Quantitative structure–property relation for negative singlet–triplet gaps

Establish a quantitative structure–property relationship that predicts and explains when molecules exhibit an inverted singlet–triplet energy gap (STG < 0) between the lowest excited singlet (S1) and triplet (T1) states, analogous to the existing quantitative relationship for zero STG, by identifying the specific molecular structural features responsible for negative STG.

Background

The paper analyzes S1–T1 energy gaps for 12,880 small closed-shell organic molecules using ADC(2) and various TDDFT/double-hybrid approaches, finding no negative STG at the ADC(2) level and highlighting frequent false positives from certain DFT methods. The authors discuss known mechanisms (e.g., dynamic spin polarization and double excitation effects) and geometric features (e.g., poor HOMO–LUMO overlap) that can lead to small or vanishing STG.

While a quantitative relation between structural features and zero STG is recognized (e.g., via vanishing exchange integral from orbital overlap considerations), the authors explicitly note the absence of a corresponding quantitative structure–property relation for negative STG, indicating a key unresolved question in the field.