Correlation vs. exchange competition drives the singlet-triplet excited-state inversion in non-alternant hydrocarbons

In this work, we focus on the understanding of the driving force behind the S₁-T₁ excited-state energy inversion (which would thus violate Hund's rule, making the S₁ state lower in energy than the T₁ state) of two non-benzenoid non-alternant hydrocarbons, composed of odd-membered rings. The molecules considered here have identical chemical composition but different atomic configuration in space. The delicate interplay between structural and electronic factors that might induce inversion and its energy extension, only by a few meV, is systematically investigated here by state-of-the-art calculations. Qualitative and quantitative accurate predictions are obtained employing post-HF methods, thanks to the balanced and careful inclusion of electron correlation effects. The obtained results might guide and rationalize new searches for molecules violating Hund's rule, concomitantly demonstrating the importance of key contributions from the theoretical method of choice.