Negative singlet-triplet gaps

A question that I was wondering about for a while: Are there molecules where the first excited singlet state lies below the first triplet? Apparently there are, as this recent paper in JPCL shows.

In the single-electron picture this is not possible. Singlet and triplet excited states can access the same configuration space and the only difference between singlet and triplet energies is a repulsive exchange term (see my recent post and preprint). This exchange term is always positive and, thus, always pushes up the singlet above the triplet with the same orbital transition. But the situation changes when double excitations come into play. The reason is that only singlets can form the type of double excitations where two electrons are placed in the same orbital and, hence, singlets and triplets have a different accessible configuration space. If a doubly excited state is close enough in energy, it can push the S₁ down enough to be lower than T₁. This is apparently the case for the cyclazine molecule at its ground-state equilibrium geometry (see DOI: 10.1021/acs.jpclett.9b02333).