Quantifying Design Principles for Light-Emitting Materials with Inverted Singlet-Triplet Energy Gaps

Molecular engineering of organic emitter molecules with inverted singlet-triplet energy gaps (INVEST) has emerged as a powerful approach for enhancing fluorescence efficiency through triplet harvesting. In these unique materials, the first excited singlet state (S₁) lies below the lowest triplet state (T₁), enabling efficient reverse intersystem crossing. Previous computational studies have focused on accurately calculating the inverted energy gap and establishing qualitative structure-property relationships. Here, we present quantitative relationships that link the molecular structure to the S₁-T₁ energy gap, ΔE_ST, by introducing a benchmark set of 15 heptazine-based INVEST molecules (HEPTA-INVEST15). We identify a strong linear correlation (R² > 0.94) between ΔE_ST and both the degree of intramolecular charge transfer and the deviation from a single-excitation character, as quantified by %R₁ values and transition density matrix norms. These trends persist across our expanded set of 44 mono-, di-, and tri-substituted heptazines (HEPTA-INVEST44), underscoring the generality of our findings. Notably, strongly electron-donating groups, such as -NH₂, minimize the magnitude of inverted gaps in mono-substituted heptazines yet produce the most negative ΔE_ST in certain tri-substituted derivatives, a result arising from competing resonance effects and excited-state aromaticity. Although ΔE_ST shows no clear correlation with Hammett parameters, our results reveal that physically meaningful, computable descriptors offer a mechanistic foundation for the future data-driven design of INVEST emitters. These findings pave the way for machine-learning approaches that connect the molecular structure to ΔE_ST without requiring high-level excited-state calculations.