On the role of electronic correlation and state-specific environment polarization in Singlet–Triplet gap inversion

Molecules characterized by an inverted singlet-triplet gap (ΔEST < 0) hold potential for optoelectronic applications. Electronic correlation and environmental polarization are key factors influencing negative ΔEST , and the latter is gaining attention for its possible role in “mimicking” correlation contributions to yield negative ΔEST . However, a comprehensive study of solvation effects on both structures and energy gaps is still lacking. In this work, we evaluate computational strategies for calculating ΔEST < 0 gaps, incorporating electronic correlation and solvent polarization in molecules exhibiting singlet-triplet inversion. Using RMS–CASPT2 as a benchmark, we demonstrate that double-hybrid density functionals and mixed-reference spin-flip TD-DFT (MRSF– TD-DFT) can partially recover electronic correlation. Furthermore, we investigate solvation effects on both singlet and triplet excited states, highlighting the limitations of linear-response schemes in continuum solvation models. We finally develop a protocol combining electronic correlation and state-specific solvent polarization using double-hybrid functionals and the Vertical Excitation Model (VEM), leveraging its Lagrangian implementation to compute structures and adiabatic energies. Applying our B2PLYP/VEM(UD) protocol to larger systems with experimentally observed negative ΔEST gaps, we quantitatively reproduce experimental emissive and non-radiative transition rates.