Insights into Symmetry and Substitution Patterns Governing Singlet-Triplet Energy Gap in the Chemical Space of Azaphenalenes

Abstract

Molecules that violate Hund's rule by exhibiting an inverted singlet-triplet gap (STG), where the first excited singlet (S$_1$) lies below the triplet (T$_1$), are rare but hold great promise as efficient fifth-generation light emitters. Azaphenalenes (APs) represent one of the few known molecular classes capable of such inversion of the S$_1$/T$_1$ energy ordering, yet a systematic exploration of all unique APs is lacking. Here, we investigate 104 distinct APs and classify them based on their adherence to or deviation from Hund's rule using S$_1$-T$_1$ gaps computed with the second-order coupled-cluster method employing the Laplace transform (L-CC2). To capture substitution-dependent pseudo-Jahn-Teller distortions that are inadequately described by MP2 and DFT methods, we employ focal-point extrapolation scheme to obtain near-CCSD(T)/cc-pVTZ-quality geometries. We find three APs to undergo $D_{\rm 3h} \rightarrow C_{\rm 3h}$ and ten to show $C_{\rm 2v}\rightarrow C_{\rm s}$ symmetry lowering, leading to a total of 117 configurations of 104 unique APs. Our study identifies top candidates with inverted STGs, revealing how substitution and symmetry-lowering modulate these gaps to uncover new stable AP cores that provide promising targets for designing molecular light-emitters.