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The basic design principle for emitters exhibiting thermally activated delayed fluorescence (TADF) is the minimization of the singlet-triplet gap. While typically this gap is positive, a possible inversion of states has been proposed as a pathway to improve the efficiency of organic light-emitting diodes. Despite the efforts to design such emitters, there are very few reports indicating that it is at all possible. We analyze the problem of gap inversion from the perspective of the electronic structure theory. The key result is that inversion is possible but requires a substantial contribution of double excitations and that commonly used cheap electronic structure methods would fail to predict it.