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 to achieve enhanced 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 inter- system crossing. Previous computational studies have focused on accurately calculating the inverted energy gap and establishing qualitative structure-property relationships; in this study we quantify relationships that correlate molecular structure with the S1- T1 energy gap, ∆EST. Using a newly developed benchmark set of 15 heptazine-based INVEST molecules (HEPTA-INVEST15), we demonstrate strong linear correlation (R2 > 0.94) between the degree of intramolecular charge transfer and ∆EST . Our analysis reveals that strongly electron-donating groups like -N(CH3)2 and -NH2 minimize the magnitude of inverted gaps in monosubstituted heptazines, while paradoxically, triple -NH2 substitution produces the most negative ∆EST among trisubstituted derivatives. This contradiction highlights the complex interplay between resonance effects, inductive stabilization, and excited-state aromaticity governing relative stabilization of the S1 and T1 states. We analyze how deviation from single-excitation character, quantified through %R1 values and transition density matrix norms, provides a mechanistic explanation for the relative stabilization of S1 versus T1 states. These correlations generalize effectively to an expanded set of 46 di- and tri-substituted heptazine molecules (HEPTA-INVEST46). Unlike approaches that rely solely on orbital symmetry or π- electron count, our findings demonstrate that strategic functionalization can fine-tune ∆EST through differential modification of excited state wavefunction character, particularly in the T1 state. These design principles provide predictive metrics for rational INVEST material development that can be efficiently computed through future machine learning approaches, enabling more effective design of high-performance organic emitters.