On the Role of Electronic Correlation and State-Specific Environment Polarization in Singlet-Triplet Gap Inversion

Molecules characterized by an inverted singlet-triplet gap ( ) hold potential for optoelectronic applications. Electronic correlation and environmental polarization are key factors influencing negative $\Delta E_{\mathrm{ST}}$ , and the latter is gaining attention for its possible role in "mimicking" correlation contributions to yield negative $\Delta E_{\mathrm{ST}}$ . 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 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 $\Delta E_{\mathrm{ST}}$ gaps, we quantitatively reproduce experimental emissive and non-radiative transition rates.