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In this paper we demonstrate the performance of several density-based methods in predicting the inversion of S$_1$ and T$_1$ states of a few N-heterocyclic fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cheap preliminary screening method. Both conventional LR-TDDFT and $\Delta$SCF methods (namely MOM, SGM, ROKS) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of the Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against FICMRCISD and/or EOM-CCSD, with the most important feature being the capture of spin-polarization in presence of correlation. A set of functionals with the least mean absolute error (MAE) is proposed for both the approaches, LR-TDDFT and $\Delta$SCF, which can be cheaper alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the DLPNO-STEOM-CCSD, which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models which identify the minimal physics governing the interactions in these molecules., Comment: 37 pages, 8 figures and under review

In this paper we investigate the role of electron correlation in predicting the S$_1$-S$_0$ and T$_1$-S$_0$ excitation energies and hence, the singlet-triplet gap ($\Delta$E$_{ST}$) in a set of cyclazines which act as templates for potential candidates for 5th generation Organic Light Emitting Diode (OLED) materials. This issue has recently garnered much interest with the focus being on the inversion of the $\Delta$E$_{ST}$, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar (\emph{J. Am. Chem. Soc. 1980, 102: 6068 , J. Am. Chem. Soc. 1986, 108: 17} ). We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cheaper theories which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally we would like to point out that the use of DLPNO-STEOM-CCSD as the benchmark for $\Delta$E$_{ST}$ (as used in \emph{J. Phys. Chem. A 2022, 126: 8: 1378, Chem. Phys. Lett. 2021, 779: 138827}) is not a suitable benchmark for this class of molecules., Comment: 34 pages, 6 figures, submitted for review