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

Molecules that violate Hund's rule by exhibiting an inverted singlet-triplet gap (STG), where the first excited singlet ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>S</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm S}_1$</mml:annotation></mml:semantics> </mml:math> ) lies below the triplet ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm T}_1$</mml:annotation></mml:semantics> </mml:math> ), 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>S</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm S}_1$</mml:annotation></mml:semantics> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm T}_1$</mml:annotation></mml:semantics> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>S</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm S}_1$</mml:annotation></mml:semantics> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:annotation>${\rm T}_1$</mml:annotation></mml:semantics> </mml:math> 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 a focal-point extrapolation scheme to obtain near-CCSD(T)/cc-pVTZ-quality geometries. We find 3 APs to undergo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>3</mml:mn> <mml:mi>h</mml:mi></mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:msub><mml:mi>C</mml:mi> <mml:mrow><mml:mn>3</mml:mn> <mml:mi>h</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$D_{\rm 3h} \rightarrow C_{\rm 3h}$</mml:annotation></mml:semantics> </mml:math> and 10 to show <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>C</mml:mi> <mml:mrow><mml:mn>2</mml:mn> <mml:mi>v</mml:mi></mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:msub><mml:mi>C</mml:mi> <mml:mi>s</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$C_{\rm 2v}\rightarrow C_{\rm s}$</mml:annotation></mml:semantics> </mml:math> 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.