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

Abstract

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.