Origin of The Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

Recent experimental and theoretical studies have shown several new organic molecules that violate Hund’s rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single reference wave function methods have successfully predicted excited state energetics of these low-lying states, conventional linear-response time-dependent density functional theory (LR-TDDFT) fails to predict the correct excited state energy ordering. Herein, we have shown that it is possible to get inverted singlet-triplet gaps within the density functional theory framework by taking into account correlation contributed by double excitations and choosing correct exchange-correctional functional. Going beyond Kohn-Sham density functional theory (KS-DFT), we have demonstrated that a combined wave function and density functional method resulting in multiconfiguration pair-density functional theory (MC-PDFT), in some cases, can predict inverted singlet-triplet gaps. Consequently, we have identified that both the missing doubly excited configurations and the form of the exchange-correlation functionals are the foremost grounds for the failure of the LR-TDDFT method. We have also compared the accuracy of single reference correlated wave function methods for these low-lying singlet and triplet excited states to multireference second-order perturbation theory.