Size and sign of inverted singlet-triplet gaps in heptazine molecules
In plain words
In almost all molecules the lowest triplet excited state lies below the lowest singlet, a pattern usually attributed to Hund's rule. A few nitrogen-rich molecules built on heptazine (a flat ring system of carbon and nitrogen) reverse this order, which could make organic light-emitting diodes more efficient.
Precise statement
For heptazine and a series of substituted derivatives, determine the adiabatic gap $\Delta_{\mathrm{ST}}=E(\mathrm{S1})-E(\mathrm{T1})$ to 0.05 eV, its sign across the series, and which electronic-structure ingredient (double excitations, spin polarization, dynamic correlation) is necessary to get the sign right. An answer is near-exact gaps for the series validated against measured delayed fluorescence and reverse intersystem crossing rates, with a design rule for negative $\Delta_{\mathrm{ST}}$.
What would settle it
High-order coupled-cluster or selected configuration interaction gaps on the full series compared with spectroscopically measured gaps.
Status in the literature
In 2022 Aizawa et al. (Nature, https://doi.org/10.1038/s41586-022-05132-y) reported delayed fluorescence from a molecule with an inverted gap; quantitative prediction across derivatives remains method-dependent.