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

## TL;DR

This paper explores how electronic correlation and solvent effects can invert energy gaps in molecules, offering insights for designing better optoelectronic materials.

## Contribution

A new computational protocol combining electronic correlation and state-specific solvent polarization is developed to accurately predict inverted singlet-triplet gaps.

## Key findings

- Double-hybrid functionals and MRSF-TD-DFT partially recover electronic correlation effects.
- Linear-response solvation models have limitations in capturing state-specific solvent polarization.
- The B2PLYP/VEM(UD) protocol reproduces experimental inverted gaps and emission rates accurately.

## Abstract

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.

Dynamic electronic correlation and state‐specific solvent polarization act cooperatively to invert the singlet–triplet energy gap in organic emitters. The B2PLYP/VEM(UD) protocol combines double‐hybrid functionals with the state‐specific Vertical Excitation Model and quantitatively reproduces experimental adiabatic inverted gaps and emission rates, offering valuable insights for the design of next‐generation TADF and INVEST materials.