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 (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-corrected TDDFT and multi-configuration pair-density functional theory for the calculation of inverted singlet-triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet-triplet gaps both by using doubles-corrected TDDFT with a proper choice of double-hybrid functionals or by using eDFT.