Computation of Chemically Accurate Singlet-Triplet Gaps for Aryl-carbenes at Hybrid Functional Cost

The two nonbonding electrons in a carbene can occupy the same orbital, resulting in a singlet state, or different orbitals, typically resulting in a triplet state. Since the spin state of a carbene largely influences its properties and reactivity, the singlet-triplet gap is a common quantity of interest. However, its theoretical prediction is challenging, and chemically accurate singlet-triplet gaps were previously thought to require expensive wave-function methods or density functional theory with double hybrid functionals. By evaluating two recent test sets of aryl-carbenes (AC12 and AC18), we show that local hybrid functionals with position-dependent exact-exchange governed by a common t-LMF achieve mean absolute errors below 1kcal/mol thus enabling chemically accurate predictions at a computational cost comparable to other "rung 4" hybrid functionals.