating (by default) the energy stability of the triplet state and how (nonempirical) formulations of double-hybrid functional are able to cope with that initial bias. We recommend double-hybrid functionals (e.g., PBE-QIDH) to get robust and sufficiently accurate results (averaged deviation of ±1-2 kcal/mol with respect to reference results) for other applications and studies involving these challenging carbene species.