Reliable Diradical Characterization via Precise Singlet-Triplet Gap Calculations: Application to Thiele, Chichibabin, and Müller Analogous Diradicals

Accurately calculating the diradical character (y₀) of molecular systems remains a significant challenge due to the scarcity of experimental data and the inherent multireference nature of the electronic structure. In this study, various quantum mechanical approaches, including broken symmetry density functional theory (BS-DFT), spin-flip time-dependent density functional theory (SF-TDDFT), mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT), complete active space self-consistent field (CASSCF), complete active space second-order perturbation theory (CASPT2), and multiconfigurational pair-density functional theory (MCPDFT), are employed to compute the singlet-triplet energy gaps (E_ST) and y₀ values in Thiele, Chichibabin, and Müller analogous diradicals. By systematically comparing the results from these computational methods, we identify optimally tuned long-range corrected functional CAM-B3LYP in the BS-DFT framework as a most efficient method for accurately and affordably predicting both E_ST and y₀ values. Additionally, our results demonstrate that (i) MRSF-TDDFT performs much better than SF-TDDFT; (ii) the MCPDFT method is robust in determining E_ST with minimal dependence on the choice of active space. These findings provide insight into the electronic structure and diradical character of the investigated molecules and highlight effective computational strategies for future studies in this domain. Thus, this work not only advances our understanding of diradical systems but also offers practical guidelines for their computational investigation.