  Molecules that violate Hund's rule and exhibit an inverted gap between the
lowest singlet $S_1$ and triplet $T_1$ excited states have attracted
considerable attention due to their potential applications in optoelectronics.
Amongst these molecules, the triangular-shaped heptazine, and its derivatives,
have been in the limelight. However, conflicting reports have arisen regarding
the relative energies of $S_1$ and $T_1$. Here, we employ highly accurate
levels of theory, such as CC3, to not only resolve the debate concerning the
sign but also quantify the magnitude of the $S_1$-$T_1$ gap. We also determine
the 0-0 energies to evaluate the significance of the vertical approximation. In
addition, we compute reference $S_1$-$T_1$ gaps for a series of 10 related
molecules. This enables us to benchmark lower-order methods for future
applications on larger systems within the same family of compounds. This
contribution can serve as a reliable foundation for the design of
triangular-shaped molecules with enhanced photophysical properties.
